5th Grade Multiplication as Scaling Worksheet Answer Key (PDF)

Q: What are the run totals in problem 19?

Team A scored 12 runs. Team B scored two thirds of 12, which is 8 runs. Team C scored five fourths of 12, which is 15 runs. A quick check like this takes only a few seconds and prevents most errors.

5th grade multiplication as scaling worksheet answers – Maths PDF

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This 5th grade multiplication as scaling worksheet answers covers multiplication as scaling (Common Core 5.NF.B.5a, 5.NF.B.5b), with a free PDF to print.

Key takeaway: This answer key helps fifth grade students and parents check scaling work and see the reason behind each prediction.

Topic: Multiplication as Scaling (5th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 5.NF.B.5a, 5.NF.B.5b
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fifth grade students and parents check scaling work and see the reason behind each prediction. Each solution names the scale factor, states whether it is greater than, equal to, or less than one, and then gives the product.

The key covers all 20 problems, including the order of products in problem 4 and the symbols in problem 5. Also, word problem answers use full sentences with units. If your answer differs, check the scale factor first. Then, plan about 15 minutes to compare and fix your work.

This answer key explains each of the 20 problems. Prediction problems state how the scale factor compares with 1. Calculation problems show the multiplication steps and then compare the product with the original factor. Final answers are in bold.

Grade 5 · Common Core State Standards: 5.NF.B.5a, 5.NF.B.5b

5th grade multiplication as scaling worksheet answers: worksheet problems 1 to 10

1 – Predict the size

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.

2 – Factor greater than 1

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.

3 – Factor equal to 1

The fraction $\frac{4}{4}$ equals 1.

Multiplying by 1 does not change the other factor.

Equal to 7.

4 – Order the products

The bars show 5, 15, and 10.

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

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

5 – Fill in the symbols

(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: $9 \times \frac{9}{8} > 9$.

6 – Compare to one factor

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 $\frac{5}{6}$.

Worksheet problem 7 and after

7 – Compute and compare

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 $\frac{3}{4} < 1$.

8 – Scaling up

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 $\frac{5}{3} > 1$.

9 – Smaller than both factors

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.

10 – Resize a ribbon

Three fourths of 8 inches is 6 inches.

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.

Worksheet problems 11 and up

11 – Which products are larger?

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.

12 – Mixed number scaled down

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 $\frac{4}{5} < 1$.

13 – Mixed number scaled up

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 $1\frac{1}{5} > 1$.

14 – Explain two products

$\frac{1}{4} \times 8 = \frac{8}{4} = 2$.

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

$\frac{1}{4}$ 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.

Worksheet problem 15 and after

15 – Bigger batch of pancakes

One and a half times 3 is 4 1/2.

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.

16 – Puppy and kitten

The kitten weighs 6 pounds.

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.

17 – Enlarged photo

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.

Worksheet problem 18 and after

18 – Plant growth

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.

19 – Little League runs

Also, Team B scored 8 runs and Team C scored 15 runs.

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.

20 – School store prices

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.

Key facts behind this 5th grade multiplication as scaling worksheet answers

Key facts

A scale factor greater than 1 makes the product larger.
Also, a scale factor equal to 1 leaves the product the same.
Also, a scale factor less than 1 makes the product smaller.
Then, a fraction times a fraction less than 1 is smaller than both factors.
Compare the factor to 1 to predict the size before you calculate.

Common mistakes with this 5th grade multiplication as scaling worksheet answers

Students compare only the product. Instead, check the reason about the scale factor. Slow down at that step and check it twice.
Students skip the unit in word problems. Instead, answers use inches, cups, pounds, feet, or dollars. Slow down at that step and check it twice.
Students ignore the second question in problem 16. The key also finds how much less the kitten weighs.
Students forget that a factor of one leaves a product unchanged. Also, the key states this in problem 3.

How to use these solutions

Read the reason in each solution aloud. Then, the reason is the main skill. Repeat this habit on every problem for the best results.
Redo each missed problem by naming the scale factor. Finally, the name tells the answer. Repeat this habit on every problem for the best results.
Parents can ask the child to explain why five fourths makes a product larger. Repeat this habit on every problem for the best results.

Download the 5th grade multiplication as scaling worksheet answers as a PDF with the button below and keep it with your notes.

5th grade multiplication as scaling worksheet answers: frequently asked questions

What are the answers to problems 1 to 3?

In problem 1, the factor three fourths is less than one, so the product is less than 8. Also, in problem 2, five fourths is greater than one, so the product is greater than 6. In problem 3, four fourths equals one, so the product equals 7.

How does the key solve problem 17?

The new width is five halves times 6 inches, which is 15 inches. The frame is 12 inches wide, so the photo does not fit. A quick check like this takes only a few seconds and prevents most errors.

What are the run totals in problem 19?

Team A scored 12 runs. Also, Team B scored two thirds of 12, which is 8 runs. Team C scored five fourths of 12, which is 15 runs. A quick check like this takes only a few seconds and prevents most errors.

All Grade 5 chapters: Grade 5 math.

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