NEWCOLORs_basic_math_rev 3/31/08 3:52 PM Page 1
Basic Math Review Key Words and Symbols Integers (continued) Fractions (continued) Rates, Ratios, Proportions, The following words and symbols are used for the and Percents MULTIPLYING AND DIVIDING WITH NEGATIVES operations listed. # Equivalent fractions are found by multiplying the numerator -a b =-ab and denominator of the fraction by the same number. In the RATES AND RATIOS Addition previous example, - # - = A rate is a comparison of two quantities with different units. Numbers Important Properties Sum, total, increase, plus a b ab # # - 2 2 4 8 1 1 3 3 For example, a car that travels 110 miles in 2 hours is mov- a = a = = and = = . addend addend = sum # # ing at a rate of 110 miles/2 hours or 55 mph. NATURAL NUMBERS PROPERTIES OF ADDITION -b b 3 3 4 12 4 4 3 12 Subtraction a A ratio is a comparison of two quantities with the same {1, 2, 3, 4, 5, …} Identity Property of Zero: a + 0 = a -a , b =- Difference, decrease, minus b MULTIPLYING AND DIVIDING FRACTIONS units. For example, a class with 23 students has a WHOLE NUMBERS Inverse Property: a + -a = 0 When multiplying and dividing fractions, a common student–teacher ratio of 23:1 or23 . 1 2 minuend subtrahend = difference Some examples: 1 denominator is not needed. To multiply, take the product {0, 1, 2, 3, 4, …} + = + Multiplication - # =- Commutative Property: a b b a 3 5 15 of the numerators and the product of the denominators: PROPORTIONS Product, of, times -7 -6 = 42 # INTEGERS Associative Property: a + b + c = a + b + c 1 21 2 a # c a c ac A proportion is a statement in which two ratios or rates are 1 2 1 2 * # - - = = = {…, 3, 2, 1, 0, 1, 2, …} a b, a b, a b , ab 24 8 3 # equal. PROPERTIES OF MULTIPLICATION 1 21 2 1 2>1 2 b d b d bd factor factor = product 18 36 An example of a proportion is the following statement: The Number Line # or 18 To divide fractions, invert the second fraction and then Property of Zero: a 0 = 0 2 36 30 dollars is to 5 hours as 60 dollars is to 10 hours. # Division 2 multiply the numerators and denominators: Identity Property of One: a 1 = a, when a Z 0. Quotient, per, divided by a c a d ad This is written –5–5 – 4–4 –3–3 –2–2 –1–1 0 1 2 3 4 5 # 1 , = = # = Z a b d b c bc $30 = $60 Negative integers Positive integers Inverse Property: a 1, when a 0. a b a b b a . a # # b > Fractions 5 hr 10 hr Commutative Property: a b = b a Some examples: Zero A typical proportion problem will have one unknown # # # # 3 2 6 Associative Property: a b c = a b c dividend divisor = quotient LEAST COMMON MULTIPLE # = quantity, such as 1 2 1 2 5 7 35 The LCM of a set of numbers is the smallest number that is a 1 mile x miles RATIONAL NUMBERS PROPERTIES OF DIVISION = . multiple of all the given numbers. 5 1 5 2 10 5 20 min 60 min All numbers that can be written in the form a b , where a 0 , = # = = Z > Property of Zero: = 0, when a Z 0. Order of Operations For example, the LCM of 5 and 6 is 30, since 5 and 6 have no 12 2 12 1 12 6 and b are integers andb 0 . a We can solve this equation by cross multiplying as shown: 1st: Parentheses factors in common. IRRATIONAL NUMBERS a = # Property of One: = 1, when a Z 0. Simplify any expressions inside parentheses. REDUCING FRACTIONS 20x 60 1 Real numbers that cannot be written as the quotient of two a GREATEST COMMON FACTOR 2nd: Exponents To reduce a fraction, divide both the numerator and denom- 60 integers but can be represented on the number line. a # x = = 3. Identity Property of One: = a 1 The GCF of a set of numbers is the largest number that can inator by common factors. In the last example, 20 1 Work out any exponents. be evenly divided into each of the given numbers. 10 10 , 2 5 REAL NUMBERS 3rd: Multiplication and Division = = . So, it takes 60 minutes to walk 3 miles. For example, the GCF of 24 and 27 is 3, since both 24 and 12 12 , 2 6 Include all numbers that can be represented on the number Solve all multiplication and division, working from 27 are divisible by 3, but they are not both divisible by any line, that is, all rational and irrational numbers. PERCENTS Absolute Value left to right. numbers larger than 3. 4th: Addition and Subtraction MIXED NUMBERS A percent is the number of parts out of 100. To write a per- cent as a fraction, divide by 100 and drop the percent sign. Real Numbers The absolute value of a number is always ≥ 0. These are done last, from left to right. FRACTIONS A mixed number has two parts: a whole number part and a ƒ ƒ 3 _4 2 If a 7 0, a = a . fractional part. An example of a mixed number is 5 . This For example, Rational Numbers 23, 22.4, 21 5 , 0, 0.6, 1, etc. For example, Fractions are another way to express division. The top num- 8 Irrational 6 ƒ - ƒ = 57 Numbers If a 0, a a . - # + - , 2 ber of a fraction is called the numerator, and the bottom really represents = p 23, 22, 21, 0, 1, 2, 3, p 15 2 3 30 3 3 3 57% . 25VN3, Integers ƒ - ƒ = ƒ ƒ = # 1 2 number is called the denominator. 5 + , 100 For example, 5 5 and 5 5 . In each case, the = 15 - 2 3 + 27 , 9 VN2, p, etc. answer is positive. 8 Whole Numbers 0, 1, 2, 3, p = 15 - 6 + 3 ADDING AND SUBTRACTING FRACTIONS To write a fraction as a percent, first check to see if the which can be written as denominator is 100. If it is not, write the fraction as an = Natural Numbers 1, 2, 3, p 12. Fractions must have the same denominator before they can 40 3 43 equivalent fraction with 100 in the denominator. Then the + = . be added or subtracted. 