5th Grade Multiplication as Scaling Quiz: 10 Questions with Explanations

A \(10 \times \frac{2}{3}\)B \(10 \times \frac{3}{2}\)C \(10 \times \frac{1}{2}\)D \(10 \times \frac{1}{3}\)

Bar B is longer than bar A, so the factor is greater than 1. 10 x 3/2 = 15.

A \(\frac{10}{9}\)B \(\frac{9}{10}\)C \(\frac{15}{15}\)D \(\frac{5}{4}\)

Only 9/10 is less than 1. The factor 15/15 equals 1, so the product stays 15, and 10/9 and 5/4 are greater than 1, so their products are greater than 15.

A \(14 \times \frac{6}{6}\)B \(14 \times \frac{6}{7}\)C \(14 \times \frac{7}{6}\)D \(14 \times \frac{1}{6}\)

6/6 equals 1, and multiplying by 1 keeps the number the same.

A 16B 9C 15D 4

12 x 3/4 = 36/4 = 9. Since 3/4 is less than 1, the answer must be less than 12. The answer 16 comes from multiplying by 4/3.

A \(1\frac{3}{5}\)B \(6\frac{1}{2}\)C 2D 10

4 x 5/2 = 20/2 = 10. Because 5/2 is greater than 1, the answer is greater than 4.

A It is greater than both factors.B It is equal to 2/3.C It is greater than 4/5.D It is less than both factors.

Both factors are less than 1, so the product is smaller than each factor. 2/3 x 4/5 = 8/15.

A Point AB Point BC Point CD Point D

Point C is 9/8, which is greater than 1. Points A and D are less than 1, and point B equals 1.

A \(4\frac{1}{2}\) cupsB 2 cupsC \(1\frac{1}{2}\) cupsD \(3\frac{3}{4}\) cups

3 x 3/2 = 9/2 = 4 1/2. The factor is greater than 1, so Maya needs more than 3 cups. Dividing gives 2, which is the wrong operation.

A \(10\frac{2}{3}\) inchesB \(8\frac{3}{4}\) inchesC 6 inchesD 11 inches

8 x 3/4 = 6. The factor 3/4 is less than 1, so the new length must be less than 8.

A Sam’s dog weighs 50 pounds.B Sam’s dog weighs 32 pounds.C Sam’s dog weighs 45 pounds.D Both dogs weigh 40 pounds.

40 x 5/4 = 50. The factor 5/4 is greater than 1, so Sam’s dog is heavier. Adding 5 gives 45, which is not the same as multiplying.