Lesson 6.1 Integers Name: ________________________________ Integer: A positive or negative whole number, or zero. Positive Integer: All whole numbers greater than zero. Negative Integer: All whole numbers less than zero. Opposite Integer: Two integers that are the same distance from zero on a number line. For example, -2 and 2 are opposites. Zero is considered the opposite of zero. The sum of two opposite integers is always zero. Finding Integers based on statements Statement Integer The runner lost 7 yards -7 The temperature rose 22 degrees 22 The player gained 5 yards 5 The temperature fell 16 degrees -16 PRACTICE: Page 252 For #4 to 15 – just print the integer (don’t graph it) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) ____ & ____ 15) For #16 to 23 – just print the opposite integer (don’t graph it) 16) 17) 18) 19) 20) 21) 22) 23) 26) 27) 28) 29) 32) over Addition with Integers 1) 12 + -5 = ___ 2) 6 + -9 = ____ 3) -7 + -3 = ___ 4) 12 + -12 = ____ 5) -5 + -11 = ____ 6) 4 + -8 = ____ Subtraction with Integers 1) 11 – 6 = ____ 2) 11 - -6 = ____ 3) -11 – 6 = ____ 4) -11 - -6 = ____ 5) 12 - -12 = ____ 6) 5 – 11 = ____ 6.1 HW Name: __________________________ Print the integer that matches each statement below: 1) The hiker hiked 2 miles up the mountain. _____ 2) The temperature increased by 17 degrees. _____ 3) The runner lost 4 yards. _____ 4) The airplane rose 2,000 feet. _____ 5) The temperature fell 10 degrees. _____ 6) The coal miner went 200 feet down into the mine. _____ Print the opposite of each integer below: 7) 12 ____ 8) -25 ____ 9) 0 ____ 10) -88 ____ 11) 45 ____ 12) 8 ____ 13) -11 ____ 14) 5 ____ Multiple Choice: Circle the best answer 15) Which of the following is a positive integer? -4 0 2.5 8 16) Which of the following is not a negative integer? -4 -½ 0 -8 17) When an integer is added to its opposite, the sum will always be: Equal to the positive integer Zero The difference of the 2 numbers 18) The smallest positive integer is: 0 1 ½ -1 19) The largest negative integer is: 0 1 -1 negative infinity Lesson 6.2 Comparing and Ordering Integers Name: __________________ The key thing to remember when comparing or ordering integers from least to greatest is this: When comparing or ordering negative integers – the larger the number itself is (without the negative sign), the smaller the value. For example: -5 is less than -3. And -2 is greater than -8. Practice: Page 258 For #4 to 11 – Print both integers and CIRCLE the one that is larger 4) 5) 6) 7) 8) 9) 10) 11) 14) ____ _____ _____ _____ _____ 15) ____ _____ _____ _____ _____ 16) ____ _____ _____ _____ _____ 17) ____ _____ _____ _____ _____ 18) ____ _____ _____ _____ _____ 19) ____ _____ _____ _____ _____ 20) a) _____ b) _____ 21) ______ OVER Page 259 22) least ____ greatest ____ 23) 24) 26) 27) 28) a) b) 6.2 HW Name: _____________________________________ For each group of integers below, put them in order from LEAST to GREATEST: 1) 2, -3, -5, 0, -1 ____ ____ ____ ____ ____ 2) 5, -5, -8, -9, 2 ____ ____ ____ ____ ____ 3) -16, -17, -19, -14, -10 ____ ____ ____ ____ ____ 4) -101, -103, -111, -100, -99 ____ ____ ____ ____ ____ 5) 0, 5, -22, -23, -11 ____ ____ ____ ____ ____ 6) -59, -58, -60, -61, -57 ____ ____ ____ ____ ____ 7) -35, 0, -33, -36, 20 ____ ____ ____ ____ ____ 8) 27, -27, 26, -26, 2 ____ ____ ____ ____ ____ Circle TRUE or FALSE 9) -112 is less than -120. TRUE FALSE 10) -120 is greater than -112. TRUE FALSE 11) There are no integers between -11 and -12. TRUE FALSE 12) 0 is less than -5. TRUE FALSE Lesson 6.3 Fractions and Decimals on the Number Line Name: _____________ Graphing Negative Fractions and Decimals The number line below shows integers only, with an equal number of spaces between each integer. You are asked to graph the following negative numbers: - 1 - .5 - 1 3 - 1.75 4 4 -2 -1 0 1 2 -1.75 & -1 3 -.5 - 1 4 4 Comparing Fractions When comparing two positive fractions with the same denominator, the fraction with the largest numerator is greater. If the fractions are negative, then the fraction with the largest numerator is less than the other. 