8 8 8 numerator becomes the percent. For example, a b a + b 4 80 + = , with d Z 0 . Similarly, an improper fraction can be written as a mixed = = 80%. Integers d d d 5 100 PRIME NUMBERS number. For example, a b a - b - = Z 20 2 To find a percent of a quantity, multiply the percent by the A prime number is a number greater than 1 that has only ADDING AND SUBTRACTING WITH NEGATIVES , with d 0. can be written as 6 , ISBN-13: 978-0-321-39476-7 d d d 3 3 quantity. itself and 1 as factors. - - = - + - ISBN-10: 0-321-39476-3 a b a b If the fractions have different denominators, rewrite them as Some examples: 1 2 1 2 since 20 divided by 3 equals 6 with a remainder of 2. For example, 30% of 5 is 90000 -a + b = b - a equivalent fractions with a common denominator. Then add 2, 3, and 7 are prime numbers. 30 # 150 3 a - -b = a + b or subtract the numerators, keeping the denominators the 5 = = . COMPOSITE NUMBERS 1 2 same. For example, 100 100 2 Some examples: A composite number is a number that is not prime. For 2 1 8 3 11 -3 - 17 = -3 + -17 =-20 + = + = example, 8 is a composite number since 1 2 1 2 . # # -19 + 4 = 4 - 19 =-15 3 4 12 12 12 8 = 2 2 2 = 23. 9 780321 394767 more➤ more➤
1 2 3 NEWCOLORs_basic_math_rev 3/31/08 3:52 PM Page 1
Basic Math Review Key Words and Symbols Integers (continued) Fractions (continued) Rates, Ratios, Proportions, The following words and symbols are used for the and Percents MULTIPLYING AND DIVIDING WITH NEGATIVES operations listed. # Equivalent fractions are found by multiplying the numerator -a b =-ab and denominator of the fraction by the same number. In the RATES AND RATIOS Addition previous example, - # - = A rate is a comparison of two quantities with different units. Numbers Important Properties Sum, total, increase, plus a b ab # # - 2 2 4 8 1 1 3 3 For example, a car that travels 110 miles in 2 hours is mov- a = a = = and = = . addend addend = sum # # ing at a rate of 110 miles/2 hours or 55 mph. NATURAL NUMBERS PROPERTIES OF ADDITION -b b 3 3 4 12 4 4 3 12 Subtraction a A ratio is a comparison of two quantities with the same {1, 2, 3, 4, 5, …} Identity Property of Zero: a + 0 = a -a , b =- Difference, decrease, minus b MULTIPLYING AND DIVIDING FRACTIONS units. For example, a class with 23 students has a WHOLE NUMBERS Inverse Property: a + -a = 0 When multiplying and dividing fractions, a common student–teacher ratio of 23:1 or23 . 1 2 minuend subtrahend = difference Some examples: 1 denominator is not needed. To multiply, take the product {0, 1, 2, 3, 4, …} + = + Multiplication - # =- Commutative Property: a b b a 3 5 15 of the numerators and the product of the denominators: PROPORTIONS Product, of, times -7 -6 = 42 # INTEGERS Associative Property: a + b + c = a + b + c 1 21 2 a # c a c ac A proportion is a statement in which two ratios or rates are 1 2 1 2 * # - - = = = {…, 3, 2, 1, 0, 1, 2, …} a b, a b, a b , ab 24 8 3 # equal. PROPERTIES OF MULTIPLICATION 1 21 2 1 2>1 2 b d b d bd factor factor = product 18 36 An example of a proportion is the following statement: The Number Line # or 18 To divide fractions, invert the second fraction and then Property of Zero: a 0 = 0 2 36 30 dollars is to 5 hours as 60 dollars is to 10 hours. # Division 2 multiply the numerators and denominators: Identity Property of One: a 1 = a, when a Z 0. Quotient, per, divided by a c a d ad This is written –5–5 – 4–4 –3–3 –2–2 –1–1 0 1 2 3 4 5 # 1 , = = # = Z a b d b c bc $30 = $60 Negative integers Positive integers Inverse Property: a 1, when a 0. a b a b b a . a # # b > Fractions 5 hr 10 hr Commutative Property: a b = b a Some examples: Zero A typical proportion problem will have one unknown # # # # 3 2 6 Associative Property: a b c = a b c dividend divisor = quotient LEAST COMMON MULTIPLE # = quantity, such as 1 2 1 2 5 7 35 The LCM of a set of numbers is the smallest number that is a 1 mile x miles RATIONAL NUMBERS PROPERTIES OF DIVISION = . multiple of all the given numbers. 5 1 5 2 10 5 20 min 60 min All numbers that can be written in the form a b , where a 0 , = # = = Z > Property of Zero: = 0, when a Z 0. Order of Operations For example, the LCM of 5 and 6 is 30, since 5 and 6 have no 12 2 12 1 12 6 and b are integers andb 0 . a We can solve this equation by cross multiplying as shown: 1st: Parentheses factors in common. IRRATIONAL NUMBERS a = # Property of One: = 1, when a Z 0. Simplify any expressions inside parentheses. REDUCING FRACTIONS 20x 60 1 Real numbers that cannot be written as the quotient of two a GREATEST COMMON FACTOR 2nd: Exponents To reduce a fraction, divide both the numerator and denom- 60 integers but can be represented on the number line. a # x = = 3. Identity Property of One: = a 1 The GCF of a set of numbers is the largest number that can inator by common factors. In the last example, 20 1 Work out any exponents. be evenly divided into each of the given numbers. 10 10 , 2 5 REAL NUMBERS 3rd: Multiplication and Division = = . So, it takes 60 minutes to walk 3 miles. For example, the GCF of 24 and 27 is 3, since both 24 and 12 12 , 2 6 Include all numbers that can be represented on the number Solve all multiplication and division, working from 27 are divisible by 3, but they are not both divisible by any line, that is, all rational and irrational numbers. PERCENTS Absolute Value left to right. numbers larger than 3. 