Adding and Subtracting Fractions with Unlike Denominators: Grade 5 Math Test Answer Key – PDF Download

Grade 5 Add Test Answer Key: questions 1–5

Question 1: Rename and add (2 points)

1. \(\frac{3}{4} = \frac{9}{12}\) and \(\frac{5}{6} = \frac{10}{12}\).
2. \(\frac{3}{4} + \frac{5}{6} = \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}\). \(1\frac{7}{12}\)

Scoring: 1 point for two correct equivalent fractions with the same denominator (any common denominator is accepted); 1 point for the sum as a mixed number.

Question 2: Fraction bars (2 points)

1. \(\frac{1}{2} = \frac{5}{10}\) and \(\frac{1}{5} = \frac{2}{10}\).
2. \(\frac{5}{10} + \frac{2}{10} = \frac{7}{10}\). \(\frac{7}{10}\)

Scoring: 1 point for both tenths equivalents, 1 point for the sum.

Question 3: Subtract fractions (2 points)

1. \(\frac{7}{8} – \frac{1}{3} = \frac{21}{24} – \frac{8}{24} = \frac{13}{24}\). \(\frac{13}{24}\)
2. \(\frac{5}{6} – \frac{3}{10} = \frac{25}{30} – \frac{9}{30} = \frac{16}{30} = \frac{8}{15}\). \(\frac{8}{15}\)

Scoring: 1 point for each difference in simplest form. If the answer is correct but not simplified, award the point and note it.

Question 4: Add mixed numbers (2 points)

1. \(3\frac{2}{3} + 1\frac{1}{4} = \frac{11}{3} + \frac{5}{4} = \frac{44}{12} + \frac{15}{12} = \frac{59}{12} = 4\frac{11}{12}\). \(4\frac{11}{12}\)
2. \(2\frac{5}{6} + 3\frac{3}{4} = \frac{17}{6} + \frac{15}{4} = \frac{34}{12} + \frac{45}{12} = \frac{79}{12} = 6\frac{7}{12}\). \(6\frac{7}{12}\)

Scoring: 1 point for each sum written as a mixed number in simplest form.

Question 5: Subtract mixed numbers (2 points)

1. \(6\frac{1}{3} – 2\frac{5}{6} = \frac{19}{3} – \frac{17}{6} = \frac{38}{6} – \frac{17}{6} = \frac{21}{6} = \frac{7}{2} = 3\frac{1}{2}\). \(3\frac{1}{2}\)
2. \(8 – 4\frac{3}{8} = 8 – \frac{35}{8} = \frac{64}{8} – \frac{35}{8} = \frac{29}{8} = 3\frac{5}{8}\). \(3\frac{5}{8}\)

Scoring: 1 point for each difference in simplest form.

Grade 5 Add Test Answer Key: questions 6–9

Question 6: Benchmark estimation (2 points)

1. \(\frac{3}{7}\) is close to \(\frac{1}{2}\) and \(\frac{7}{8}\) is close to 1, so the sum is about \(\frac{1}{2} + 1 = 1\frac{1}{2}\).
2. \(\frac{10}{15} = \frac{2}{3}\) is less than \(\frac{7}{8}\), but a sum must be greater than each addend. Zoe added the numerators and the denominators. The exact sum is \(\frac{24}{56} + \frac{49}{56} = \frac{73}{56} = 1\frac{17}{56}\).

Scoring: 1 point for the estimate 1 1/2 (accept 1 1/2 or about 1.5); 1 point for an explanation that compares the claimed sum with an addend or with the estimate.

Question 7: Cutting a board (2 points)

1. \(6\frac{1}{4} – 2\frac{1}{2} = \text{?}\)
2. \(6\frac{1}{4} – 2\frac{1}{2} = \frac{25}{4} – \frac{5}{2} = \frac{25}{4} – \frac{10}{4} = \frac{15}{4} = 3\frac{3}{4}\). \(3\frac{3}{4}\) feet

Scoring: 1 point for an equation that subtracts 2 1/2 from 6 1/4; 1 point for 3 3/4 feet with a unit.

Question 8: Smoothie recipe (3 points)

1. \(\frac{2}{3} + \frac{1}{2} = \frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1\frac{1}{6}\). \(1\frac{1}{6}\) cups
2. \(\frac{2}{3} + \frac{1}{2} + \frac{1}{4} = \frac{8}{12} + \frac{6}{12} + \frac{3}{12} = \frac{17}{12} = 1\frac{5}{12}\). \(1\frac{5}{12}\) cups
3. \(2 – 1\frac{5}{12} = 1\frac{12}{12} – 1\frac{5}{12} = \frac{7}{12}\). \(\frac{7}{12}\) cup

Scoring: 1 point for each part; part (c) may use an incorrect total from part (b).

Question 9: Hiking trip (3 points)

1. \(2\frac{3}{4} + 1\frac{5}{6} = \frac{11}{4} + \frac{11}{6} = \frac{33}{12} + \frac{22}{12} = \frac{55}{12} = 4\frac{7}{12}\). \(4\frac{7}{12}\) miles
2. \(6 – 4\frac{7}{12} = 6 – \frac{55}{12} = \frac{72}{12} – \frac{55}{12} = \frac{17}{12} = 1\frac{5}{12}\). \(1\frac{5}{12}\) miles
3. \(2\frac{3}{4}\) is close to 3 and \(1\frac{5}{6}\) is close to 2, so the total is about 5 miles. \(4\frac{7}{12}\) is a little less than 5, so it is reasonable.

Scoring: 1 point for each part; part (b) may use an incorrect total from part (a); part (c) needs both benchmark roundings.

Scoring summary

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