About the Book YIKES!

Chapter 1

Fractions and Decimals

About the Book

• Utilize and memorize the inside jacket (except Dimensional Analysis Method) • Read the MATH TIP boxes in each chapter • Know the RULE boxes in each chapter • Read the QUICK REVIEW box for every chapter • Practice the Review Sets from each chapter

YIKES!

1 How can You succeed in this class?

LISTEN

FOLLOW DIRECTIONS

PRACTICE

2 Category of Fractions

• Common Fractions, aka “fractions” example: ½

• Decimal Fractions, aka “decimals” example: 0.5

Fractions

numerator denominator • Math tip: – Denominator begins with “d” and is “down” • Below fraction line

4 Types of Fractions

• Proper – Value of numerator is less than value of denominator (the result will always be less than 1 in this case) –Example: 5 is less than 1 8

3 Types of Fractions

• Improper – Value of improper fraction (numerator is greater than denominator) is greater than 1 –Example: 8 is greater than 1 5

Types of Fractions

• When the numerator and denominator are the equal, the result is 1 •Examples: 4 11  1 and  1 4 11

Types of Fractions

• Mixed numbers – Whole number + proper fraction combined –Example: 5 1 is greater than 1 8

4 Types of Fractions

• Complex – Numerator, denominator, or both contain fraction, decimal, or mixed number – Value may be: • Less than 1 • Greater than 1 • Equal to 1 5 Example: 5 1 5 2 10 5 8       1 8 2 8 1 8 4 2

Equivalent Fractions

• Express fraction in different form while maintaining value • Dosage calculation requires conversion of fractions to equivalent values by: – Reducing to lowest terms – Enlarging fraction – Converting to different type of fraction

2 2  2 1 1 1  3 3 Example:     4 4  2 2 3 3  3 9

Reducing Fractions

• Divide both terms by largest nonzero whole number that will divide evenly into both numerator and denominator • Value remains same • Example: 6 6  2 3   10 10  2 5

Note: If you don’t see the largest number right off, you may divide by smaller numbers until they are in lowest terms.

5 Enlarging Fractions

• Multiply both terms by same nonzero number • Value remains same • Example: 1 1 2 2   12 12 2 24 1 2 and Note: The fractions 12 24 are the same value, as are the two fractions on the previous slide, 63 and . 10 5

Converting Mixed Numbers to Improper Fractions

• Multiply whole number by denominator • Add product to numerator • Denominator and value remain same • Example: 5(28)516521  2  88 88

Converting Improper Fractions to Mixed Numbers

• Divide numerator by denominator • Remainder becomes numerator • If necessary, reduce to lowest terms • Example: 10 2 1 10 4 2 2 442

6 Comparing Fractions

Adding or Subtracting Fractions

• Convert to equivalent fractions with least common denominators • Add or subtract numerators • Place value in numerator • Place least common denominator as denominator

Adding or Subtracting Fractions

• Convert answer to mixed number and/or reduce to lowest terms • Example: 3123126 1  1 444 4 4 2

Note: When adding and subtracting fractions, once you get the denominators the same, you only combine the numerators, not the denominators … leave the denominators alone.

7 Multiplying and Dividing Fractions

• To multiply: – Cancel terms in the numerators with terms in the denominators, multiply numerators, and multiply denominators • To divide: – Invert fraction after the divisor, change division sign to multiplication, cancel terms in numerator with terms in the denominator, and multiply • Convert results to mixed number and/or reduce to lowest terms

Multiplying Fractions

Example: 1 1 32 1 464 2 2 Example: 15 2 15 1  (rename to ) 30 5 30 2 12 1  (the 2's cancel) = 25 5

Multiplying Fractions

• To multiply mixed numerals, first convert them to improper fractions, and then multiply.

