Generate and Explain Equivalent Fractions - 3rd Grade Math

Look at the fraction models below. Which statement correctly explains why $\frac{3}{4}$ and $\frac{6}{8}$ are equivalent fractions?
Answer: They are equivalent because both fractions show exactly the same amount of area shaded Equivalent fractions represent the same amount or portion of a whole. When we look at visual models, 3/4 and 6/8 show the same shaded area, proving they are equivalent. We can verify this by multiplying 3/4 by 2/2 to get 6/8. Choice A incorrectly suggests addition creates equivalent fractions. Choice C focuses on differences rather than ratios. Choice D mentions irrelevant properties of the denominators.
Two students each shaded part of a same-sized rectangle. Marco shaded $\frac{3}{6}$ and Kim shaded $\frac{1}{2}$ . Which statement is true?
Answer: They shaded the same amount because $\frac{3}{6}$ and $\frac{1}{2}$ are equivalent. When you compare fractions, you can't just look at the numbers on top or bottom by themselves — you have to think about how much of the whole each fraction actually represents. Two fractions that look different can still name the same amount; these are called equivalent fractions. Picture the same-sized rectangle split two ways. Kim's rectangle is cut into 2 equal pieces, and she shades 1 of them — that's half the rectangle. Marco's rectangle is cut into 6 equal pieces, and he shades 3 of them. Since 3 out of 6 is also half the rectangle, both boys shaded exactly the same amount. You can also check this by simplifying: $\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$ . That confirms C is correct. A is a classic trap — comparing only the numerators (3 vs. 1) ignores that Marco's pieces are much smaller than Kim's, so more pieces doesn't mean more shaded area. B makes the opposite mistake, assuming bigger pieces automatically mean more shaded; Kim has bigger pieces but only shades one, so the totals still match. D is wrong because you can compare fractions with different-sized pieces — that's exactly what equivalent fractions let you do. Study tip: When comparing fractions, try to simplify them or draw them out on same-sized shapes. If you can reduce one fraction to match the other (like $\frac{3}{6} \to \frac{1}{2}$ ), they're equivalent — no matter how different the numbers look.
Maria cut a pizza into 6 equal pieces and ate 2 pieces. Jake cut an identical pizza into 12 equal pieces. How many pieces must Jake eat to have the same amount of pizza as Maria?
Answer: 4 pieces, because $\frac{2}{6} = \frac{4}{12}$ To find equivalent fractions, we need to determine what fraction is equal to 2/6. Since Jake's pizza is cut into 12 pieces (double Maria's 6 pieces), we multiply both numerator and denominator by 2: 2/6 = (2×2)/(6×2) = 4/12. Therefore Jake must eat 4 pieces. Choice A incorrectly adds 1 to the numerator. Choice C confuses the total pieces with pieces eaten. Choice D ignores the different denominators.
The number line shows a point at $\frac{2}{4}$ . Which fraction names the same point?
Answer: $\frac{1}{2}$ $\frac{2}{4}$ is located halfway between 0 and 1, which is also the location of $\frac{1}{2}$ . B equals 1, C is only one-quarter of the way, and D equals 2.
Ms. Chen's class is making equivalent fractions. If $\frac{6}{9} = \frac{2}{3}$ , which operation was used to create this equivalent fraction?
Answer: Divided by 3 To go from 6/9 to 2/3, both the numerator and denominator were divided by 3 (6 divided by 3 is 2, and 9 divided by 3 is 3), making Choice A correct. Choice B describes multiplying, which would make the fraction larger, not simpler. Choice C only changes the numerator, which would not produce an equivalent fraction. Choice D divides by the wrong number, since dividing 6/9 by 2 would not give whole numbers.
Ana has a ribbon that is $\frac{2}{3}$ meter long. She wants to mark it into sixths. How many sixths of a meter are equal to $\frac{2}{3}$ meter?
