Elementary School Math Quiz: Explain Effects Of Fraction Multiplication

What this quiz covers

This quiz focuses on Explain Effects Of Fraction Multiplication, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $15\times\frac{4}{3}$ is greater than 15 because $\frac{4}{3}$ is greater than 1, and $15\times\frac{2}{3}$ is less than 15 because $\frac{2}{3}$ is less than 1. (correct answer)
2. Both products are less than 15 because multiplying by a fraction always reduces the original number.
3. Both products are greater than 15 because multiplication always increases the original number.
4. $15\times\frac{4}{3}$ is less than 15 because fractions mean a smaller amount, and $15\times\frac{2}{3}$ is greater than 15 because you are multiplying.

Question 2

1. $6\times\frac{3}{2}$ will be greater than 6 because $\frac{3}{2}$ is greater than 1.
2. $6\times\frac{1}{2}$ will be less than 6 because $\frac{1}{2}$ is less than 1.
3. The fraction's size compared to 1 tells whether the product is larger or smaller than the original 6.
4. Both products must be less than 6 because both multipliers are fractions. (correct answer)

Question 3

1. The original number is 15; both products are larger because 6 and 4 are both greater than 1.
2. The original number is 15; Experiment X makes a smaller product because dividing by 5 always makes things smaller, and Experiment Y makes a larger product because 4 is close to 5.
3. The original number is 15; Experiment X makes a larger product because $\frac{6}{5}>1$, and Experiment Y makes a smaller product because $\frac{4}{5}<1$. (correct answer)
4. The original number is 15; both products are smaller than 15 because multiplying by a fraction always makes the original number smaller.

Question 4

1. Both products are smaller than 8 because multiplying by any fraction always makes a number smaller.
2. Batch A's product is larger than 8 because $\frac{5}{4}>1$, and Batch B's product is smaller than 8 because $\frac{3}{4}<1$. (correct answer)
3. Batch A's product is smaller than 8 because fractions mean "part of," and Batch B's product is larger than 8 because you are multiplying.
4. Both products are larger than 8 because multiplication is repeated addition and always increases the amount.

Question 5

1. The original number is 5; the student is correct because any time you see a denominator, the product must get smaller than the original number.
2. The original number is 5; the student is correct because multiplying by a fraction always makes a smaller product than the original number.
3. The original number is 5; the student is incorrect because $\frac{8}{5}>1$, so multiplying 5 by it makes a product larger than 5. (correct answer)
4. The original number is 5; the student is incorrect because multiplication is repeated addition, and you cannot add $\frac{8}{5}$ five times.

Question 6

1. $\frac{6}{5}\times 10$ is larger than 10 because $\frac{6}{5}$ is greater than 1, and $\frac{4}{5}\times 10$ is smaller than 10 because $\frac{4}{5}$ is less than 1. (correct answer)
2. Both products are smaller than 10 because fractions are parts and parts are always less than the whole.
3. Both products are larger than 10 because multiplication always increases the number you start with.
4. You can't tell if the product will be larger or smaller unless you multiply and find the exact answers.

Question 7

1. The original number is 10; both products are smaller because the numbers 5 and 3 are less than 10.
2. The original number is 10; $10\times\frac{5}{4}$ is larger than 10 because $\frac{5}{4}>1$, and $10\times\frac{3}{5}$ is smaller than 10 because $\frac{3}{5}<1$. (correct answer)
3. The original number is 10; both products are larger than 10 because multiplying always increases the number.
4. The original number is 10; $10\times\frac{5}{4}$ is smaller than 10 because fractions make numbers smaller, and $10\times\frac{3}{5}$ is larger than 10 because 3 and 5 are big numbers.

Question 8

1. Both products are smaller than 10 because fractions always make a product smaller than the original number.
2. Change 1 makes the product larger than 10 because $\frac{6}{5}$ is greater than 1, and Change 2 makes the product smaller than 10 because $\frac{2}{5}$ is less than 1. (correct answer)
3. Change 1 makes the product smaller than 10 because you are dividing into fifths, and Change 2 makes the product larger than 10 because multiplying always increases.
4. Both products are larger than 10 because multiplying by a fraction is the same as adding the number again and again.

Question 9

1. Both products are greater than 15 because multiplying always increases time.
2. Both products are less than 15 because fractions always make products smaller.
3. Plan A's product is greater than 15 because $\frac{9}{5}>1$, and Plan B's product is less than 15 because $\frac{1}{5}<1$. (correct answer)
4. You can't compare the products because the fractions have different denominators.

Question 10

1. The larger batch is larger because $\frac{3}{2}$ is greater than 1, and the smaller batch is smaller because $\frac{1}{2}$ is less than 1. (correct answer)
2. Both batches are smaller because fractions always make the product smaller than the original number.
3. Both batches are larger because multiplying means adding 14 again and again.
4. The batch size depends only on the denominator, so both products must be smaller than 14 because 2 is bigger than 1.