Example: 11 34 23 71391 convert to improper fractions   23 6 1 convert to a mixed numeral = 15 6

8 Division of Fractions

 changed to  1 2 1 7 7     4 7 4 2 8

Dividend Divisor Inverted Quotient Divisor

Decimals

X X X X X . X X X X tens ones tenths hundreds thousands hundredths thousandths ten thousands ten ten thousandths ten Whole numbers Decimal point Decimal fractions

Decimals

• Words for all decimals end in “th(s)” – 0.001 read as one thousandth – 0.02 read as two hundredths – 0.7 read as seven tenths • 4.125 is read as four and one hundred twenty- five thousandths • A decimal is read as “and” • A decimal separates the whole and fractional part of the number

9 Reading Decimals

4 . 1 2 5 four and one-hundred twenty Ones Tenths Hundreds Thousandths five thousandths

Rule: The decimal number is read by stating the whole number first, the decimal point as “and”, and then the decimal fraction by naming the value of the last decimal place.

Decimal Values: Decimal Point and Zeros • If decimal value less than one, add zero before decimal point – Does not change value – Example: .5 = 0.5 • Read as five tenths

• You do not read the zero when it appears alone before the decimal. It is there to emphasize the decimal.

Decimal Values: Decimal Point and Zeros • Example: .5 – Avoid this writing of decimal fraction – Could be mistaken for whole number five • Example: 0.50 – Avoid trailing zero – Decimal may be missed • Example: 0.5 – Correct method of writing decimal fraction

10 Comparing Decimals • Compare 0.125, 0.05, and 0.2 to find largest decimal fraction • Align decimal points and add zeros so that the decimal numbers are the same length. This doesn’t change the values. • 0.125 • 0.050 • 0.200 Which decimal is bigger?

Comparing Decimals

125 0.125 or one hundred twenty-five thousandths 1, 000 50 0.050  or fifty thousandths 1,000 200 0.200  or two hundred thousandths 1,000 • 0.2 is largest decimal • 0.05 is smallest decimal

Converting between Fractions and Decimals • Converting fraction to decimal – Divide numerator by denominator • Example: Convert 1 to decimal 4

.25 1 4 1.00 0.25 4 8 20 20

11 Converting Between Fractions and Decimals • Converting decimal to fraction – Decimal number becomes numerator – Denominator is number one followed by as many zeros as number of decimal places to right of decimal point – Reduce to lowest terms

Example: convert 0.125 to fraction Numerator = 125 Denominator = 1,000 Reduce 125 1  1, 000 8

Adding and Subtracting Decimals

• To add or subtract decimals: – Align decimal points and add zeros – If necessary, add zeros to make all decimals equal length – Eliminate any unnecessary zeros when you get your answer, to avoid confusion

Adding and Subtracting Decimals

•Examples: – Add 1.25 and 1.75 1.25 1.75 3.00  3

– Subtract 2.1 from 3.75 3.75 2.10 1.65

12 Multiplying and Dividing Decimals

• To multiply decimals: – Multiply number – Place decimal point in product by moving decimal to left number of places equal to sum of decimal places in numbers multiplied – Eliminate any unnecessary zeros • Example: 0.25 0.2  0.050  0.05

Multiplying and Dividing Decimals

• To divide decimals: – Move decimal point in divisor and dividend correct number of decimal places to make divisor a whole number – Align it in quotient • Example: 20. 1.2 24.0.

Multiplying and Dividing Decimals

• To multiply or divide by multiplier of 10:

–To multiply, move decimal point to right –To divide, move decimal point to left – Move same number of decimal places as there are zeros in multiplier of 10

13 Multiplying and Dividing Decimals

•Examples: 5.06 10 5.0.6  50.6

2.1 100 .02.1  0.021

Rounding Decimals

• Rounded to hundredths – Two places Hundredths Tenths Thousandths 0 .1 2 3  0.12 1. 7 4 4  1.74 5 . 3 2 5  5.33 0 . 6 6 6  0.67

Rounding Decimals

• Rounded to tenths – One place

0 .1Tenths 3 Hundredths  0.1 5 . 6 4  5.6 0 . 7 5  0.8 1. 6 6  1.7 0 . 9 5  1.0  1

14 Questions?