Generate Equivalent Fractions Using Multiplication - 4th Grade Math

Multiply the numerator and denominator of $\frac{3}{4}$ by $2$ . What is the equivalent fraction?
Answer: $\frac{6}{8}$ Choice B is correct because multiplying both the numerator and denominator of 3/4 by 2 gives 6/8. Choice A is incorrect because it only multiplies the numerator, leaving the denominator unchanged. Choice C is incorrect because it only multiplies the denominator, leaving the numerator unchanged. Choice D is incorrect because it does not result from multiplying both parts of the fraction by 2.
Which equation shows why $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ ?
Answer: $\frac{1\times 4}{3\times 4}=\frac{4}{12}$ 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.
Find a fraction equivalent to $\frac{2}{7}$ by multiplying the numerator and denominator by $3$ .
Answer: $\frac{6}{21}$ Choice D is correct because multiplying both the numerator and denominator of 2/7 by 3 gives 6/21. Choice A is incorrect because it only multiplies the numerator, leaving the denominator unchanged. Choice B is incorrect because it does not result from multiplying both parts of the fraction by 3. Choice C is incorrect because it does not match the multiplication described in the problem.
A number line from 0 to 1 is divided into 4 equal parts, marking $\frac{2}{4}$ . Another number line from 0 to 1 is divided into 8 equal parts, marking $\frac{4}{8}$ . Are these fractions equivalent?
Answer: Yes, because both points are halfway between 0 and 1. $\frac{2}{4}$ and $\frac{4}{8}$ are equivalent because both points fall exactly halfway between 0 and 1 -- multiplying the numerator and denominator of $\frac{2}{4}$ by 2 gives $\frac{4}{8}$ . Choice A describes adding rather than multiplying, which does not preserve a fraction's value. Choices C and D incorrectly assume that a bigger denominator or more parts means the fractions cannot be equal.
Which fraction is equivalent to $\frac{1}{2}$ ?
Answer: $\frac{2}{4}$ 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.
Look at the visual fraction model. If the same rectangle is divided into 4 times as many equal parts, what fraction would represent the same shaded amount?
Answer: $\frac{12}{20}$ The original fraction is $\frac{3}{5}$ . When divided into 4 times as many parts, multiply both numerator and denominator by 4: $\frac{3 \times 4}{5 \times 4} = \frac{12}{20}$ . Choice B only multiplies the denominator. Choice C only multiplies the numerator. Choice D uses an incorrect multiplication factor.
$\frac{3}{5} = \frac{?}{10}$ . What number goes in the blank?
Answer: 6 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.
Refer to the number line. Point A represents $\frac{3}{4}$ . If the number line were divided into segments that are half the size, what equivalent fraction would represent the same point A?
Answer: $\frac{6}{8}$ When segments become half the size, there are twice as many segments. This means multiplying both numerator and denominator by 2: $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$ . Choice B only multiplies the denominator. Choice C only multiplies the numerator. Choice D multiplies the numerator by 4.
$\frac{1}{3} = \frac{?}{6}$ . What number goes in the blank?
Answer: 2 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.
Which fraction is equivalent to $\frac{2}{5}$ ?
Answer: $\frac{4}{10}$ 4/10 is equivalent to 2/5 because multiplying both the numerator and denominator by 2 gives 4/10. Choice B doubles only the denominator, not the numerator, so the value changes. Choice C keeps the numerator but changes the denominator, breaking the equivalence. Choice A is not related to 2/5 by any equal scaling.
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?
Answer: $\frac{35}{50}$ 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.
$\frac{2}{5}=?/10$ . What number goes in the blank?
Answer: 4 The correct answer is 4, because 2/5 is equivalent to 4/10 when both the numerator and denominator are multiplied by 2. Choice A, 5, mistakes the missing numerator for the denominator value. Choice B, 2, just repeats the original numerator without scaling it up. Choice C, 8, comes from multiplying the numerator by 4 instead of by 2.
Lisa has $\frac{4}{9}$ 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?
Answer: 27 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 $\frac{4}{9}$ , you need to find what number to multiply 4 by to get 12. Since $4 \times 3 = 12$ , you multiply the numerator by 3. To keep the fraction equivalent, you must multiply the denominator by the same number: $9 \times 3 = 27$ . This gives you $\frac{12}{27}$ , which equals the original $\frac{4}{9}$ . Let's check why the other answers don't work. Choice A (21) would give you $\frac{12}{21}$ . If you simplify this by dividing both parts by 3, you get $\frac{4}{7}$ , which is not equal to $\frac{4}{9}$ . Choice C (36) creates $\frac{12}{36}$ , which simplifies to $\frac{1}{3}$ when you divide by 12. This also doesn't equal $\frac{4}{9}$ . Choice D (15) gives you $\frac{12}{15}$ , which simplifies to $\frac{4}{5}$ 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.
Which equation shows why $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ ?
Answer: $\frac{1\times 4}{3\times 4}=\frac{4}{12}$ Multiplying both the numerator and denominator of 1/3 by 4 gives 4/12, since 1 times 4 is 4 and 3 times 4 is 12, making Choice D correct. Choice A multiplies the numerator by 3 instead of 4, so the two multipliers do not match. Choice B multiplies the denominator by 3 instead of 4, so it also uses mismatched multipliers. Choice C adds instead of multiplies, which does not produce an equivalent fraction.
Which equation shows how to make an equivalent fraction to $\frac{1}{2}$ by multiplying by $\frac{3}{3}$ ?
Answer: $\frac{1\times 3}{2\times 3}=\frac{3}{6}$ 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.
Find a fraction equivalent to $\frac{3}{4}$ by multiplying the numerator and denominator by 2.
Answer: $\frac{6}{8}$ The correct answer is 6/8, because multiplying both the numerator and denominator of 3/4 by 2 gives 6/8. Choice A, 5/6, does not come from multiplying 3/4 by 2 in any consistent way and reflects an arithmetic error. Choice B, 3/8, only doubles the denominator and leaves the numerator unchanged. Choice D, 6/4, only doubles the numerator and leaves the denominator unchanged.
Which fraction is equivalent to $\frac{5}{6}$ ?
Answer: $\frac{10}{12}$ 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).
Which fraction is equivalent to $\frac{2}{3}$ ?
Answer: $\frac{4}{6}$ 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.
Multiply the numerator and denominator of $\frac{1}{4}$ by 3. What is the equivalent fraction?
Answer: $\frac{3}{12}$ Multiplying both the numerator and denominator of 1/4 by 3 gives 3/12, so Choice B is correct. Choice A, 4/7, does not come from multiplying either number in 1/4 by 3, so it does not fit the pattern at all. Choice C, 1/12, comes from multiplying only the denominator by 3 while leaving the numerator unchanged. Choice D, 3/4, comes from multiplying only the numerator by 3 while leaving the denominator unchanged. Only multiplying both numbers by the same amount keeps the fraction equal.
A number line from 0 to 1 is shown. One line is divided into 4 equal parts and marks $\frac{2}{4}$ . Another is divided into 8 equal parts and marks $\frac{4}{8}$ . Are these fractions equivalent?
Answer: Yes, because both points are halfway between 0 and 1. The correct answer is C because both $\frac{2}{4}$ and $\frac{4}{8}$ land on the same point, halfway between 0 and 1, so they are equivalent. Choice A wrongly assumes fewer parts means a smaller value. Choice B wrongly assumes a bigger denominator alone means a bigger or different value. Choice D describes a coincidental pattern rather than the real reason the fractions are equal.

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