Question 11

1. Both products land to the left of 10 because multiplying by a fraction always moves left on the number line.
2. Both products land to the right of 10 because multiplication always makes a number bigger.
3. $\frac{11}{10}\times 10$ lands to the right of 10 because $\frac{11}{10}>1$, and $\frac{7}{10}\times 10$ lands to the left of 10 because $\frac{7}{10}<1$. (correct answer)
4. Both products land at exactly 10 because multiplying keeps the original number the same.

Question 12

1. The student is correct because any fraction means taking a part, so both products must be smaller than 9.
2. The student is wrong because $\frac{3}{2}>1$ so $\frac{3}{2}\times 9$ is larger than 9, but $\frac{2}{3}<1$ so $\frac{2}{3}\times 9$ is smaller than 9. (correct answer)
3. The student is wrong because multiplication is repeated addition, so both products must be larger than 9.
4. The student is wrong because you should add the numerator and denominator first to decide if the product is larger.

Question 13

1. The original number is 6; $6\times\frac{3}{2}$ is larger than 6 because $\frac{3}{2}>1$ so it makes 6 bigger, and $6\times\frac{2}{3}$ is smaller than 6 because $\frac{2}{3}<1$ so it makes 6 smaller. (correct answer)
2. The original number is 6; both products are smaller than 6 because multiplying by any fraction always makes a number smaller.
3. The original number is 6; both products are larger than 6 because multiplication always makes numbers bigger than what you started with.
4. The original number is 6; $6\times\frac{3}{2}$ is larger than 6 because you add $\frac{3}{2}$ six times, and $6\times\frac{2}{3}$ is smaller than 6 because you add $\frac{2}{3}$ six times.

Question 14

1. The original number is 18; both products are larger because multiplying always increases the original number.
2. The original number is 18; $18\times\frac{7}{6}$ is larger than 18 because $\frac{7}{6}>1$, and $18\times\frac{1}{6}$ is smaller than 18 because $\frac{1}{6}<1$. (correct answer)
3. The original number is 18; both products are smaller because both multipliers are fractions.
4. The original number is 18; $18\times\frac{7}{6}$ is smaller because you divide by 6, and $18\times\frac{1}{6}$ is larger because you use 18 as the first number.

Question 15

1. The original number is 7; both products are smaller because both multipliers have 8 in the denominator.
2. The original number is 7; $7\times\frac{9}{8}$ is larger than 7 because $\frac{9}{8}>1$, and $7\times\frac{5}{8}$ is smaller than 7 because $\frac{5}{8}<1$. (correct answer)
3. The original number is 7; $7\times\frac{9}{8}$ is smaller than 7 because fractions make numbers smaller, and $7\times\frac{5}{8}$ is larger than 7 because 5 is a big number.
4. The original number is 7; both products are larger because multiplication means repeated addition, so you always get more than you started with.

Question 16

1. The product is smaller than 8 because multiplying by any fraction always makes a number smaller than the original number. (correct answer)
2. The original number is 8, and the product is larger than 8 because $\frac{7}{6}$ is greater than 1.
3. The fraction $\frac{7}{6}$ is more than one whole, so it stretches the original number 8 to a larger product.
4. If the fraction were less than 1, like $\frac{5}{6}$, then multiplying 8 by it would make a smaller product than 8.

Question 17

1. The original number is 9; Tape 1 is larger than 9 because $\frac{5}{3}>1$ so it shows more than one full group of 9, and Tape 2 is smaller than 9 because $\frac{2}{3}<1$ so it shows only part of 9. (correct answer)
2. The original number is 9; both tapes must be smaller than 9 because multiplying by a fraction always reduces the original number.
3. The original number is 9; Tape 2 is larger because it has fewer boxes, and Tape 1 is smaller because it has more boxes.
4. The original number is 9; Tape 1 is larger because you add $\frac{5}{3}$ nine times, and Tape 2 is smaller because you add $\frac{2}{3}$ nine times.

Question 18

1. Serving Idea 1 makes the product smaller because you are using fourths, and Serving Idea 2 makes the product larger because it is multiplication.
2. Serving Idea 1 makes the product larger because $\frac{5}{4}$ is greater than 1, and Serving Idea 2 makes the product smaller because $\frac{1}{4}$ is less than 1. (correct answer)
3. Both products are smaller than 16 because both multipliers are fractions.
4. Both products are larger than 16 because multiplying means adding 16 again and again.

Question 19

1. Since $\frac{5}{4}$ is greater than 1, $12\times\frac{5}{4}$ will be greater than 12.
2. Since $\frac{3}{4}$ is less than 1, $12\times\frac{3}{4}$ will be less than 12.
3. Because both are fractions, both products must be less than 12. (correct answer)
4. The size of the fraction compared to 1 determines whether the product is larger or smaller than 12.

Question 20

1. The original number is 12; $12\times\frac{4}{3}$ is larger than 12 because $\frac{4}{3}>1$, and $12\times\frac{3}{4}$ is smaller than 12 because $\frac{3}{4}<1$. (correct answer)
2. The original number is 12; both products are smaller than 12 because both multipliers are fractions.
3. The original number is 12; both products are larger than 12 because multiplying means adding 12 again and again.
4. The original number is 12; $12\times\frac{4}{3}$ is smaller because 4 is divided by 3, and $12\times\frac{3}{4}$ is larger because 3 is close to 4.