4th: Addition and Subtraction MIXED NUMBERS A percent is the number of parts out of 100. To write a per- cent as a fraction, divide by 100 and drop the percent sign. Real Numbers The absolute value of a number is always ≥ 0. These are done last, from left to right. FRACTIONS A mixed number has two parts: a whole number part and a ƒ ƒ 3 _4 2 If a 7 0, a = a . fractional part. An example of a mixed number is 5 . This For example, Rational Numbers 23, 22.4, 21 5 , 0, 0.6, 1, etc. For example, Fractions are another way to express division. The top num- 8 Irrational 6 ƒ - ƒ = 57 Numbers If a 0, a a . - # + - , 2 ber of a fraction is called the numerator, and the bottom really represents = p 23, 22, 21, 0, 1, 2, 3, p 15 2 3 30 3 3 3 57% . 25VN3, Integers ƒ - ƒ = ƒ ƒ = # 1 2 number is called the denominator. 5 + , 100 For example, 5 5 and 5 5 . In each case, the = 15 - 2 3 + 27 , 9 VN2, p, etc. answer is positive. 8 Whole Numbers 0, 1, 2, 3, p = 15 - 6 + 3 ADDING AND SUBTRACTING FRACTIONS To write a fraction as a percent, first check to see if the which can be written as denominator is 100. If it is not, write the fraction as an = Natural Numbers 1, 2, 3, p 12. Fractions must have the same denominator before they can 40 3 43 equivalent fraction with 100 in the denominator. Then the + = . be added or subtracted. 8 8 8 numerator becomes the percent. For example, a b a + b 4 80 + = , with d Z 0 . Similarly, an improper fraction can be written as a mixed = = 80%. Integers d d d 5 100 PRIME NUMBERS number. For example, a b a - b - = Z 20 2 To find a percent of a quantity, multiply the percent by the A prime number is a number greater than 1 that has only ADDING AND SUBTRACTING WITH NEGATIVES , with d 0. can be written as 6 , ISBN-13: 978-0-321-39476-7 d d d 3 3 quantity. itself and 1 as factors. - - = - + - ISBN-10: 0-321-39476-3 a b a b If the fractions have different denominators, rewrite them as Some examples: 1 2 1 2 since 20 divided by 3 equals 6 with a remainder of 2. For example, 30% of 5 is 90000 -a + b = b - a equivalent fractions with a common denominator. Then add 2, 3, and 7 are prime numbers. 30 # 150 3 a - -b = a + b or subtract the numerators, keeping the denominators the 5 = = . COMPOSITE NUMBERS 1 2 same. For example, 100 100 2 Some examples: A composite number is a number that is not prime. For 2 1 8 3 11 -3 - 17 = -3 + -17 =-20 + = + = example, 8 is a composite number since 1 2 1 2 . # # -19 + 4 = 4 - 19 =-15 3 4 12 12 12 8 = 2 2 2 = 23. 9 780321 394767 more➤ more➤
1 2 3 NEWCOLORs_basic_math_rev 3/31/08 3:52 PM Page 1
Basic Math Review Key Words and Symbols Integers (continued) Fractions (continued) Rates, Ratios, Proportions, The following words and symbols are used for the and Percents MULTIPLYING AND DIVIDING WITH NEGATIVES operations listed. # Equivalent fractions are found by multiplying the numerator -a b =-ab and denominator of the fraction by the same number. In the RATES AND RATIOS Addition previous example, - # - = A rate is a comparison of two quantities with different units. Numbers Important Properties Sum, total, increase, plus a b ab # # - 2 2 4 8 1 1 3 3 For example, a car that travels 110 miles in 2 hours is mov- a = a = = and = = . addend addend = sum # # ing at a rate of 110 miles/2 hours or 55 mph. NATURAL NUMBERS PROPERTIES OF ADDITION -b b 3 3 4 12 4 4 3 12 Subtraction a A ratio is a comparison of two quantities with the same {1, 2, 3, 4, 5, …} Identity Property of Zero: a + 0 = a -a , b =- Difference, decrease, minus b MULTIPLYING AND DIVIDING FRACTIONS units. For example, a class with 23 students has a WHOLE NUMBERS Inverse Property: a + -a = 0 When multiplying and dividing fractions, a common student–teacher ratio of 23:1 or23 . 1 2 minuend subtrahend = difference Some examples: 1 denominator is not needed. To multiply, take the product {0, 1, 2, 3, 4, …} + = + Multiplication - # =- Commutative Property: a b b a 3 5 15 of the numerators and the product of the denominators: PROPORTIONS Product, of, times -7 -6 = 42 # INTEGERS Associative Property: a + b + c = a + b + c 1 21 2 a # c a c ac A proportion is a statement in which two ratios or rates are 1 2 1 2 * # - - = = = {…, 3, 2, 1, 0, 1, 2, …} a b, a b, a b , ab 24 8 3 # equal. PROPERTIES OF MULTIPLICATION 1 21 2 1 2>1 2 b d b d bd factor factor = product 18 36 An example of a proportion is the following statement: The Number Line # or 18 To divide fractions, invert the second fraction and then Property of Zero: a 0 = 0 2 36 30 dollars is to 5 hours as 60 dollars is to 10 hours. # Division 2 multiply the numerators and denominators: Identity Property of One: a 1 = a, when a Z 0. Quotient, per, divided by a c a d ad This is written –5–5 – 4–4 –3–3 –2–2 –1–1 0 1 2 3 4 5 # 1 , = = # = Z a b d b c bc $30 = $60 Negative integers Positive integers Inverse Property: a 1, when a 0. a b a b b a . a # # b > Fractions 5 hr 10 hr Commutative Property: a b = b a Some examples: Zero A typical proportion problem will have one unknown # # # # 3 2 6 Associative Property: a b c = a b c dividend divisor = quotient LEAST COMMON MULTIPLE # = quantity, such as 1 2 1 2 5 7 35 The LCM of a set of numbers is the smallest number that is a 1 mile x miles RATIONAL NUMBERS PROPERTIES OF DIVISION = . multiple of all the given numbers. 