4th Grade Math Quiz: Generate Equivalent Fractions Using Multiplication
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Generate Equivalent Fractions Using MultiplicationQuestion 1 of 20

Which fraction is equivalent to 35\frac{3}{5}?

610\frac{6}{10}
53\frac{5}{3}
920\frac{9}{20}
310\frac{3}{10}
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4th Grade Math Quiz

4th Grade Math Quiz: Generate Equivalent Fractions Using Multiplication

Practice Generate Equivalent Fractions Using Multiplication in 4th Grade 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 4th Grade 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

Which fraction is equivalent to 35\frac{3}{5}?

  1. 610\frac{6}{10} (correct answer)
  2. 53\frac{5}{3}
  3. 920\frac{9}{20}
  4. 310\frac{3}{10}
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 3/5, multiplying numerator and denominator by 2 gives (3×2)/(5×2)=6/10; the visual model shows 3/5 has 3 parts shaded out of 5 total, while equivalent fraction 6/10 has 6 parts shaded out of 10 total—same amount, different partition. Choice A is correct because multiplying numerator by 2: 3×2=6, and denominator by 2: 5×2=10, giving 6/10; the visual models show the same amount shaded—3/5 and 6/10 cover the same portion of the whole. Choice B represents multiplying numerator only, which happens when students don't multiply both parts. To help students: Use visual models—show 3/5 and 6/10 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 3×2=6 AND 5×2=10, giving 6/10).

Question 2

Two students create equivalent fractions for 68\frac{6}{8}. Alex multiplies both numerator and denominator by 2 to get 1216\frac{12}{16}. Ben multiplies both numerator and denominator by 3. What fraction does Ben create?

  1. 911\frac{9}{11}
  2. 1824\frac{18}{24} (correct answer)
  3. 1811\frac{18}{11}
  4. 924\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 3

A teacher shows that 710\frac{7}{10} is equivalent to 2130\frac{21}{30} by multiplying both parts of the fraction by the same number. She then creates another equivalent fraction by multiplying 710\frac{7}{10} by a different number to get a denominator of 50. What is this new equivalent fraction?

  1. 1450\frac{14}{50}
  2. 2850\frac{28}{50}
  3. 3550\frac{35}{50} (correct answer)
  4. 4250\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 10×5=5010 \times 5 = 50, you multiply both parts of 710\frac{7}{10} by 5. This gives you 7×510×5=3550\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 1450\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 2850\frac{28}{50}, which would require multiplying by 4 in the numerator and 5 in the denominator – again, different numbers. Choice D gives 4250\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 710\frac{7}{10} and 3550\frac{35}{50} represent the same amount: 3550=35÷550÷5=710\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 4

Multiply the numerator and denominator of 23\frac{2}{3} by 22. What is the equivalent fraction?​

  1. 46\frac{4}{6} (correct answer)
  2. 43\frac{4}{3}
  3. 25\frac{2}{5}
  4. 26\frac{2}{6}
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 2/3, multiplying numerator and denominator by 2 gives (2×2)/(3×2)=4/6; the visual model shows 2/3 has 2 parts shaded out of 3 total, while equivalent fraction 4/6 has 4 parts shaded out of 6 total—same amount, different partition, demonstrating equivalent fractions. Choice B is correct because multiplying numerator by 2: 2×2=4, and denominator by 2: 3×2=6, giving 4/6; the visual models show the same amount shaded—2/3 and 4/6 cover the same portion of the whole. This shows understanding that multiplying top and bottom by the same number preserves the fraction's value. Choice A represents multiplying numerator only, which happens when students don't multiply both parts. To help students: Use visual models—show 2/3 and 4/6 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 2×2=4 AND 3×2=6, giving 4/6).

Question 5

Which fraction is equivalent to 56\frac{5}{6}?

  1. 65\frac{6}{5}
  2. 1012\frac{10}{12} (correct answer)
  3. 1011\frac{10}{11}
  4. 512\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 6

On a number line from 0 to 1, 12\frac{1}{2} and 24\frac{2}{4} are at the same point. Which equation shows why they are equivalent?

  1. 1×22×1=22\frac{1\times 2}{2\times 1} = \frac{2}{2}
  2. 1+22+2=34\frac{1+2}{2+2} = \frac{3}{4}
  3. 1×42×2=44\frac{1\times 4}{2\times 2} = \frac{4}{4}
  4. 1×22×2=24\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 12\frac{1}{2} by 2 gives 24\frac{2}{4}, showing the two fractions are equivalent. Choice A multiplies the denominator and numerator by different numbers, producing 22\frac{2}{2}, which isn't equivalent to 12\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 44\frac{4}{4} rather than 24\frac{2}{4}.

Question 7

25=□10\frac{2}{5}=\frac{\square}{10}. What number goes in the blank?

  1. 2
  2. 4 (correct answer)
  3. 8
  4. 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 8

14=?/12\frac{1}{4}=?/12. What number goes in the blank?

  1. 6
  2. 4
  3. 3 (correct answer)
  4. 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 9

Which fraction is equivalent to 56\frac{5}{6}?​

  1. 65\frac{6}{5}
  2. 1012\frac{10}{12} (correct answer)
  3. 512\frac{5}{12}
  4. 1011\frac{10}{11}
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 10

Multiply the numerator and denominator of 23\frac{2}{3} by 2. What is the equivalent fraction?