Answer: $\frac{4}{6}$ When a question asks you to rewrite a fraction using a different denominator, you're really being asked to find an equivalent fraction. The value of the ribbon doesn't change — only the size of the pieces you're counting it in does. Think of it like exchanging coins: two quarters and fifty pennies are the same amount of money, just counted differently. To change $\frac{2}{3}$ into sixths, ask yourself: "What do I multiply 3 by to get 6?" The answer is 2. Whatever you do to the bottom, you must do to the top, so multiply the numerator by 2 as well: $\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$ . That makes C correct. You can also picture the ribbon: if you cut $\frac{2}{3}$ of a meter into smaller equal pieces, each third splits into 2 sixths, giving you 4 sixths total. Choice A ( $\frac{2}{6}$ ) is the trap of just changing the denominator and leaving the numerator alone — but that shrinks the ribbon in half. Choice B ( $\frac{3}{6}$ ) equals $\frac{1}{2}$ , which is smaller than $\frac{2}{3}$ . Choice D ( $\frac{5}{6}$ ) is larger than $\frac{2}{3}$ , so the ribbon would have grown, which doesn't match the problem. Study tip: To build equivalent fractions, always multiply (or divide) the top and bottom by the same number. A quick check: if your new fraction looks bigger or smaller than the original when you picture it, you probably forgot to change one of the two numbers.
Refer to the two circles. Devon says the shaded parts show that $\frac{1}{2} = \frac{2}{4}$ . Which statement best supports his claim?
Answer: The circles are the same size and the shaded regions cover the same amount. Two fractions are equivalent when they represent the same amount of the same-sized whole. B is the key reasoning. A is false (2 pieces vs. 4). C is not mathematical reasoning. D is a misconception — more pieces do not mean more area shaded.
David drew fraction strips to show that $\frac{4}{12}$ and $\frac{1}{3}$ are equivalent. Based on the fraction strips shown, why are these fractions equivalent?
Answer: They are equivalent because both strips show exactly the same length of shaded area Fraction strips demonstrate equivalence by showing equal lengths of shaded portions. Even though 4/12 has 12 small sections with 4 shaded, and 1/3 has 3 large sections with 1 shaded, the total shaded lengths are identical. This visual proof shows the fractions represent the same amount. Choice A uses irrelevant addition. Choice C reflects a common error: multiplying 1/3 by 4 gives 4/3, not 4/12. Equivalent fractions are found by multiplying the numerator and denominator by the same factor (here, 4/4). Choice D makes an incorrect observation about the number 4.
Lisa wants to prove that $\frac{5}{10}$ and $\frac{1}{2}$ are equivalent fractions. She needs to show her work step by step. Which sequence of steps correctly proves these fractions are equivalent?
Answer: Step 1: $\frac{5}{10}$ , Step 2: Divide both by 5, Step 3: $\frac{1}{2}$ , Step 4: Equivalent fractions When you need to prove that two fractions are equivalent, you're looking for ways to show they represent the same amount. The key is finding a common factor that you can use to simplify one fraction into the other. To prove $\frac{5}{10}$ and $\frac{1}{2}$ are equivalent, you need to simplify $\frac{5}{10}$ by finding the greatest common factor of 5 and 10. Since both 5 and 10 can be divided by 5, you divide both the numerator and denominator by 5: $\frac{5÷5}{10÷5} = \frac{1}{2}$ . This shows the fractions are equivalent because they simplify to the same result. Choice A only divides the top number by 5, leaving $\frac{1}{10}$ , which breaks the fraction rule - you must do the same operation to both parts. This gives an incorrect result. Choice B multiplies both parts by 2 to get $\frac{10}{20}$ . While $\frac{10}{20}$ is equivalent to both original fractions, this approach makes the fraction more complex instead of proving equivalence through simplification. Choice C adds 5 to both parts, creating $\frac{10}{15}$ . Adding the same number to numerator and denominator doesn't create equivalent fractions - this is a common misconception. $\frac{10}{15}$ actually equals $\frac{2}{3}$ , not $\frac{1}{2}$ . Choice D correctly divides both the numerator and denominator by their greatest common factor of 5, simplifying $\frac{5}{10}$ to $\frac{1}{2}$ and proving equivalence. Remember: To prove fraction equivalence, multiply or divide both parts by the same number - never add or subtract, and never change just one part.
