Elementary School Math Quiz: Generate Equivalent Fractions Using Multiplication

20 questions · exam conditions

0:00

Generate Equivalent Fractions Using MultiplicationQuestion 1 of 20

Two students create equivalent fractions for $\frac{6}{8}$ . Alex multiplies both numerator and denominator by 2 to get $\frac{12}{16}$ . Ben multiplies both numerator and denominator by 3. What fraction does Ben create?

\frac{9}{11}

\frac{18}{24}

\frac{18}{11}

\frac{9}{24}

← Back to quizzes

Elementary School Math Quiz

Elementary School Math Quiz: Generate Equivalent Fractions Using Multiplication

Practice Generate Equivalent Fractions Using Multiplication in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Generate Equivalent Fractions Using 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.

All questions

Question 1

$\frac{9}{11}$
$\frac{18}{24}$ (correct answer)
$\frac{18}{11}$
$\frac{9}{24}$

Explanation: Multiplying both the numerator and denominator of 6/8 by 3 gives 18/24, so Choice B is correct. Choice A, 9/11, looks like it comes from adding 3 to the numerator, 6 plus 3 equals 9, and changing the denominator in a way that does not match multiplying by 3. Choice C, 18/11, multiplies the numerator correctly, 6 times 3 equals 18, but does not multiply the denominator the same way. Choice D, 9/24, multiplies the denominator correctly, 8 times 3 equals 24, but adds 3 to the numerator instead of multiplying it. Multiplying both numbers by the same factor is what keeps the fraction's value the same.

Question 2

A teacher shows that $\frac{7}{10}$ is equivalent to $\frac{21}{30}$ by multiplying both parts of the fraction by the same number. She then creates another equivalent fraction by multiplying $\frac{7}{10}$ by a different number to get a denominator of 50. What is this new equivalent fraction?

$\frac{14}{50}$
$\frac{28}{50}$
$\frac{35}{50}$ (correct answer)
$\frac{42}{50}$

Explanation: When you're working with equivalent fractions, you're finding different ways to write the same amount by multiplying or dividing both the numerator and denominator by the same number. This keeps the fraction's value unchanged. To find the equivalent fraction with denominator 50, you need to figure out what number to multiply 10 by to get 50. Since

10 \times 5 = 50

, you multiply both parts of

\frac{7}{10}

by 5. This gives you

\frac{7 \times 5}{10 \times 5} = \frac{35}{50}

, which is answer choice C. Let's see why the other answers don't work. Choice A gives

\frac{14}{50}

, which would mean you multiplied the numerator by 2 but the denominator by 5 – that's not allowed since you must use the same number for both parts. Choice B gives

\frac{28}{50}

, which would require multiplying by 4 in the numerator and 5 in the denominator – again, different numbers. Choice D gives

\frac{42}{50}

, which would mean multiplying by 6 in the numerator but 5 in the denominator. You can verify that C is correct by checking if

\frac{7}{10}

and

\frac{35}{50}

represent the same amount:

\frac{35}{50} = \frac{35 \div 5}{50 \div 5} = \frac{7}{10}

✓ Remember: to create equivalent fractions, always multiply (or divide) the top and bottom by the exact same number. Find what number transforms your current denominator into the target denominator, then apply that same number to the numerator.

Question 3

Which fraction is equivalent to $\frac{5}{6}$ ?

