5th Grade Multiplication as Scaling Worksheet Solutions (PDF)

The factor \(\frac{3}{4}\) is less than 1.

Multiplying by a number less than 1 makes the product smaller than the other factor.

Less than 8.

The factor \(\frac{5}{4}\) is greater than 1.

Multiplying by a number greater than 1 makes the product larger than the other factor.

Greater than 6.

The fraction \(\frac{4}{4}\) equals 1.

Multiplying by 1 does not change the other factor.

Equal to 7.

\(10 \times \frac{1}{2} = 5\), \(10 \times \frac{3}{2} = 15\), and \(10 \times 1 = 10\).

Least to greatest: \(10 \times \frac{1}{2}\), \(10 \times 1\), \(10 \times \frac{3}{2}\).

(a) \(\frac{7}{8} < 1\), so the product is smaller: \(9 \times \frac{7}{8} < 9\).

(b) \(\frac{9}{8} > 1\), so the product is larger: \(9 \times \frac{9}{8} > 9\).

(c) \(\frac{8}{8} = 1\), so the product is the same: \(9 \times \frac{8}{8} = 9\).

The factor \(\frac{1}{2}\) is less than 1.

Multiplying by a number less than 1 makes the product smaller than the other factor.

Multiply the numerators and multiply the denominators: \(\frac{5}{6} \times \frac{1}{2} = \frac{5 \times 1}{6 \times 2} = \frac{5}{12}\).

\(\frac{5}{12}\)

The product \(\frac{5}{12}\) is less than \(\frac{5}{6}\).

Write the whole number 12 as \(\frac{12}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{12}{1} \times \frac{3}{4} = \frac{12 \times 3}{1 \times 4} = \frac{36}{4}\).

Simplify: \(\frac{36}{4} = 9\).

\(9\)

\(9 < 12\), which matches the prediction because \(\frac{3}{4} < 1\).

Write the whole number 6 as \(\frac{6}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{6}{1} \times \frac{5}{3} = \frac{6 \times 5}{1 \times 3} = \frac{30}{3}\).

Simplify: \(\frac{30}{3} = 10\).

\(10\)

\(10 > 6\), which matches the prediction because \(\frac{5}{3} > 1\).

Multiply the numerators and multiply the denominators: \(\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}\).

Simplify: \(\frac{6}{12} = \frac{1}{2}\).

\(\frac{1}{2}\)

Compare with \(\frac{2}{3}\): \(\frac{1}{2} = \frac{3}{6}\) and \(\frac{2}{3} = \frac{4}{6}\), so \(\frac{1}{2} < \frac{2}{3}\).

Compare with \(\frac{3}{4}\): \(\frac{1}{2} = \frac{2}{4}\), so \(\frac{1}{2} < \frac{3}{4}\).

The product is less than both factors.

The factor \(\frac{3}{4}\) is less than 1.

Multiplying by a number less than 1 makes the product smaller than the other factor.

Write the whole number 8 as \(\frac{8}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{8}{1} \times \frac{3}{4} = \frac{8 \times 3}{1 \times 4} = \frac{24}{4}\).

Simplify: \(\frac{24}{4} = 6\).

\(6\)

The new ribbon is 6 inches long.

The factors \(\frac{7}{6}\) and \(\frac{5}{4}\) are greater than 1. The factor \(\frac{2}{3}\) is less than 1, and 1 equals 1.

Check: \(14 \times \frac{2}{3} = 9\frac{1}{3}\), \(14 \times \frac{7}{6} = 16\frac{1}{3}\), \(14 \times 1 = 14\), \(14 \times \frac{5}{4} = 17\frac{1}{2}\).

\(14 \times \frac{7}{6}\) and \(14 \times \frac{5}{4}\) are greater than 14.

Write the mixed number as improper fraction: \(2\frac{1}{2} = \frac{5}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{2} \times \frac{4}{5} = \frac{5 \times 4}{2 \times 5} = \frac{20}{10}\).

Simplify: \(\frac{20}{10} = 2\).

\(2\)

\(2 < 2\frac{1}{2}\), which matches the prediction because \(\frac{4}{5} < 1\).

Write the mixed numbers as improper fractions: \(3\frac{1}{3} = \frac{10}{3}\) and \(1\frac{1}{5} = \frac{6}{5}\).

Multiply the numerators and multiply the denominators: \(\frac{10}{3} \times \frac{6}{5} = \frac{10 \times 6}{3 \times 5} = \frac{60}{15}\).

Simplify: \(\frac{60}{15} = 4\).

\(4\)

\(4 > 3\frac{1}{3}\), which matches the prediction because \(1\frac{1}{5} > 1\).

\(\frac{1}{4} \times 8 = \frac{8}{4} = 2\).

\(\frac{5}{4} \times 8 = \frac{40}{4} = 10\).

\(\frac{1}{4}\) is less than 1, so the product 2 is less than 8. \(\frac{5}{4}\) is greater than 1, so the product 10 is greater than 8.

The factor \(1\frac{1}{2}\) is greater than 1, so he needs more than 3 cups.

Write the mixed number as improper fraction: \(1\frac{1}{2} = \frac{3}{2}\).

Write the whole number 3 as \(\frac{3}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{3}{2} \times \frac{3}{1} = \frac{3 \times 3}{2 \times 1} = \frac{9}{2}\).

Write as a mixed number: \(\frac{9}{2} = 4\frac{1}{2}\).

\(4\frac{1}{2}\)

Jamal needs \(4\frac{1}{2}\) cups of flour, which is more than 3 cups.

The factor \(\frac{3}{4}\) is less than 1.

Multiplying by a number less than 1 makes the product smaller than the other factor.

Write the whole number 8 as \(\frac{8}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4}\).

Simplify: \(\frac{24}{4} = 6\).

\(6\)

The kitten weighs less than the puppy. It weighs 6 pounds.

Write the whole number 6 as \(\frac{6}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{6}{1} \times \frac{5}{2} = \frac{6 \times 5}{1 \times 2} = \frac{30}{2}\).

Simplify: \(\frac{30}{2} = 15\).

\(15\)

The new width is 15 inches. Compare: \(15 > 12\).

The new photo is 15 inches wide, so it will not fit in the 12-inch frame.

The factor \(\frac{4}{3}\) is greater than 1, so the plant is taller now.

Write the mixed number as improper fraction: \(2\frac{1}{4} = \frac{9}{4}\).

Multiply the numerators and multiply the denominators: \(\frac{9}{4} \times \frac{4}{3} = \frac{9 \times 4}{4 \times 3} = \frac{36}{12}\).

Simplify: \(\frac{36}{12} = 3\).

\(3\)

Growth: \(3 – 2\frac{1}{4} = \frac{3}{4}\) foot.

The plant is 3 feet tall now, and it grew \(\frac{3}{4}\) foot.

Team B: \(\frac{2}{3} \times 12 = 8\). The factor is less than 1, so B scored fewer than 12.

Team C: \(\frac{5}{4} \times 12 = 15\). The factor is greater than 1, so C scored more than 12.

Team B scored 8 runs and Team C scored 15 runs. Team C scored the most.

Eraser: \(0.80 \times \frac{3}{4} = 0.60\), since one fourth of $0.80 is $0.20 and three fourths is $0.60.

Notebook: \(0.80 \times 2\frac{1}{2} = 0.80 \times 2.5 = 2.00\).

Total: \(0.80 + 0.60 + 2.00 = 3.40\).

The eraser costs $0.60, the notebook costs $2.00, and the total is $3.40.