Emma says $\frac{2}{8}$ and $\frac{1}{4}$ are equivalent fractions. Which explanation best describes why Emma is correct?
Answer: Dividing both the numerator and denominator of $\frac{2}{8}$ by $2$ gives $\frac{1}{4}$ , so the fractions are equal Dividing both the numerator and denominator of 2/8 by 2 gives 1/4, so the two fractions represent the same amount, making B correct. Choice A is incorrect because having small numerators does not by itself make two fractions equal. Choice C is incorrect because having even numbers does not make fractions equivalent. Choice D is incorrect because multiplying 2/8 by 4 does not result in 1/4.
A pan of cornbread is cut into 8 equal pieces. Ben eats 2 pieces. Which fraction is equivalent to the part he ate?
Answer: $\frac{1}{4}$ When you see a fraction question about equal parts of a whole, remember that equivalent fractions name the same amount using different numbers. You can find them by multiplying or dividing both the top (numerator) and bottom (denominator) by the same number. Ben ate 2 out of 8 pieces, which is $\frac{2}{8}$ . To simplify, divide both the numerator and denominator by 2: $\frac{2 \div 2}{8 \div 2} = \frac{1}{4}$ So $\frac{2}{8}$ and $\frac{1}{4}$ represent the same amount of cornbread, making A correct. Now let's look at why the others don't work. **B ( $\frac{1}{2}$ ) would mean Ben ate 4 out of 8 pieces — that's half the pan, way more than he actually ate. C ( $\frac{2}{4}$ )** also equals $\frac{1}{2}$ (divide top and bottom by 2), so it's the same as B — too much. **D ( $\frac{1}{6}$ )** uses a denominator of 6, but the pan wasn't cut into 6 pieces, and $\frac{1}{6}$ isn't equal to $\frac{2}{8}$ anyway. A helpful strategy: when checking if two fractions are equivalent, try to simplify the bigger one or multiply the smaller one up. If $\frac{1}{4}$ is equivalent to $\frac{2}{8}$ , multiplying both parts of $\frac{1}{4}$ by 2 should give you $\frac{2}{8}$ — and it does! This "multiply to check" trick works every time.
Which pair of fractions is NOT equivalent?
Answer: $\frac{2}{3}$ and $\frac{3}{4}$ Equivalent fractions represent the same amount, even though they use different numbers. The quickest way to check if two fractions are equivalent is to see whether you can multiply (or divide) the numerator and denominator of one fraction by the same number to get the other. Another reliable test: cross-multiply. If the products match, the fractions are equivalent. Look at D: $\frac{2}{3}$ and $\frac{3}{4}$ . Cross-multiplying gives $2 \times 4 = 8$ and $3 \times 3 = 9$ . Since $8 \neq 9$ , these fractions are not equal. You can also see there's no single whole number you can multiply 2 and 3 by to get 3 and 4, so they can't be equivalent. Choice A works because multiplying $\frac{1}{2}$ by $\frac{3}{3}$ gives $\frac{3}{6}$ — same value, just cut into more pieces. Choice B works because $\frac{2}{4}$ times $\frac{2}{2}$ equals $\frac{4}{8}$ (both also simplify to $\frac{1}{2}$ ). Choice C works because $\frac{1}{3}$ times $\frac{2}{2}$ equals $\frac{2}{6}$ . So D is the pair that is NOT equivalent. A helpful strategy: when a question asks which pair is NOT equivalent, quickly simplify each fraction to its lowest terms. If both fractions in a pair simplify to the same thing, they're equivalent. Also, watch out for questions with the word "NOT" — it's easy to pick an equivalent pair by mistake, so underline "NOT" before you begin.