$\frac{6}{5}$
$\frac{10}{12}$ (correct answer)
$\frac{10}{11}$
$\frac{5}{12}$

Explanation: This question tests 4th grade understanding of why a fraction a/b is equivalent to (n×a)/(n×b) by using visual fraction models, with attention to how number and size of parts differ even though the fractions represent the same amount (CCSS.4.NF.1). Equivalent fractions represent the same amount but have different numbers of parts. To generate an equivalent fraction, multiply both the numerator and denominator by the same whole number—this is like multiplying by n/n, which equals 1, so the value doesn't change. The key understanding: when you multiply both parts by the same number, you get MORE parts (denominator increases) but each part is SMALLER, so the total amount stays the same. Starting with 5/6, multiplying numerator and denominator by 2 gives (5×2)/(6×2)=10/12; the visual model shows 5/6 has 5 parts shaded out of 6 total, while equivalent fraction 10/12 has 10 parts shaded out of 12 total—same amount, different partition. Choice B is correct because multiplying numerator by 2: 5×2=10, and denominator by 2: 6×2=12, giving 10/12; the visual models show the same amount shaded—5/6 and 10/12 cover the same portion of the whole. Choice C represents multiplying numerator only, which happens when students don't multiply both parts. To help students: Use visual models—show 5/6 and 10/12 with area models where the SAME AMOUNT is shaded but with different numbers of parts. Emphasize the pattern: multiply both numerator AND denominator by the same number (if multiply by 2, do 5×2=10 AND 6×2=12, giving 10/12).

Question 4

On a number line from 0 to 1, $\frac{1}{2}$ and $\frac{2}{4}$ are at the same point. Which equation shows why they are equivalent?

$\frac{1\times 2}{2\times 1} = \frac{2}{2}$
$\frac{1+2}{2+2} = \frac{3}{4}$
$\frac{1\times 4}{2\times 2} = \frac{4}{4}$
$\frac{1\times 2}{2\times 2} = \frac{2}{4}$ (correct answer)

Explanation: The correct answer is D because multiplying both the numerator and denominator of

\frac{1}{2}

by 2 gives

\frac{2}{4}

, showing the two fractions are equivalent. Choice A multiplies the denominator and numerator by different numbers, producing

\frac{2}{2}

, which isn't equivalent to

\frac{1}{2}

. Choice B adds instead of multiplying, which isn't a valid way to find an equivalent fraction. Choice C multiplies by 4 and 2 instead of matching multipliers, giving

\frac{4}{4}

rather than

\frac{2}{4}

Question 5

$\frac{2}{5}=\frac{\square}{10}$ . What number goes in the blank?

2
4 (correct answer)
8
5

Explanation: 2/5 equals 4/10 because multiplying both the numerator and denominator by 2 gives 4/10. Choice A repeats the original numerator without scaling it up. Choice C doubles the numerator too much, matching the wrong scale factor. Choice D confuses the denominator's scale factor with the answer itself.

Question 6

$\frac{1}{4}=?/12$ . What number goes in the blank?

6
4
3 (correct answer)
2

Explanation: Since 12 divided by 4 is 3, multiplying the numerator 1 by that same factor of 3 gives 3, so 1/4 equals 3/12, making Choice C correct. Choice A, 6, would come from multiplying by 6 instead of the correct factor of 3. Choice B, 4, mistakes the denominator's growth factor for the missing numerator itself. Choice D, 2, is too small to keep the fraction equivalent to 1/4.

Question 7

Multiply the numerator and denominator of $\frac{3}{8}$ by $2$ . What is the equivalent fraction?

$\frac{6}{16}$ (correct answer)
$\frac{3}{16}$
$\frac{6}{8}$
$\frac{5}{10}$

Explanation: Multiplying both the numerator and denominator of

\frac{3}{8}

by 2 gives

\frac{6}{16}

, an equivalent fraction. Choice B only multiplies the numerator, not the denominator. Choice C only multiplies the denominator, not the numerator. Choice D uses different numbers entirely and is not a valid multiple of

\frac{3}{8}

Question 8

$\frac{1}{3} = \frac{?}{6}$ . What number goes in the blank?

3
1
6
2 (correct answer)

Explanation: The correct answer is 2, because 1/3 is equivalent to 2/6 when both the numerator and denominator are multiplied by 2. Choice A, 3, mistakes the missing numerator for the denominator's scale factor. Choice B, 1, just repeats the original numerator without scaling it. Choice C, 6, uses the new denominator instead of finding the new numerator.

Question 9

Multiply the numerator and denominator of $\frac{3}{4}$ by $2$ . What is the equivalent fraction?