3 > 2 - 3 < - 2 5 5 5 5 When two fractions have different denominators, you must first find the Least Common Denominator (LCD) and change both fractions, so that the denominators are the same. Then follow the rules above to find which is greater. EXAMPLE: Which is greater; 2 or 4 ? 5 9 The LCD is 45. 2 = 18 and 4 = 20 therefore, 4 > 2 5 45 9 45 9 5 Comparing Decimals When comparing two decimals, compare each digit place position by place position to see which is larger. EXAMPLE: Which is greater; .32 or .4 ? .4 is greater because the digit in the tenths place in .4 is larger than it is in .32 Another way to compare decimals is to add zeros to one so that the number of decimal places is the same in both numbers. EXAMPLE: Which is greater; .358 or .51 ? Add a zero to .51 to make it .510. Now you can see that 510 is larger than 358, so .51 is greater than .358. -2 -1 0 1 2 Graph each of the following numbers on the number line above, and label them with the letter below the number: a) - .25 b) - 1 3 c) 1.75 d) – 2 1 4 2 Page 264: For #10 to 18, just print the number that is LARGER 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) small or large (circle one) 20) _____ _____ _____ _____ _____ 21) _____ _____ _____ _____ _____ 22) _____ _____ _____ _____ _____ 23) _____ _____ _____ _____ _____ CHALLENGE 27) There are 2 positive integers that make the statement true. What are they? _____ and _____. Also, any negative number less than _____ also makes the statement true. 6.3 HW Name: __________________________________________ Circle the LARGER of each pair of numbers: 1) - 3 - 2 2) -.5 -.48 3) -2 2 -2 2 5 5 3 5 4) -5.66 -5.6 5) - 3 - 2 6) -51.02 -51.1 5 3 7) - 4 - 4 8) 0 -.01 9) - 5 - 3 9 11 6 4 10) 2.1 - 2.1 11) - 1 5 - 1 7 12) -44.001 -44.3 8 8 Lesson 6.4 Absolute Value Name: ____________________________ The Absolute Value of a number is the distance of that number from zero on a number line. The absolute value of 4 is 4, because 4 is 4 positions away from zero on a number line. The absolute value of -4 is 4, because -4 is also 4 positions away from zero on a number line. The symbol for absolute value is: | 5 | | 5 | = 5 | -5 | = 5 CHAPTER 6 REVIEW 1) | 3 | = ___ 2) | -7 | = ___ 3) | -5.2 | = ___ 4) | 3 | = ___ 4 Print the integer that matches the statement: 5) 4 degrees below zero ___ 6) The hiker climbed 3,000 feet ___ 7) The miner went down 2 miles ___ 8) The plane dropped 500 feet ___ 9) The customer deposited $500 into his account ____ 10) We lost 12 men ___ Print the OPPOSITE of each integer: 11) -22 ___ 12) 0 ___ 13) 48 ___ 14) 9 ___ CIRCLE the LARGER for each pair of numbers: 15) -15 -17 16) -4.3 -4.6 17) - 3 - 3 4 5 18) -.3 -.05 19) - 1 3 - 1 5 20) -4.22 -4.216 4 6 Over 21) - 3 - 3 22) -3.4 -3.09 23) - 4 - 5 8 5 5 7 24) -5.2 -5.012 25) - 7 - 3 10 4 CHALLENGE PROBLEMS 1) I am a number. I am halfway between -25 and 7 on an integer number line. What number am I? ____ 2) This set of integers is missing one integer. -2, 5, -5, 4, -8, 7 With the missing integer, the median will be -2. The missing integer must be equal or less than what integer? ____ 3) This set of integers is missing one integer. -2, 5, -5, 4, -8, 7, -9 With the missing integer, the median will be zero. What is the missing integer? ____ 4) Find the LARGEST 6-digit whole number with these conditions: • The difference of the first and last digit is half the sum of the two middle digits • No single digit may be used more than once • The sum of all digits must be less than 30 _____ _____ _____ , _____ _____ _____ 5) Challenge 24 Only + and - No addition 13 ____________ ___________ 31 3 9 ____________ ___________ ____________ ___________ .