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Module 2: Fractions

Arithmetic with Fractions

Much like comparing fractions, adding fractions requires LCM to provide the same basis of addition. When adding fractions, the only part that is actually added together are the numerators.

Fractions—Addition by Sheridan Learning Services

Tutorial 12: How to Add Fractions

For example:

1 1 4 + 2 5 18 {"version":"1.1","math":"1\dfrac{1}{4} + 2\dfrac{5}{18}"}

 

5 4 + 41 18 = 45 36 + 82 36 = 127 36 {"version":"1.1","math":"\dfrac{5}{4} + \dfrac{41}{18} = \dfrac{45}{36} + \dfrac{82}{36} = \dfrac{127}{36} "}

  1. Convert all mixed fractions into improper fractions.

    1 1 4 + 2 5 18 {"version":"1.1","math":"1\dfrac{1}{4} + 2\dfrac{5}{18} "}

    = 5 4 + 41 18 {"version":"1.1","math":"= \dfrac{5}{4} + \dfrac{41}{18}"}

  2. Make the denominators the same using lowest common multiple (LCM) and apply it to all fractions. Refer to Properties of Numbers > Multiples in Module 1: Numbers and Whole Numbers for more information.

    5 4 + 41 18 = 45 36 82 36 {"version":"1.1","math":"\dfrac{5}{4} + \dfrac{41}{18} = \dfrac{45}{36} \dfrac{82}{36} "}

    Since 36 ÷ 4 = 9 {"version":"1.1","math":"36\div4=9"}, multiply the numerator of the first fraction by 9.

    Since 36 ÷ 18 = 2 {"version":"1.1","math":"36\div18=2"}, multiply the numerator of the second fraction by 2.

  3. Add the numerators together, keeping the denominator the same in the sum.
  4. Convert to mixed fraction and reduce where possible. Refer to the Types of Fractions section and/or the Properties of Fractions > Reducing sections in this module for more information.

    127 36 = 3 19 36 {"version":"1.1","math":"\dfrac{127}{36} = 3\dfrac{19}{36} "}

Tutorial 13: How to Subtract Fractions

For example:

2 5 18 − 1 1 4 {"version":"1.1","math":"2\dfrac{5}{18} - 1\dfrac{1}{4}"}

 

  1. Convert all improper fractions into proper fractions.

    2 5 18 − 1 1 4 {"version":"1.1","math":"2\dfrac{5}{18} - 1\dfrac{1}{4} "}

    = 41 18 − 5 4 {"version":"1.1","math":"= \dfrac{41}{18} - \dfrac{5}{4} "}

  2. Make the denominators the same using LCM and apply it to all fractions (Refer to Tutorial 11 in the Properties of Fractions > Comparing Fractions section in this module). LCM of 4 and 18 is 36

    41 18 − 5 4 = 82 36 − 45 36 {"version":"1.1","math":"\dfrac{41}{18} - \dfrac{5}{4} = \dfrac{82}{36} - \dfrac{45}{36}"}

    Since 36 ÷ 4 = 9 {"version":"1.1","math":"36\div4=9"}, multiply the numerator of the first fraction by 9.

    Since 36 ÷ 18 = 2 {"version":"1.1","math":"36\div18=2"}, multiply the numerator of the second fraction by 2.

  3. Subtract the numerators, keeping the denominator the same in the difference

    41 18 − 5 4 = 82 36 − 45 36 = 37 36 {"version":"1.1","math":"\dfrac{41}{18} - \dfrac{5}{4} = \dfrac{82}{36} - \dfrac{45}{36} = \dfrac{37}{36} "}

  4. Convert to mixed fraction and reduce where possible (Refer to Tutorial 9 in the Types of Fractions section and Tutorial 10 in the Properties of Fractions > Reducing section in this module).

    37 36 = 1 1 36 {"version":"1.1","math":"\dfrac{37}{36} = 1\dfrac{1}{36} "}

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