$\frac{6}{4}$
$\frac{6}{8}$ (correct answer)
$\frac{5}{6}$
$\frac{3}{8}$

Explanation: Multiplying both the numerator and denominator of 3/4 by 2 gives 6/8, since 3 times 2 is 6 and 4 times 2 is 8, making Choice B correct. Choice A, 6/4, multiplies the numerator by 2 but leaves the denominator unchanged, which breaks the equivalence. Choice C, 5/6, does not come from multiplying either part by 2 and is an unrelated fraction. Choice D, 3/8, keeps the original numerator but doubles only the denominator, which changes the value.

Question 10

Which fraction is equivalent to $\frac{1}{2}$ ?

$\frac{2}{4}$ (correct answer)
$\frac{3}{4}$
$\frac{1}{4}$
$\frac{2}{2}$

Explanation: Multiplying both the numerator and denominator of 1/2 by 2 gives 2/4, so Choice A is correct. Choice B, 3/4, is greater than 1/2 and does not come from multiplying both numbers in 1/2 by the same amount. Choice C, 1/4, is less than 1/2 and would result only if the denominator were doubled while the numerator stayed the same. Choice D, 2/2, equals 1, which is twice as large as 1/2, not equivalent to it. A fraction stays equivalent only when both the numerator and denominator are multiplied by the same number.

Question 11

$\frac{3}{6} = \frac{?}{12}$ . What number goes in the blank?

4
9
3
6 (correct answer)

Explanation: Since 12 divided by 6 is 2, multiplying the numerator 3 by that same factor of 2 gives 6, so 3/6 equals 6/12, making Choice D correct. Choice A, 4, does not come from multiplying 3 by a consistent factor. Choice B, 9, is too large to keep the fraction equivalent to 3/6. Choice C, 3, repeats the original numerator without adjusting it to match the new denominator.

Question 12

Which fraction is equivalent to $\frac{2}{3}$ ?

$\frac{3}{4}$
$\frac{2}{9}$
$\frac{4}{6}$ (correct answer)
$\frac{2}{6}$

Explanation: Choice C is correct because 4/6 simplifies to 2/3, making it equivalent to the original fraction. Choice A is incorrect because 3/4 does not simplify to 2/3. Choice B is incorrect because 2/9 is not equivalent to 2/3. Choice D is incorrect because 2/6 simplifies to 1/3, not 2/3.

Question 13

Which equation shows how to make an equivalent fraction to $\frac{1}{2}$ by multiplying by $\frac{3}{3}$ ?

$\frac{1}{2\times 3}=\frac{1}{6}$
$\frac{1\times 3}{2}=\frac{3}{2}$
$\frac{1\times 3}{2\times 3}=\frac{3}{6}$ (correct answer)
$\frac{1+3}{2+3}=\frac{4}{5}$

Explanation: Multiplying both the numerator and denominator of 1/2 by 3 gives (1 times 3) over (2 times 3), which equals 3/6, so Choice C is correct. Choice A shows multiplying only the denominator by 3, leaving the numerator unchanged. Choice B shows multiplying only the numerator by 3, leaving the denominator unchanged. Choice D adds 3 to both the numerator and denominator instead of multiplying, which does not keep the fraction equivalent. Multiplying both the numerator and denominator by the same number is what makes the two fractions equal.

Question 14

Multiply the numerator and denominator of $\frac{1}{4}$ by $3$ . What is the equivalent fraction?

$\frac{1}{12}$
$\frac{4}{12}$
$\frac{3}{7}$
$\frac{3}{12}$ (correct answer)

Explanation: Multiplying both the numerator and denominator of 1/4 by 3 gives 3/12, since 1 times 3 is 3 and 4 times 3 is 12, making Choice D correct. Choice A, 1/12, multiplies only the denominator by 3 and leaves the numerator unchanged. Choice B, 4/12, multiplies only the numerator, turning the 1 into a 4 instead of a 3. Choice C, 3/7, adds 3 to the denominator instead of multiplying it.

Question 15

Find a fraction equivalent to $\frac{2}{7}$ by multiplying the numerator and denominator by $3$ .

