Learn on PengienVision, Mathematics, Grade 5Chapter 7: Use Equivalent Fractions to Add and Subtract Fractions

Lesson 5: Add and Subtract Fractions

In Lesson 7-5 of enVision Mathematics Grade 5, students learn to add and subtract fractions with unlike denominators by writing equivalent fractions using a common denominator. The lesson guides fifth graders through multi-step problems that combine both operations, such as finding how much paint remains after using measured amounts. Students practice applying this skill across a range of fraction problems, including those with expressions in parentheses.

Section 1

Adding and Subtracting Unlike Fractions

Property

Fractions that have different denominators are called unlike fractions.

To add or subtract unlike fractions:

  1. Find an LCD for the fractions.
  2. Build each fraction to the LCD.
  3. Combine the resulting like fractions.

Examples

  • To add 14+56\frac{1}{4} + \frac{5}{6}, the LCD is 12. We build the fractions: 1×34×3+5×26×2=312+1012=1312\frac{1 \times 3}{4 \times 3} + \frac{5 \times 2}{6 \times 2} = \frac{3}{12} + \frac{10}{12} = \frac{13}{12}.

Section 2

Solving Word Problems with Unlike Fractions

Property

To solve word problems involving fractions, first identify the operation (addition or subtraction) based on the context. Then, apply the rules for adding or subtracting fractions, which may require finding a common denominator. The final step is to interpret the numerical answer in the context of the problem.

ab+cd=ad+bcbd \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
ab−cd=ad−bcbd \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

Examples

  • Maria ran 23\frac{2}{3} of a mile on Monday and 34\frac{3}{4} of a mile on Tuesday. How many miles did she run in total?
23+34=812+912=1712=1512 miles \frac{2}{3} + \frac{3}{4} = \frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12} \text{ miles}
  • A jug contained 78\frac{7}{8} of a gallon of juice. If you poured out 14\frac{1}{4} of a gallon, what fraction of a gallon is left in the jug?
78−14=78−28=58 of a gallon \frac{7}{8} - \frac{1}{4} = \frac{7}{8} - \frac{2}{8} = \frac{5}{8} \text{ of a gallon}
  • A recipe uses 12\frac{1}{2} cup of sugar and 13\frac{1}{3} cup of honey. After mixing, 14\frac{1}{4} cup of the mixture is spilled. How much of the mixture is left?
12+13−14=612+412−312=712 of a cup\frac{1}{2} + \frac{1}{3} - \frac{1}{4} = \frac{6}{12} + \frac{4}{12} - \frac{3}{12} = \frac{7}{12} \text{ of a cup}

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Adding and Subtracting Unlike Fractions

Property

Fractions that have different denominators are called unlike fractions.

To add or subtract unlike fractions:

  1. Find an LCD for the fractions.
  2. Build each fraction to the LCD.
  3. Combine the resulting like fractions.

Examples

  • To add 14+56\frac{1}{4} + \frac{5}{6}, the LCD is 12. We build the fractions: 1×34×3+5×26×2=312+1012=1312\frac{1 \times 3}{4 \times 3} + \frac{5 \times 2}{6 \times 2} = \frac{3}{12} + \frac{10}{12} = \frac{13}{12}.

Section 2

Solving Word Problems with Unlike Fractions

Property

To solve word problems involving fractions, first identify the operation (addition or subtraction) based on the context. Then, apply the rules for adding or subtracting fractions, which may require finding a common denominator. The final step is to interpret the numerical answer in the context of the problem.

ab+cd=ad+bcbd \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
ab−cd=ad−bcbd \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

Examples

  • Maria ran 23\frac{2}{3} of a mile on Monday and 34\frac{3}{4} of a mile on Tuesday. How many miles did she run in total?
23+34=812+912=1712=1512 miles \frac{2}{3} + \frac{3}{4} = \frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12} \text{ miles}
  • A jug contained 78\frac{7}{8} of a gallon of juice. If you poured out 14\frac{1}{4} of a gallon, what fraction of a gallon is left in the jug?
78−14=78−28=58 of a gallon \frac{7}{8} - \frac{1}{4} = \frac{7}{8} - \frac{2}{8} = \frac{5}{8} \text{ of a gallon}
  • A recipe uses 12\frac{1}{2} cup of sugar and 13\frac{1}{3} cup of honey. After mixing, 14\frac{1}{4} cup of the mixture is spilled. How much of the mixture is left?
12+13−14=612+412−312=712 of a cup\frac{1}{2} + \frac{1}{3} - \frac{1}{4} = \frac{6}{12} + \frac{4}{12} - \frac{3}{12} = \frac{7}{12} \text{ of a cup}