1. Fractions and Decimals
Chapter 1
Fractions and Decimals
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

2. Fractions
Math Tip
Denominator begins with d and is down below the line in a fraction
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3. Types of Fractions Proper fraction Example
Value of numerator is less than value of denominator
Example
is less than 1 because 5 < 8
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4. Types of Fractions (Continued)
Improper fraction
Value is greater than or equal to 1
Example
is greater than 1 because 8 > 5
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5. Types of Fractions (Continued)
Mixed number fraction
Value is always greater than 1
Example
is greater than 1
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6. Types of Fractions (Continued)
Complex fraction
Value may be
Less than 1, greater than 1, or equal to 1
Numerator and denominator have a fraction
Example
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7. Comparing Fractions © Cengage Learning 2013
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

8. Reducing Fractions Divide both terms by Value remains the same
Largest nonzero whole number that will divide both numerator and denominator evenly
Value remains the same
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9. Enlarging Fractions Multiply both terms by Value remains the same
Same nonzero number
Value remains the same
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10. Adding or Subtracting Fractions
Convert to equivalent fractions with least common denominators
Add or subtract the numerators
Place that value in numerator
Place least common denominator as denominator
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11. Adding or Subtracting Fractions (Continued)
Convert answer to mixed number and/or reduce to lowest terms
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

12. Multiply and Divide Fractions
To multiply
Cancel terms, multiply numerators, and multiply denominators
To divide
Invert divisor, cancel terms, and multiply
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13. Multiply and Divide Fractions (Continued)
Convert results to a mixed number and/or reduce to lowest terms
Another example
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14. Division of Fractions changed to Dividend Inverted Divisor Divisor
Quotient
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15. Decimals X X X X X . X X X X Whole Numbers Decimal Decimal Fractions
tens
ones
tenths
thousands
hundreds
hundredths
thousandths
ten thousands
ten thousandths
Whole Numbers
Decimal
Decimal Fractions
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

16. Decimals (Continued) 0.001 = one thousandth 0.02 = two hundredths
= seven tenths
Tenth is like 10 (one zero), so it’s one place after the decimal
Hundredth is like 100 (two zeros), so it’s two places after the decimal
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

17. Comparing Decimals Compare Align decimal points and add zeros
0.125, 0.05, and 0.2 to find largest decimal fraction
Align decimal points and add zeros
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18. Comparing Decimals (Continued)
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19. Decimal Values: Decimal Point and Zeros
In a decimal number
Zeros added before the decimal point or at the end of the decimal fraction do not change the value
.5 = 0.5 = 0.50
0.5 is the preferred notation
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20. Decimal Values: Decimal Point and Zeros (Continued)
In a decimal number
Zeros added before or after the decimal point do change the value
and 1.5 ≠ 10.5 ≠
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

21. Decimal Values: Decimal Point and Zeros (Continued)
To avoid overlooking the decimal point in a decimal fraction
Always place a zero to the left of decimal point
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22. Decimal Values: Decimal Point and Zeros (Continued)
Avoid writing a decimal fraction this way. It could be mistaken for the whole number 5
Example: .5
Example: 0.5
Preferred method of writing a decimal fraction
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23. Add and Subtract Decimals
To add or subtract decimals
Align decimal points and add zeros at the end if needed
Make all decimals of equal length
Eliminate unnecessary zeros in final answer
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24. Multiply and Divide Decimals
To multiply decimals
Place decimal point in product to left, as many decimal places as there are in the two decimals being multiplied
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25. Multiply and Divide Decimals (Continued)
To divide decimals
Move decimal point in both divisor and dividend to the right the correct number of decimal places to make divisor a whole number
Align decimal in quotient
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26. Multiply and Divide Decimals (Continued)
Multiply or divide by a multiplier of 10
Move decimal point to right (to multiply)
Move decimal point to left (to divide)
Move number of decimal places as there are zeros in the multiplier of 10
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27. Multiply and Divide Decimals (Continued)
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

28. Rounding Decimals 0.123 = 0.12 Rounded to hundredths 1.744 = 1.74
Thousandths
Hundredths
Tenths
0.123 = 0.12
1.744 = 1.74
5.235 = 5.24
0.666 = 0.67
Rounded to hundredths
(two places)
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29. Rounding Decimals (Continued)
Hundredths
Tenths
0.13 = 0.1
5.64 = 5.6
0.75 = 0.8
1.66 = 1.7
0.95 = 1.0 = 1
Rounded to tenths
(one place)
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.