5 1 5 2 10 5 20 min 60 min All numbers that can be written in the form a b , where a 0 , = # = = Z > Property of Zero: = 0, when a Z 0. Order of Operations For example, the LCM of 5 and 6 is 30, since 5 and 6 have no 12 2 12 1 12 6 and b are integers andb 0 . a We can solve this equation by cross multiplying as shown: 1st: Parentheses factors in common. IRRATIONAL NUMBERS a = # Property of One: = 1, when a Z 0. Simplify any expressions inside parentheses. REDUCING FRACTIONS 20x 60 1 Real numbers that cannot be written as the quotient of two a GREATEST COMMON FACTOR 2nd: Exponents To reduce a fraction, divide both the numerator and denom- 60 integers but can be represented on the number line. a # x = = 3. Identity Property of One: = a 1 The GCF of a set of numbers is the largest number that can inator by common factors. In the last example, 20 1 Work out any exponents. be evenly divided into each of the given numbers. 10 10 , 2 5 REAL NUMBERS 3rd: Multiplication and Division = = . So, it takes 60 minutes to walk 3 miles. For example, the GCF of 24 and 27 is 3, since both 24 and 12 12 , 2 6 Include all numbers that can be represented on the number Solve all multiplication and division, working from 27 are divisible by 3, but they are not both divisible by any line, that is, all rational and irrational numbers. PERCENTS Absolute Value left to right. numbers larger than 3. 4th: Addition and Subtraction MIXED NUMBERS A percent is the number of parts out of 100. To write a per- cent as a fraction, divide by 100 and drop the percent sign. Real Numbers The absolute value of a number is always ≥ 0. These are done last, from left to right. FRACTIONS A mixed number has two parts: a whole number part and a ƒ ƒ 3 _4 2 If a 7 0, a = a . fractional part. An example of a mixed number is 5 . This For example, Rational Numbers 23, 22.4, 21 5 , 0, 0.6, 1, etc. For example, Fractions are another way to express division. The top num- 8 Irrational 6 ƒ - ƒ = 57 Numbers If a 0, a a . - # + - , 2 ber of a fraction is called the numerator, and the bottom really represents = p 23, 22, 21, 0, 1, 2, 3, p 15 2 3 30 3 3 3 57% . 25VN3, Integers ƒ - ƒ = ƒ ƒ = # 1 2 number is called the denominator. 5 + , 100 For example, 5 5 and 5 5 . In each case, the = 15 - 2 3 + 27 , 9 VN2, p, etc. answer is positive. 8 Whole Numbers 0, 1, 2, 3, p = 15 - 6 + 3 ADDING AND SUBTRACTING FRACTIONS To write a fraction as a percent, first check to see if the which can be written as denominator is 100. If it is not, write the fraction as an = Natural Numbers 1, 2, 3, p 12. Fractions must have the same denominator before they can 40 3 43 equivalent fraction with 100 in the denominator. Then the + = . be added or subtracted. 8 8 8 numerator becomes the percent. For example, a b a + b 4 80 + = , with d Z 0 . Similarly, an improper fraction can be written as a mixed = = 80%. Integers d d d 5 100 PRIME NUMBERS number. For example, a b a - b - = Z 20 2 To find a percent of a quantity, multiply the percent by the A prime number is a number greater than 1 that has only ADDING AND SUBTRACTING WITH NEGATIVES , with d 0. can be written as 6 , ISBN-13: 978-0-321-39476-7 d d d 3 3 quantity. itself and 1 as factors. - - = - + - ISBN-10: 0-321-39476-3 a b a b If the fractions have different denominators, rewrite them as Some examples: 1 2 1 2 since 20 divided by 3 equals 6 with a remainder of 2. For example, 30% of 5 is 90000 -a + b = b - a equivalent fractions with a common denominator. Then add 2, 3, and 7 are prime numbers. 30 # 150 3 a - -b = a + b or subtract the numerators, keeping the denominators the 5 = = . COMPOSITE NUMBERS 1 2 same. For example, 100 100 2 Some examples: A composite number is a number that is not prime. For 2 1 8 3 11 -3 - 17 = -3 + -17 =-20 + = + = example, 8 is a composite number since 1 2 1 2 . # # -19 + 4 = 4 - 19 =-15 3 4 12 12 12 8 = 2 2 2 = 23. 9 780321 394767 more➤ more➤
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Basic Math Review
Decimal Numbers Percents to Decimals and Scientific Notation (continued) Measurements Geometry Geometry (continued) Decimals to Percents U.S. Measurement Units The perimeter of a geometric figure is the distance around it The numbers after the decimal point represent fractions with MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION PYTHAGOREAN THEOREM To change a number from a percent to a decimal, divide by or the sum of the lengths of its sides. denominators that are powers of 10. The decimal point sep- To multiply or divide numbers in scientific notation, we can in. = inch oz = ounce In any right triangle, if a and b are the lengths of the legs arates the whole number part from the fractional part. 100 and drop the percent sign: The perimeter of a rectangle is 2 times the length plus 2 change the order and grouping, so that we multiply or divide ft = foot c = cup times the width: and c is the length of the hypotenuse, then 9 58% = 58/100 = 0.58. first the decimal parts and then the powers of 10. For example, 2 + 2 = 2 For example, 0.9 represents 10 . min = minute mi = mile a b c . * -3 # * 8 To change a number from a decimal to a percent, multiply 3.7 10 2.5 10 sec = second hr = hour L 1 2# 1 - 2 Place Value Chart by 100 and add the percent sign: = 3.7 * 2.5 10 3 * 108 1 2 1 2 gal = gallon lb = pound W 0.73 = .73* 100 = 73%. = * 5 c 9.25 10 . yd = yard qt = quart a pt = pint T = ton P = 2L + 2W