$\frac{5}{10}$
$\frac{6}{7}$
$\frac{2}{21}$
$\frac{6}{21}$ (correct answer)

Explanation: Multiplying both the numerator and denominator of 2/7 by 3 gives 6/21, so Choice D is correct. Choice A, 5/10, does not come from multiplying either number in 2/7 by 3, so it does not fit the pattern at all. Choice B, 6/7, comes from multiplying only the numerator by 3 while leaving the denominator unchanged. Choice C, 2/21, comes from multiplying only the denominator by 3 while leaving the numerator unchanged. Only multiplying both numbers by the same amount keeps the fraction equal.

Question 16

Maria has $\frac{2}{5}$ of a pizza. She wants to cut each fifth into 3 equal pieces to share with more friends. What equivalent fraction represents the same amount of pizza Maria has, but shows the smaller pieces?

$\frac{6}{15}$ (correct answer)
$\frac{6}{8}$
$\frac{5}{12}$
$\frac{2}{15}$

Explanation: Cutting each fifth into 3 equal pieces means both the numerator and denominator multiply by 3, so 2/5 becomes 6/15, making Choice A correct. Choice B, 6/8, multiplies the numerator by 3 but adds 3 to the denominator instead of multiplying it, which breaks the equivalence. Choice C, 5/12, does not use a consistent multiplier for the numerator and denominator, so it is not the same amount of pizza. Choice D, 2/15, changes the denominator without adjusting the numerator to match, so it represents a smaller amount than Maria actually has.

Question 17

Which fraction is equivalent to $\frac{4}{9}$ ?

$\frac{5}{9}$
$\frac{9}{4}$
$\frac{8}{18}$ (correct answer)
$\frac{4}{18}$

Explanation: Multiplying both the numerator and denominator of 4/9 by 2 gives 8/18, an equivalent fraction. Choice A does not result from multiplying the numerator and denominator of 4/9 by the same factor. Choice B reverses the numerator and denominator, changing the fraction's value. Choice D multiplies only the denominator, not the numerator, so it is not equivalent.

Question 18

Which fraction is equivalent to $\frac{3}{5}$ ?

$\frac{9}{20}$
$\frac{3}{10}$
$\frac{5}{3}$
$\frac{6}{10}$ (correct answer)

Explanation: Multiplying both the numerator and denominator of 3/5 by 2 gives 6/10, an equivalent fraction. Choice A does not result from multiplying the numerator and denominator of 3/5 by the same factor. Choice B multiplies only the denominator, not the numerator, so it is not equivalent. Choice C reverses the numerator and denominator, changing the fraction's value.

Question 19

Which equation shows why $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ ?

$\frac{1\times 4}{3\times 4}=\frac{4}{12}$ (correct answer)
$\frac{1\times 4}{3\times 3}=\frac{4}{12}$
$\frac{1\times 3}{3\times 4}=\frac{4}{12}$
$\frac{1+4}{3+4}=\frac{4}{12}$

Explanation: The correct answer is (1 times 4) over (3 times 4) equals 4/12, because multiplying both the numerator and denominator by the same number, 4, keeps the fraction equivalent. Choice B multiplies the numerator by 4 but the denominator by 3, using two different multipliers instead of the same one. Choice C swaps which part gets multiplied by 3 and which gets multiplied by 4, mismatching the numerator and denominator. Choice D adds 4 to the numerator and denominator instead of multiplying by 4.

Question 20

Multiply the numerator and denominator of $\frac{2}{5}$ by $2$ . What is the equivalent fraction?

$\frac{4}{10}$ (correct answer)
$\frac{3}{7}$
$\frac{2}{10}$
$\frac{4}{5}$

Explanation: Multiplying both the numerator and denominator of 2/5 by 2 gives 4/10, so 4/10 is the equivalent fraction. Choice B, 3/7, does not come from multiplying either number in 2/5 by 2, so it does not fit the pattern at all. Choice C, 2/10, comes from doubling only the denominator while leaving the numerator unchanged, which changes the value of the fraction. Choice D, 4/5, comes from doubling only the numerator while leaving the denominator unchanged, which also changes the value. Only multiplying both numbers by the same amount keeps the fraction equal.