Tommy says that $\frac{2}{3} = \frac{4}{6}$ because when you multiply the top and bottom of $\frac{2}{3}$ by 2, you get $\frac{4}{6}$ . Using Tommy's method of multiplying both the top and bottom by the same number, which fraction is equivalent to $\frac{1}{4}$ ?
Answer: $\frac{4}{16}$ , because we multiply the top and bottom by 4 Tommy's method means multiplying both the top and bottom of a fraction by the same number to get an equivalent fraction. Multiplying the top and bottom of 1/4 by 4 gives 4/16, matching choice C. Choice A only multiplies the bottom number, which is not the method Tommy used and does not give an equivalent fraction. Choices B and D use addition instead of multiplication, which also does not follow Tommy's method.
Which fraction is equivalent to $\frac{2}{4}$ ?
Answer: $\frac{1}{2}$ Dividing both the numerator and denominator of 2/4 by 2 gives 1/2, so choice D is correct. Choice A comes from doubling the denominator instead of finding an equivalent fraction. Choice B mixes up the numerator and denominator. Choice C uses only part of the original fraction.
A brownie pan began with 4 equal-sized brownies. Emma ate $\tfrac{2}{4}$ . What is another name for the fraction that Emma ate?
Answer: $1/2$ $1/2$ is correct because $2/4$ simplifies to $1/2$ . $3/4$ is incorrect; it's a different fraction than $2/4$ . $2/8$ is incorrect because it's not equivalent to $2/4$ , since it represents a smaller amount. $2/3$ is incorrect; it doesn't equal $2/4$ in value.
Which fraction is equivalent to $\frac{4}{6}$ ?
Answer: $\frac{2}{3}$ Equivalent fractions represent the same amount, just written with different numbers. To find one, you either multiply or divide the top (numerator) and bottom (denominator) by the same number. Think of it as simplifying: if both numbers share a common factor, you can shrink the fraction to a simpler form that still equals the same value. Look at $\frac{4}{6}$ . Both 4 and 6 can be divided by 2. So $\frac{4 \div 2}{6 \div 2} = \frac{2}{3}$ . That makes B the equivalent fraction. Now consider the wrong choices. A) $\frac{2}{4}$ simplifies to $\frac{1}{2}$ , which is smaller than $\frac{4}{6}$ — imagine half a pizza versus four out of six slices; the six-slice version is more. C) $\frac{3}{4}$ is larger than $\frac{4}{6}$ (which equals about $\frac{2}{3}$ ), so it can't be equivalent. D) $\frac{4}{8}$ also simplifies to $\frac{1}{2}$ , the same trap as A — the numerator matches 4, which might tempt you, but the value is smaller. A helpful tip: whenever you're asked for an equivalent fraction, try simplifying the given fraction first by dividing the top and bottom by the same number. Then match your simplified version to the answer choices. And remember — just because two fractions share a number (like the 4 in $\frac{4}{6}$ and $\frac{4}{8}$ ) doesn't mean they're equal!
Use the number lines to answer the question. Which fraction on the second number line is equivalent to $\frac{2}{3}$ ?
Answer: $\frac{4}{6}$ The point at $\frac{2}{3}$ on the top number line lines up with $\frac{4}{6}$ on the sixths number line because each third equals 2 sixths. A copies the numerator, B is at $\frac{1}{2}$ , D is beyond $\frac{2}{3}$ .
Lily wrote: $\frac{1}{3} = \frac{?}{6}$ . What number makes the fractions equivalent?