tens ones billions tenths illionths millions b thousandshundreds m Statistics The perimeter of a square is 4 times the length of a side: hundredths ten millions thousandthsn thousandths Simple Interest Metric Units ten thousands hundred millions hundred thousands te hundred thousandths There are several ways to study a list of data. 9 327604985326894 Given the principal (amount of money to be borrowed or mm = millimeter s CIRCLES invested), interest rate, and length of time, the amount of Mean, or average, is the sum of all the data values divided by cm = centimeter = # 2 Whole numbers Decimals interest can be found using the formula the number of values. s Area: A p r # # km = kilometer = # = # # I = p r t Median is the number that separates the list of data into two Circumference: C p d 2 p r m = meter equal parts. To find the median, list the data in order from = where d is the diameter, r is the radius, or half the diameter, ADDING AND SUBTRACTING DECIMAL NUMBERS where I = interest dollar amount P 4s 1 2 smallest to largest. If the number of data is odd, the median is mL = milliliter p 22 To add or subtract decimal numbers, line up the numbers so = and is approximately 3.14 or 7 . p principal the middle number. If the number of data is even, the median Area is always expressed in square units, since it is two- that the decimal points are aligned. Then add or subtract as cL = centiliter = is the average of the two middle numbers. dimensional. usual, keeping the decimal point in the same place. r percentage rate of interest L = liter = Mode is the number in the list that occurs the most fre- The formula for area of a rectangle is For example, 23 - 0.37 = 23.00 t time period. kL = kiloliter quently. There can be more than one mode. = # d For example, find the amount of simple interest on a $3800 mg = milligram A L W. 0.37 For example, consider the following list of test scores: loan at an annual rate of 5.5% for 5 years: 22.63 cg = centigram The formula for area of a square is = {87, 56, 69, 87, 93, 82} # r p $3800 g = gram A = s s orA = s2 . MULTIPLYING AND DIVIDING DECIMAL NUMBERS = = To find the mean, first add: r 5.5% 0.055 kg = kilogram = + + + + + = The area of a triangle is one-half the product of the height To multiply decimal numbers, multiply them as though they t 5 years 87 56 69 87 93 82 474. and base: A circle has an angle of 360 degrees. were whole numbers. The number of decimal places in the I = 3800 0.055 5 = 1045. Then divide by 6: U.S. AND METRIC CONVERSIONS product is the sum of the number of decimal places in the 1 21 21 2 A straight line has an angle of 180 degrees. factors. For example, 3.72 * 4.5 is 474 U.S. The amount of interest is $1045. = 79. 2 decimal places 6 12 in. = 1 ft 3 ft = 1 yd h The mean score is 79. 1760 yd = 1 mi 5280 ft = 1 mi Algebraic Terms 3.72 1 decimal place 4.5 Scientific Notation To find the median, first list the data in order: 2 c = 1 pt 1 c = 8 oz b Variable: A variable is a letter that represents a number 56, 69, 82, 87, 87, 93. 4 qt = 1 gal 2 pt = 1 qt because the number is unknown or because it can change. 16.740 Scientific notation is a convenient way to express very large 1 # A = b h For example, the number of days until your vacation 3 decimal places or very small numbers. A number in this form is written as Since there is an even number of data, we take the average 2000 lb = 1 T 16 oz = 1 lb 2 * n … ƒ ƒ 6 changes every day, so it could be represented by a a 10 , where 1 a 10 and n is an integer. For of 82 and 87: * 5 - * -4 variable, x. To divide decimal numbers, first make sure the divisor is a example, 3.62 10 and 1.2 10 are expressed + Metric The sum of all three angles in any triangle always equals 82 87 = 169 = Constant: A constant is a term that does not change. For whole number. If it is not, move the decimal place to the right in scientific notation. 84.5. 180 degrees. 2 2 1000 mm = 1 m 100 cm = 1 m example, the number of days in the week, 7, does not (multiply by 10, 100, and so on) to make it a whole number. To change a number from scientific notation to a number 1000 m = 1 km 100 cL = 1 L change, so it is a constant. Then move the decimal point the same number of places in without exponents, look at the power of ten. If that number is The median score is 84.5. x the dividend. positive, move the decimal point to the right. If it is negative, The mode is 87, since this number appears twice and each 1000 mL = 1 L 100 cg = 1 g z Expression: An algebraic expression consists of constants, move the decimal point to the left. The number tells you how 1000 mg = 1 g 1000 g = 1 kg y variables, numerals and at least one operation. For example, For example, of the other numbers appears only once. + many places to move the decimal point. x 7 is an expression. 0.42 , 1.2 = 4.2 , 12 0.001 m = 1 mm 0.01 m = 1 cm + + = x° y° z° 180° Equation: An equation is basically a mathematical sentence 0.35 For example, 0.001 g = 1 mg 0.01 g = 1 cg * 3 = Distance Formula A right triangle is a triangle with a 90° (right) angle. The indicating that two expressions are equal. For example, 12 4.20 . 3.97 10 3970. 