  1. 35\frac{3}{5}
  2. 26\frac{2}{6}
  3. 43\frac{4}{3}
  4. 46\frac{4}{6} (correct answer)
Explanation: This question tests 4th grade understanding of why a fraction ab\frac{a}{b} is equivalent to n×an×b\frac{n \times a}{n \times 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 23\frac{2}{3}, multiplying numerator and denominator by 2 gives 2×23×2=46\frac{2 \times 2}{3 \times 2} = \frac{4}{6}; the visual model shows 2/3 has 2 parts shaded out of 3 total, while equivalent fraction 4/6 has 4 parts shaded out of 6 total—same amount, different partition, demonstrating equivalent fractions. Choice A is correct because multiplying numerator by 2: 2×2=42 \times 2 = 4, and denominator by 2: 3×2=63 \times 2 = 6, giving 4/6; the visual models show the same amount shaded—2/3 and 4/6 cover the same portion of the whole. This shows understanding that multiplying top and bottom by the same number preserves the fraction's value. Choice B represents multiplying numerator only, which happens when students don't multiply both parts. To help students: Use visual models—show 1/2 and 2/4 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 1×2=21 \times 2 = 2 AND 2×2=42 \times 2 = 4, giving 2/4). Explain: more parts means each part is smaller, but total amount is the same. Connect to multiplying by 1: multiplying by n/n (like 2/2 or 3/3) equals multiplying by 1, which doesn't change the value. Show pattern: 12=24=36=48\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} (each time multiply by next whole number). Watch for: multiplying only numerator or only denominator, adding instead of multiplying, using different numbers for top and bottom, and not understanding that MORE parts with SMALLER size equals SAME amount.

Question 11

35=?10\frac{3}{5} = \frac{?}{10}. What number goes in the blank?

  1. 3
  2. 5
  3. 6 (correct answer)
  4. 10
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 3/5, to get denominator 10 multiply by 2, so numerator becomes 3×2=6, giving 6/10; the visual model shows 3/5 has 3 parts shaded out of 5 total, while equivalent fraction 6/10 has 6 parts shaded out of 10 total—same amount, different partition, demonstrating equivalent fractions. Choice C is correct because multiplying numerator by 2: 3×2=6, and denominator by 2: 5×2=10, giving 6/10; the visual models show the same amount shaded—3/5 and 6/10 cover the same portion of the whole. This shows understanding that multiplying top and bottom by the same number preserves the fraction's value. Choice A represents using the original numerator without multiplication, which happens when students don't multiply both parts. To help students: Use visual models—show 3/5 and 6/10 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 3×2=6 AND 5×2=10, giving 6/10); explain: more parts means each part is smaller, but total amount is the same; connect to multiplying by 1: multiplying by n/n (like 2/2 or 3/3) equals multiplying by 1, which doesn't change the value; show pattern: 3/5 = 6/10 = 9/15 = 12/20 (each time multiply by next whole number); watch for: multiplying only numerator or only denominator, adding instead of multiplying, using different numbers for top and bottom, and not understanding that MORE parts with SMALLER size equals SAME amount.

Question 12

Multiply the numerator and denominator of 38\frac{3}{8} by 22. What is the equivalent fraction?

  1. 616\frac{6}{16} (correct answer)
  2. 316\frac{3}{16}
  3. 68\frac{6}{8}
  4. 510\frac{5}{10}
Explanation: Multiplying both the numerator and denominator of 38\frac{3}{8} by 2 gives 616\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 38\frac{3}{8}.

Question 13

13=?6\frac{1}{3} = \frac{?}{6}. What number goes in the blank?

  1. 3
  2. 1
  3. 6
  4. 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 14

Multiply the numerator and denominator of 34\frac{3}{4} by 22. What is the equivalent fraction?

  1. 64\frac{6}{4}
  2. 68\frac{6}{8} (correct answer)
  3. 56\frac{5}{6}
  4. 38\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 15

Which fraction is equivalent to 12\frac{1}{2}?

  1. 24\frac{2}{4} (correct answer)
  2. 34\frac{3}{4}
  3. 14\frac{1}{4}
  4. 22\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 16

36=?12\frac{3}{6} = \frac{?}{12}. What number goes in the blank?

  1. 4
  2. 9
  3. 3
  4. 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 17

Which fraction is equivalent to 23\frac{2}{3}?

  1. 34\frac{3}{4}
  2. 29\frac{2}{9}
  3. 46\frac{4}{6} (correct answer)
  4. 26\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 18

Which equation shows how to make an equivalent fraction to 12\frac{1}{2} by multiplying by 33\frac{3}{3}?

  1. 12×3=16\frac{1}{2\times 3}=\frac{1}{6}
  2. 1×32=32\frac{1\times 3}{2}=\frac{3}{2}
  3. 1×32×3=36\frac{1\times 3}{2\times 3}=\frac{3}{6} (correct answer)
  4. 1+32+3=45\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 19

Multiply the numerator and denominator of 14\frac{1}{4} by 33. What is the equivalent fraction?

  1. 112\frac{1}{12}
  2. 412\frac{4}{12}
  3. 37\frac{3}{7}
  4. 312\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 20

Find a fraction equivalent to 27\frac{2}{7} by multiplying the numerator and denominator by 33.

  1. 510\frac{5}{10}
  2. 67\frac{6}{7}
  3. 221\frac{2}{21}
  4. 621\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.