5th Grade Multiplication as Scaling Test with Answer Key (Free PDF)

First, write <, >, or = in each blank. Do not calculate.

1. \(7 \times \frac{5}{6}\) ___ 7 (1 point)
2. \(7 \times \frac{11}{8}\) ___ 7 (1 point)

Next, write these expressions in order from least to greatest value: \(20 \times \frac{3}{2}\), \(20 \times \frac{1}{4}\), \(20 \times 1\), \(20 \times \frac{5}{4}\).

Then, the bars show 16 and 12. The number 12 is the product of 16 and a scale factor.

1. What is the scale factor? (1 point)
2. Is the scale factor greater than 1 or less than 1? Explain how you know from the bars. (1 point)

1. Find \(18 \times \frac{5}{6}\). (1 point)
2. Find \(3\frac{1}{2} \times 1\frac{3}{7}\). (1 point)
3. For each product, tell whether it is greater than or less than the first factor. (1 point)

Liam says, “Multiplying always makes a number bigger, so \(9 \times \frac{2}{3}\) is greater than 9.”

1. Explain Liam’s mistake. (1 point)
2. Find the product \(9 \times \frac{2}{3}\). (1 point)

First, a photo is 6 inches wide and 4 inches tall.

1. Mei enlarges the photo to \(\frac{3}{2}\) times its size. Find the new width and the new height. (2 points)
2. Noah shrinks the original photo to \(\frac{2}{3}\) times its size. Find the new width. (1 point)

Next, a smoothie recipe uses \(2\frac{1}{4}\) cups of yogurt.

1. Noah makes \(\frac{2}{3}\) of the recipe. How much yogurt does he use? (1 point)
2. Mei makes \(\frac{4}{3}\) times the recipe. How much yogurt does she use? (1 point)

Then, the number line shows \(\frac{3}{4}\). Without calculating, will \(\frac{3}{4} \times \frac{2}{3}\) be to the left or to the right of \(\frac{3}{4}\)?

1. Choose left or right and explain why. (1 point)
2. Find \(\frac{3}{4} \times \frac{2}{3}\). (1 point)

Now, a playground has a slide that is 20 feet long. A small slide is \(\frac{3}{5}\) as long as the big slide. A giant slide is \(\frac{9}{4}\) times as long as the big slide.

1. How long is the small slide? (1 point)
2. How long is the giant slide? (1 point)