0.001 L = 1 mL 0.01 L = 1 cL + = hypotenuse of a right triangle is the side opposite the right x 7 18 is an equation. To change a number to scientific notation, move the deci- Given the rate at which you are traveling and the length of The decimal point in the answer is placed directly above the angle. Solution: A number that makes an equation true is a mal point so it is to the right of the first nonzero digit. If the time you will be traveling, the distance can be found by new decimal point in the dividend. solution to that equation. For example, in using the above decimal point is moved n places to the left and this makes using the formula equation, x + 7 = 18, we know that the statement is true = # the number smaller, n is positive; otherwise, n is negative. If d r t if x = 11. the decimal point is not moved, n is 0. where d = distance hypotenuse - For example, 0.0000216 = 2.16 * 10 5. r = rate t = time more➤ 90°
more➤ 4 5 6 NEWCOLORs_basic_math_rev 3/31/08 3:52 PM Page 2
Basic Math Review
Decimal Numbers Percents to Decimals and Scientific Notation (continued) Measurements Geometry Geometry (continued) Decimals to Percents U.S. Measurement Units The perimeter of a geometric figure is the distance around it The numbers after the decimal point represent fractions with MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION PYTHAGOREAN THEOREM To change a number from a percent to a decimal, divide by or the sum of the lengths of its sides. denominators that are powers of 10. The decimal point sep- To multiply or divide numbers in scientific notation, we can in. = inch oz = ounce In any right triangle, if a and b are the lengths of the legs arates the whole number part from the fractional part. 100 and drop the percent sign: The perimeter of a rectangle is 2 times the length plus 2 change the order and grouping, so that we multiply or divide ft = foot c = cup times the width: and c is the length of the hypotenuse, then 9 58% = 58/100 = 0.58. first the decimal parts and then the powers of 10. For example, 2 + 2 = 2 For example, 0.9 represents 10 . min = minute mi = mile a b c . * -3 # * 8 To change a number from a decimal to a percent, multiply 3.7 10 2.5 10 sec = second hr = hour L 1 2# 1 - 2 Place Value Chart by 100 and add the percent sign: = 3.7 * 2.5 10 3 * 108 1 2 1 2 gal = gallon lb = pound W 0.73 = .73* 100 = 73%. = * 5 c 9.25 10 . yd = yard qt = quart a pt = pint T = ton P = 2L + 2W
tens ones billions tenths illionths millions b thousandshundreds m Statistics The perimeter of a square is 4 times the length of a side: hundredths ten millions thousandthsn thousandths Simple Interest Metric Units ten thousands hundred millions hundred thousands te hundred thousandths There are several ways to study a list of data. 9 327604985326894 Given the principal (amount of money to be borrowed or mm = millimeter s CIRCLES invested), interest rate, and length of time, the amount of Mean, or average, is the sum of all the data values divided by cm = centimeter = # 2 Whole numbers Decimals interest can be found using the formula the number of values. s Area: A p r # # km = kilometer = # = # # I = p r t Median is the number that separates the list of data into two Circumference: C p d 2 p r m = meter equal parts. To find the median, list the data in order from = where d is the diameter, r is the radius, or half the diameter, ADDING AND SUBTRACTING DECIMAL NUMBERS where I = interest dollar amount P 4s 1 2 smallest to largest. If the number of data is odd, the median is mL = milliliter p 22 To add or subtract decimal numbers, line up the numbers so = and is approximately 3.14 or 7 . p principal the middle number. If the number of data is even, the median Area is always expressed in square units, since it is two- that the decimal points are aligned. Then add or subtract as cL = centiliter = is the average of the two middle numbers. dimensional. usual, keeping the decimal point in the same place. r percentage rate of interest L = liter = Mode is the number in the list that occurs the most fre- The formula for area of a rectangle is For example, 23 - 0.37 = 23.00 t time period. kL = kiloliter quently. There can be more than one mode. = # d For example, find the amount of simple interest on a $3800 mg = milligram A L W. 0.37 For example, consider the following list of test scores: loan at an annual rate of 5.5% for 5 years: 22.63 cg = centigram The formula for area of a square is = {87, 56, 69, 87, 93, 82} # r p $3800 g = gram A = s s orA = s2 . MULTIPLYING AND DIVIDING DECIMAL NUMBERS = = To find the mean, first add: r 5.5% 0.055 kg = kilogram = + + + + + = The area of a triangle is one-half the product of the height To multiply decimal numbers, multiply them as though they t 5 years 87 56 69 87 93 82 474. and base: A circle has an angle of 360 degrees. were whole numbers. The number of decimal places in the I = 3800 0.055 5 = 1045. Then divide by 6: U.S. AND METRIC CONVERSIONS product is the sum of the number of decimal places in the 1 21 21 2 A straight line has an angle of 180 degrees. factors. For example, 3.72 * 4.5 is 474 U.S. The amount of interest is $1045. = 79. 2 decimal places 6 12 in. = 1 ft 3 ft = 1 yd h The mean score is 79. 1760 yd = 1 mi 5280 ft = 1 mi Algebraic Terms 3.72 1 decimal place 4.5 Scientific Notation To find the median, first list the data in order: 2 c = 1 pt 1 c = 8 oz b Variable: A variable is a letter that represents a number 56, 69, 82, 87, 87, 93. 