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.
Question 1
Maria has 52 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?
156
8
Explanation: To find the equivalent fraction, multiply both numerator and denominator by 3: 52=5×3. Choice B incorrectly adds 3 to the denominator instead of multiplying. Choice C represents a different amount entirely. Choice D only multiplies the denominator by 3.
Question 2
Jake claims that 83 and 32 represent the same amount because he multiplied both the numerator and denominator of by the same number. What number did Jake multiply by?
Question 3
Lisa has 94 of a chocolate bar. She wants to express this same amount using a fraction with a numerator of 12. What should the denominator be to create an equivalent fraction?
21
27
36
Question 4
Two students create equivalent fractions for 86. Alex multiplies both numerator and denominator by 2 to get 16. Ben multiplies both numerator and denominator by 3. What fraction does Ben create?
Question 5
A number line from 0 to 1 is shown. One line is divided into 4 equal parts and marks 42. Another is divided into 8 equal parts and marks 8. Are these fractions equivalent?
Question 6
A teacher shows that 107 is equivalent to 30 by multiplying both parts of the fraction by the same number. She then creates another equivalent fraction by multiplying by a different number to get a denominator of 50. What is this new equivalent fraction?
Question 7
A recipe calls for 64 cup of flour. Emma wants to write this using twelfths instead of sixths. Which fraction is equivalent to 6 and has a denominator of 12?
Question 8
Which fraction is equivalent to 94?
Question 9
Which fraction is equivalent to 53?
Question 10
A number line from 0 to 1 is shown. One line is divided into 4 equal parts and marks 42. Another is divided into 8 equal parts and marks 8. Are these fractions equivalent?
Question 11
Which fraction is equivalent to 65?
Question 12
Which fraction is equivalent to 43?
Question 13
On a number line from 0 to 1, 21 and 4 are at the same point. Which equation shows why they are equivalent?
Question 14
Which fraction is equivalent to 52?
Question 15
53=10. What number goes in the blank?
Question 16
Which fraction is equivalent to 65?
Question 17
52=?/10. What number goes in the blank?
2
4
Question 18
Multiply the numerator and denominator of 32 by 2. What is the equivalent fraction?
Question 19
41=?/12. What number goes in the blank?
6
4
Question 20
Which equation shows why 31 is equivalent to 12?
6
125
152
2×3
=
156
12
83
4
9
24
8
Explanation: To get from 83 to 3212, both 3 and 8 must be multiplied by 4: 3×4=12 and 8×4=32. Choice B is the difference between 12 and 3. Choice C is the product of 3 and 8. Choice D is just the original denominator.
15
Explanation: When you see a question about equivalent fractions, you're looking for fractions that represent the same value but are written differently. To find equivalent fractions, you multiply or divide both the numerator and denominator by the same number.Starting with 94, you need to find what number to multiply 4 by to get 12. Since 4×3=12, you multiply the numerator by 3. To keep the fraction equivalent, you must multiply the denominator by the same number: 9×3=27. This gives you 2712, which equals the original 94.Let's check why the other answers don't work. Choice A (21) would give you 2112. If you simplify this by dividing both parts by 3, you get 74, which is not equal to . Choice C (36) creates , which simplifies to when you divide by 12. This also doesn't equal . Choice D (15) gives you , which simplifies to when you divide by 3, again not matching our original fraction.Remember this key strategy: whatever you multiply the numerator by to create an equivalent fraction, you must multiply the denominator by that exact same number. This keeps the fractions truly equivalent and prevents common mistakes.
12
119
2418
1118
249
Explanation: When you're creating equivalent fractions, you multiply both the numerator (top number) and denominator (bottom number) by the same value. This keeps the fraction equal to the original while changing how it looks.Let's follow Ben's work step by step. He starts with 86 and multiplies both parts by 3. For the numerator: 6×3=18. For the denominator: 8×3=24. So Ben creates 2418, which is answer choice B.You can verify this is equivalent to the original by checking that both fractions reduce to 43 when simplified.Now let's see why the other answers are wrong. Choice A (119) comes from a common mistake where someone multiplies the numerator by 3 correctly (6×3=18... wait, that's 18, not 9) but then adds 3 to the denominator instead of multiplying (). Actually, this answer involves multiple errors. Choice C () gets the numerator right but makes that addition error with the denominator. Choice D () correctly multiplies the denominator by 3 but incorrectly adds 3 to the numerator instead of multiplying.The key strategy here is remembering that equivalent fractions require multiplying both the top AND bottom by the same number. If you multiply one part and add to the other, or use different numbers for each part, you'll get a completely different fraction that's not equivalent to your starting fraction.
