5th Grade Multiplication as Scaling Quiz: 10 Questions with Explanations Home 5th Grade Math Worksheets, Lessons and Tests (Free PDF) 5th Grade Multiplication as Scaling Quiz: 10 Questions with Explanations
Answer these 10 multiple-choice questions about multiplication as scaling. Each question has one correct answer. Compare each scale factor with 1 before you calculate, then read the explanation after each answer.
Grade 5 · Common Core State Standards: 5.NF.B.5a, 5.NF.B.5b
Question 1 Bar B is the product of 10 and a scale factor. Which multiplication shows it?
Bar A 10 Bar B 15 Bar B is longer than bar A. 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.
Question 2 Which scale factor makes the product \(15 \times \text{ (factor)}\) less than 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.
Question 3 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.
Question 4 The shorter bar is \(\frac{3}{4}\) of 12 cups. How many cups is that?
Whole 12 cups 3/4 of it ? The shorter bar is 3/4 of the longer bar. A 16B 9C 15D 412 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.
Question 5 Find \(4 \times \frac{5}{2}\).
A \(1\frac{3}{5}\)B \(6\frac{1}{2}\)C 2D 104 x 5/2 = 20/2 = 10. Because 5/2 is greater than 1, the answer is greater than 4.
Question 6 Which statement is true about \(\frac{2}{3} \times \frac{4}{5}\)?
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.
Question 7 Which point on the number line shows a scale factor that makes \(6 \times the factor\) greater than 6?
0 1 2 A B C D Four possible scale factors. A Point AB Point BC Point CD Point DPoint C is 9/8, which is greater than 1. Points A and D are less than 1, and point B equals 1.
Question 8 Maya's cake recipe uses 3 cups of sugar. She makes \(1\frac{1}{2}\) times the recipe. How much sugar does she need?
A \(4\frac{1}{2}\) cupsB 2 cupsC \(1\frac{1}{2}\) cupsD \(3\frac{3}{4}\) cups3 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.
Question 9 A rectangle is 8 inches long. A new rectangle is \(\frac{3}{4}\) as long. How long is the new rectangle?
8 in 5 in A rectangle. A \(10\frac{2}{3}\) inchesB \(8\frac{3}{4}\) inchesC 6 inchesD 11 inches8 x 3/4 = 6. The factor 3/4 is less than 1, so the new length must be less than 8.
Question 10 Jamal's dog weighs 40 pounds. Sam's dog weighs \(\frac{5}{4}\) as much. Which statement is correct?
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.
Remember
A scale factor greater than 1 makes the product larger.
A scale factor equal to 1 leaves the product the same.
A scale factor less than 1 makes the product smaller.
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.
All Grade 5 chapters: Grade 5 math .
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