4 qt = 1 gal 2 pt = 1 qt because the number is unknown or because it can change. 16.740 Scientific notation is a convenient way to express very large 1 # A = b h For example, the number of days until your vacation 3 decimal places or very small numbers. A number in this form is written as Since there is an even number of data, we take the average 2000 lb = 1 T 16 oz = 1 lb 2 * n … ƒ ƒ 6 changes every day, so it could be represented by a a 10 , where 1 a 10 and n is an integer. For of 82 and 87: * 5 - * -4 variable, x. To divide decimal numbers, first make sure the divisor is a example, 3.62 10 and 1.2 10 are expressed + Metric The sum of all three angles in any triangle always equals 82 87 = 169 = Constant: A constant is a term that does not change. For whole number. If it is not, move the decimal place to the right in scientific notation. 84.5. 180 degrees. 2 2 1000 mm = 1 m 100 cm = 1 m example, the number of days in the week, 7, does not (multiply by 10, 100, and so on) to make it a whole number. To change a number from scientific notation to a number 1000 m = 1 km 100 cL = 1 L change, so it is a constant. Then move the decimal point the same number of places in without exponents, look at the power of ten. If that number is The median score is 84.5. x the dividend. positive, move the decimal point to the right. If it is negative, The mode is 87, since this number appears twice and each 1000 mL = 1 L 100 cg = 1 g z Expression: An algebraic expression consists of constants, move the decimal point to the left. The number tells you how 1000 mg = 1 g 1000 g = 1 kg y variables, numerals and at least one operation. For example, For example, of the other numbers appears only once. + many places to move the decimal point. x 7 is an expression. 0.42 , 1.2 = 4.2 , 12 0.001 m = 1 mm 0.01 m = 1 cm + + = x° y° z° 180° Equation: An equation is basically a mathematical sentence 0.35 For example, 0.001 g = 1 mg 0.01 g = 1 cg * 3 = Distance Formula A right triangle is a triangle with a 90° (right) angle. The indicating that two expressions are equal. For example, 12 4.20 . 3.97 10 3970. 0.001 L = 1 mL 0.01 L = 1 cL + = hypotenuse of a right triangle is the side opposite the right x 7 18 is an equation. To change a number to scientific notation, move the deci- Given the rate at which you are traveling and the length of The decimal point in the answer is placed directly above the angle. Solution: A number that makes an equation true is a mal point so it is to the right of the first nonzero digit. If the time you will be traveling, the distance can be found by new decimal point in the dividend. solution to that equation. For example, in using the above decimal point is moved n places to the left and this makes using the formula equation, x + 7 = 18, we know that the statement is true = # the number smaller, n is positive; otherwise, n is negative. If d r t if x = 11. the decimal point is not moved, n is 0. where d = distance hypotenuse - For example, 0.0000216 = 2.16 * 10 5. r = rate t = time more➤ 90°
more➤ 4 5 6 NEWCOLORs_basic_math_rev 3/31/08 3:52 PM Page 2
Basic Math Review
Decimal Numbers Percents to Decimals and Scientific Notation (continued) Measurements Geometry Geometry (continued) Decimals to Percents U.S. Measurement Units The perimeter of a geometric figure is the distance around it The numbers after the decimal point represent fractions with MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION PYTHAGOREAN THEOREM To change a number from a percent to a decimal, divide by or the sum of the lengths of its sides. denominators that are powers of 10. The decimal point sep- To multiply or divide numbers in scientific notation, we can in. = inch oz = ounce In any right triangle, if a and b are the lengths of the legs arates the whole number part from the fractional part. 100 and drop the percent sign: The perimeter of a rectangle is 2 times the length plus 2 change the order and grouping, so that we multiply or divide ft = foot c = cup times the width: and c is the length of the hypotenuse, then 9 58% = 58/100 = 0.58. first the decimal parts and then the powers of 10. For example, 2 + 2 = 2 For example, 0.9 represents 10 . min = minute mi = mile a b c . * -3 # * 8 To change a number from a decimal to a percent, multiply 3.7 10 2.5 10 sec = second hr = hour L 1 2# 1 - 2 Place Value Chart by 100 and add the percent sign: = 3.7 * 2.5 10 3 * 108 1 2 1 2 gal = gallon lb = pound W 0.73 = .73* 100 = 73%. = * 5 c 9.25 10 . yd = yard qt = quart a pt = pint T = ton P = 2L + 2W