4
Yes, because you add 4 to the numerator and denominator.
Yes, because both points are halfway between 0 and 1.
No, because 84 has a bigger denominator.
No, because 42 has fewer parts.
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. The visual model on the number line shows 2/4 as halfway between 0 and 1 with 4 parts, and 4/8 also halfway with 8 parts—same amount, different partition, demonstrating equivalent fractions. Choice C is correct because both points are halfway between 0 and 1, showing the same value; this demonstrates understanding that multiplying top and bottom by the same number preserves the fraction's value. Choice D represents adding instead of multiplying, which happens when students think adding creates equivalence. To help students: Use visual models—show 2/4 and 4/8 on number lines where the points align at the same position but with different divisions. Emphasize the pattern: multiply both numerator AND denominator by the same number (from 1/2, multiply by 2 for 2/4, by 4 for 4/8).
21
107
5014
5028
5035
5042
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=50, you multiply both parts of 107 by 5. This gives you 10×57×5=5035, which is answer choice C.Let's see why the other answers don't work. Choice A gives 5014, 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 5028, which would require multiplying by 4 in the numerator and 5 in the denominator – again, different numbers. Choice D gives , which would mean multiplying by 6 in the numerator but 5 in the denominator.You can verify that C is correct by checking if 107 and 5035 represent the same amount: ✓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.
4
126
124
1216
128
Explanation: When you need to find an equivalent fraction with a different denominator, you're looking for a fraction that represents the same amount but is written differently. Think of it like having the same amount of pizza, but cutting it into more pieces.To change 64 to twelfths, you need to figure out what to multiply both the numerator and denominator by. Since you want the denominator to be 12, ask yourself: "What do I multiply 6 by to get 12?" The answer is 2, because 6×2=12.Whatever you do to the denominator, you must do to the numerator to keep the fractions equivalent. So multiply the numerator by 2 as well: 4×2=8. This gives you 128, which is answer choice D.Let's see why the other answers are incorrect. Choice A (126) would mean someone just used 6 as the new numerator without doing the proper calculation. Choice B (124) happens when you change the denominator but forget to change the numerator at all. Choice C () occurs if you accidentally multiply 4 by 4 instead of 2, perhaps confusing this with a different conversion.Here's your key strategy: always find the multiplication factor first by comparing denominators, then apply that same factor to the numerator. Remember the golden rule of equivalent fractions: whatever you do to the bottom, you must do to the top.
9
5
49
188
184
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 4/9, multiplying numerator and denominator by 2 gives (4×2)/(9×2) = 8/18; the visual model shows 4/9 has 4 parts shaded out of 9 total, while equivalent fraction 8/18 has 8 parts shaded out of 18 total—same amount, different partition, demonstrating equivalent fractions. Choice A is correct because multiplying numerator by 2: 4×2=8, and denominator by 2: 9×2=18, giving 8/18; the visual models show the same amount shaded—4/9 and 8/18 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 or an arithmetic error, which happens when students don't multiply both parts. To help students: Use visual models—show 4/9 and 8/18 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 4×2=8 AND 9×2=18, giving 8/18); 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: 4/9 = 8/18 = 12/27 = 16/36 (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.
10
6
35
209
103
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).
4
No, because 42 has fewer parts.
No, because 84 has a bigger denominator.
Yes, because both points are halfway between 0 and 1.
Yes, because you add 4 to the numerator and denominator.
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. The visual model on the number line shows 2/4 as halfway between 0 and 1 with 4 parts, and 4/8 also halfway with 8 parts—same amount, different partition, demonstrating equivalent fractions. Choice C is correct because both points are halfway between 0 and 1, showing the same value; this demonstrates understanding that multiplying top and bottom by the same number preserves the fraction's value. Choice D represents adding instead of multiplying, which happens when students think adding creates equivalence. To help students: Use visual models—show 2/4 and 4/8 on number lines where the points align at the same position but with different divisions. Emphasize the pattern: multiply both numerator AND denominator by the same number (from 1/2, multiply by 2 for 2/4, by 4 for 4/8).