Answer: 2 Equivalent fractions represent the same amount, just written with different numbers. To find them, you multiply (or divide) both the top number (numerator) and the bottom number (denominator) by the same value. Whatever you do to one part, you must do to the other — that's the golden rule of equivalent fractions. Look at the denominators: $3$ became $6$ . Ask yourself, "What did I multiply 3 by to get 6?" The answer is 2, because $3 \times 2 = 6$ . Now apply that same operation to the numerator: $1 \times 2 = 2$ . So $\frac{1}{3} = \frac{2}{6}$ , making B correct. Choice A (1) is wrong because it keeps the numerator the same while the denominator doubled — that would change the value of the fraction, not preserve it. Choice C (3) is a trap that comes from adding 2 to the top (since 2 was added to the bottom: $3+2=5$ ... wait, actually students often just copy the original denominator). Either way, $\frac{3}{6}$ equals $\frac{1}{2}$ , not $\frac{1}{3}$ . Choice D (6) matches the new denominator, giving $\frac{6}{6} = 1$ whole, which is much bigger than $\frac{1}{3}$ . A helpful trick: whenever you see an equivalent fraction problem, find the "multiplier" between the two parts you can see (here, the denominators), then use that same multiplier on the missing part. Never add or subtract to make equivalent fractions — always multiply or divide.
Maya says that $\frac{2}{3}$ is equivalent to $\frac{4}{6}$ . Which explanation best shows why she is correct?
Answer: When each third is split into 2 equal parts, you get 6 parts and 4 are shaded. Equivalent fractions represent the same amount of a whole, even though they use different numbers. The best way to prove two fractions are equivalent is to show how one can be created from the other by splitting the same whole into more (or fewer) equal pieces. Start with $\frac{2}{3}$ : imagine a bar cut into 3 equal parts with 2 shaded. Now split each of those thirds into 2 equal pieces. The bar now has $3 \times 2 = 6$ equal parts, and the shaded region now contains $2 \times 2 = 4$ of those parts. The shaded amount didn't change — you just cut the pieces smaller. That's exactly what choice B describes, and it's the true reason $\frac{2}{3} = \frac{4}{6}$ . Choice A is wrong because sharing a digit like "2" tells you nothing about a fraction's value — $\frac{2}{9}$ and $\frac{2}{5}$ both contain a 2 but aren't equal. Choice C uses a "difference" trick (3−2 = 1 and 6−4 = 2, so this isn't even true here), but subtracting the numerator from the denominator never determines equivalence. Choice D adds the same numbers to top and bottom, which changes a fraction's value; for example, $\frac{1}{2}$ is not equal to $\frac{2}{3}$ even though you added 1 to each. Tip: To check equivalent fractions, ask "Was the whole cut into more equal pieces?" Multiplying (or dividing) the top and bottom by the same number works — adding does not.
Which fraction is equivalent to $\frac{6}{8}$ ?
Answer: $\frac{3}{4}$ Equivalent fractions represent the same amount, just written with different numbers. To find one, you divide (or multiply) both the numerator and denominator by the same number. Think of it as shrinking or growing the fraction proportionally. Starting with $\frac{6}{8}$ , look for a number that divides evenly into both 6 and 8. Both are divisible by 2: $\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$ That matches choice D. You can also picture it: if you shade 6 out of 8 equal parts of a rectangle, the same shaded area covers 3 out of 4 larger parts. Choice A, $\frac{2}{4}$ , simplifies to $\frac{1}{2}$ , which is smaller than $\frac{6}{8}$ ( $\frac{6}{8}$ is more than half since 6 is more than half of 8). Choice B, $\frac{6}{4}$ , is greater than 1, but $\frac{6}{8}$ is less than 1, so they can't be equal. Choice C, $\frac{4}{6}$ , flips the idea — you can't just swap or subtract from the top and bottom. Dividing 4 and 6 by 2 gives $\frac{2}{3}$ , not $\frac{3}{4}$ . A helpful tip: to check if two fractions are equivalent, try cross-multiplying. For $\frac{6}{8}$ and $\frac{3}{4}$ : $6 \times 4 = 24$ and $8 \times 3 = 24$ . Equal products mean equivalent fractions — a quick trick that works every time.

Start this quiz