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.

Fractions Math Tip Denominator begins with d and is down below the line in a fraction © 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.

Types of Fractions Proper fraction Example Value of numerator is less than value of denominator Example is less than 1 because 5 < 8 © 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.

Types of Fractions (Continued) Improper fraction Value is greater than or equal to 1 Example is greater than 1 because 8 > 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.

Types of Fractions (Continued) Mixed number fraction Value is always greater than 1 Example is greater than 1 © 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.

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 © 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.

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.

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 © 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.

Enlarging Fractions Multiply both terms by Value remains the same Same nonzero number Value remains the same © 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.

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 © 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.

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.

Multiply and Divide Fractions To multiply Cancel terms, multiply numerators, and multiply denominators To divide Invert divisor, cancel terms, and multiply © 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.

Multiply and Divide Fractions (Continued) Convert results to a mixed number and/or reduce to lowest terms Another example © 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.

Division of Fractions changed to Dividend Inverted Divisor Divisor Quotient © 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.

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.

Decimals (Continued) 0.001 = one thousandth 0.02 = two hundredths 0.7 = 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.

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 © 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.

Comparing 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.

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 © 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.

Decimal Values: Decimal Point and Zeros (Continued) In a decimal number Zeros added before or after the decimal point do change the value 1.5 1.05 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.

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 © 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.

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 © 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.

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 © 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.

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 © 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.

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 © 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.

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 © 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.

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.

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) © 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.

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.