5
6
1210
1110
125
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).
8
6
87
83
64
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 3/4, multiplying numerator and denominator by 2 gives (3×2)/(4×2) = 6/8; the visual model shows 3/4 has 3 parts shaded out of 4 total, while equivalent fraction 6/8 has 6 parts shaded out of 8 total—same amount, different partition, demonstrating equivalent fractions. Choice B is correct because multiplying numerator by 2: 3×2=6, and denominator by 2: 4×2=8, giving 6/8; the visual models show the same amount shaded—3/4 and 6/8 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 or an arithmetic error, which happens when students don't multiply both parts or make calculation errors. To help students: Use visual models—show 3/4 and 6/8 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 4×2=8, giving 6/8); 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: 3/4 = 6/8 = 9/12 = 12/16 (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.
2
2×11×2=22
2+21+2=4
2×21×4=4
2×21×2=4
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 1/2, multiplying numerator and denominator by 2 gives (1×2)/(2×2)=2/4; the visual model shows 1/2 has 1 part shaded out of 2 total, while equivalent fraction 2/4 has 2 parts shaded out of 4 total—same amount, different partition, demonstrating equivalent fractions. Choice A is correct because multiplying numerator by 2: 1×2=2, and denominator by 2: 2×2=4, giving 2/4; the visual models show the same amount shaded—1/2 and 2/4 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 adding instead of multiplying, which happens when students think adding creates equivalence. 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=2 AND 2×2=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: 1/2=2/4=3/6=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.
5
3
105
102
104
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 2/5, multiplying numerator and denominator by 2 gives (2×2)/(5×2)=4/10; the visual model shows 2/5 has 2 parts shaded out of 5 total, while equivalent fraction 4/10 has 4 parts shaded out of 10 total—same amount, different partition, demonstrating equivalent fractions. Choice A is correct because multiplying numerator by 2: 2×2=4, and denominator by 2: 5×2=10, giving 4/10; the visual models show the same amount shaded—2/5 and 4/10 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 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=2 AND 2×2=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: 1/2=2/4=3/6=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.
?
3
5
6
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.
5
6
1210
125
1110
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).
8
5
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 2/5, to get denominator 10, multiply by 2 since 5×2=10, so numerator 2×2=4, giving 4/10; the visual model shows 2/5 has 2 parts shaded out of 5 total, while equivalent fraction 4/10 has 4 parts shaded out of 10 total—same amount, different partition. Choice B is correct because the missing numerator is 4, as 2×2=4 and 5×2=10, giving 4/10; the visual models show the same amount shaded—2/5 and 4/10 cover the same portion of the whole. Choice A represents no multiplication, which happens when students make calculation errors. To help students: Use visual models—show 2/5 and 4/10 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 (here by 2).
64
34
52
62
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).
3
2
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 1/4, to get denominator 12, multiply by 3 since 4×3=12, so numerator 1×3=3, giving 3/12; the visual model shows 1/4 has 1 part shaded out of 4 total, while equivalent fraction 3/12 has 3 parts shaded out of 12 total—same amount, different partition. Choice B is correct because the missing numerator is 3, as 1×3=3 and 4×3=12, giving 3/12; the visual models show the same amount shaded—1/4 and 3/12 cover the same portion of the whole. Choice A represents multiplying denominator only, which happens when students don't multiply both parts. To help students: Use visual models—show 1/4 and 3/12 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 (here by 3).
4
3×41×3=124
3×31×4=12
3+41+4=12
3×41×4=12
Explanation: This question tests 4th grade understanding of why a fraction ba is equivalent to n×bn×a 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 31, multiplying numerator and denominator by 4 gives 3×41×4=124; the visual model shows 31 has 1 part shaded out of 3 total, while equivalent fraction 124 has 4 parts shaded out of 12 total—same amount, different partition. Choice A is correct because it shows multiplying numerator by 4: 1×4=4, and denominator by 4: 3×4=12, giving 124; this shows understanding that multiplying top and bottom by the same number preserves the fraction's value. Choice B represents adding instead of multiplying, which happens when students think adding creates equivalence. To help students: Use visual models—show 31 and 124 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 4, do 1×4=4 AND 3×4=12, giving 124).