tens ones billions tenths illionths millions b thousandshundreds m Statistics The perimeter of a square is 4 times the length of a side: hundredths ten millions thousandthsn thousandths Simple Interest Metric Units ten thousands hundred millions hundred thousands te hundred thousandths There are several ways to study a list of data. 9 327604985326894 Given the principal (amount of money to be borrowed or mm = millimeter s CIRCLES invested), interest rate, and length of time, the amount of Mean, or average, is the sum of all the data values divided by cm = centimeter = # 2 Whole numbers Decimals interest can be found using the formula the number of values. s Area: A p r # # km = kilometer = # = # # I = p r t Median is the number that separates the list of data into two Circumference: C p d 2 p r m = meter equal parts. To find the median, list the data in order from = where d is the diameter, r is the radius, or half the diameter, ADDING AND SUBTRACTING DECIMAL NUMBERS where I = interest dollar amount P 4s 1 2 smallest to largest. If the number of data is odd, the median is mL = milliliter p 22 To add or subtract decimal numbers, line up the numbers so = and is approximately 3.14 or 7 . p principal the middle number. If the number of data is even, the median Area is always expressed in square units, since it is two- that the decimal points are aligned. Then add or subtract as cL = centiliter = is the average of the two middle numbers. dimensional. usual, keeping the decimal point in the same place. r percentage rate of interest L = liter = Mode is the number in the list that occurs the most fre- The formula for area of a rectangle is For example, 23 - 0.37 = 23.00 t time period. kL = kiloliter quently. There can be more than one mode. = # d For example, find the amount of simple interest on a $3800 mg = milligram A L W. 0.37 For example, consider the following list of test scores: loan at an annual rate of 5.5% for 5 years: 22.63 cg = centigram The formula for area of a square is = {87, 56, 69, 87, 93, 82} # r p $3800 g = gram A = s s orA = s2 . MULTIPLYING AND DIVIDING DECIMAL NUMBERS = = To find the mean, first add: r 5.5% 0.055 kg = kilogram = + + + + + = The area of a triangle is one-half the product of the height To multiply decimal numbers, multiply them as though they t 5 years 87 56 69 87 93 82 474. and base: A circle has an angle of 360 degrees. were whole numbers. The number of decimal places in the I = 3800 0.055 5 = 1045. Then divide by 6: U.S. AND METRIC CONVERSIONS product is the sum of the number of decimal places in the 1 21 21 2 A straight line has an angle of 180 degrees. factors. For example, 3.72 * 4.5 is 474 U.S. The amount of interest is $1045. = 79. 2 decimal places 6 12 in. = 1 ft 3 ft = 1 yd h The mean score is 79. 1760 yd = 1 mi 5280 ft = 1 mi Algebraic Terms 3.72 1 decimal place 4.5 Scientific Notation To find the median, first list the data in order: 2 c = 1 pt 1 c = 8 oz b Variable: A variable is a letter that represents a number 56, 69, 82, 87, 87, 93. 4 qt = 1 gal 2 pt = 1 qt because the number is unknown or because it can change. 16.740 Scientific notation is a convenient way to express very large 1 # A = b h For example, the number of days until your vacation 3 decimal places or very small numbers. A number in this form is written as Since there is an even number of data, we take the average 2000 lb = 1 T 16 oz = 1 lb 2 * n … ƒ ƒ 6 changes every day, so it could be represented by a a 10 , where 1 a 10 and n is an integer. For of 82 and 87: * 5 - * -4 variable, x. To divide decimal numbers, first make sure the divisor is a example, 3.62 10 and 1.2 10 are expressed + Metric The sum of all three angles in any triangle always equals 82 87 = 169 = Constant: A constant is a term that does not change. For whole number. If it is not, move the decimal place to the right in scientific notation. 84.5. 180 degrees. 2 2 1000 mm = 1 m 100 cm = 1 m example, the number of days in the week, 7, does not (multiply by 10, 100, and so on) to make it a whole number. To change a number from scientific notation to a number 1000 m = 1 km 100 cL = 1 L change, so it is a constant. Then move the decimal point the same number of places in without exponents, look at the power of ten. If that number is The median score is 84.5. x the dividend. positive, move the decimal point to the right. If it is negative, The mode is 87, since this number appears twice and each 1000 mL = 1 L 100 cg = 1 g z Expression: An algebraic expression consists of constants, move the decimal point to the left. The number tells you how 1000 mg = 1 g 1000 g = 1 kg y variables, numerals and at least one operation. For example, For example, of the other numbers appears only once. + many places to move the decimal point. x 7 is an expression. 0.42 , 1.2 = 4.2 , 12 0.001 m = 1 mm 0.01 m = 1 cm + + = x° y° z° 180° Equation: An equation is basically a mathematical sentence 0.35 For example, 0.001 g = 1 mg 0.01 g = 1 cg * 3 = Distance Formula A right triangle is a triangle with a 90° (right) angle. The indicating that two expressions are equal. For example, 12 4.20 . 3.97 10 3970. 0.001 L = 1 mL 0.01 L = 1 cL + = hypotenuse of a right triangle is the side opposite the right x 7 18 is an equation. To change a number to scientific notation, move the deci- Given the rate at which you are traveling and the length of The decimal point in the answer is placed directly above the angle. Solution: A number that makes an equation true is a mal point so it is to the right of the first nonzero digit. If the time you will be traveling, the distance can be found by new decimal point in the dividend. solution to that equation. For example, in using the above decimal point is moved n places to the left and this makes using the formula equation, x + 7 = 18, we know that the statement is true = # the number smaller, n is positive; otherwise, n is negative. If d r t if x = 11. the decimal point is not moved, n is 0. where d = distance hypotenuse - For example, 0.0000216 = 2.16 * 10 5. r = rate t = time more➤ 90°
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