Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 3 · Worksheet 2

1. 2/3 = ?/6 Answer: 4 Solution: Look at the denominators. The first fraction has a denominator of 3, and the second fraction has a denominator of 6. To go from 3 to 6, you multiply by 2 (because 3 × 2 = 6).
   Full step-by-step solution

   Step 1: Look at the denominators. The first fraction has a denominator of 3, and the second fraction has a denominator of 6. Step 2: To go from 3 to 6, you multiply by 2 (because 3 × 2 = 6). Step 3: To find the equivalent fraction, you must do the same to the numerator. The first numerator is 2. Step 4: Multiply the numerator by 2: 2 × 2 = 4. Step 5: The equivalent fraction is 4/6. The answer is 4.

2. A rectangular garden is divided into 16 equal square plots. The gardener plants tomatoes in 12 of these plots. What fraction of the garden has tomatoes? Write your answer in simplest form. Answer: 3/4 Solution: The garden is divided into 16 equal plots, so the total number of parts is 16. Tomatoes are planted in 12 plots, so the fraction is 12/16. To simplify 12/16, find the greatest common factor of 12 and 16, which is 4.
   Full step-by-step solution

   Step 1: The garden is divided into 16 equal plots, so the total number of parts is 16. Step 2: Tomatoes are planted in 12 plots, so the fraction is 12/16. Step 3: To simplify 12/16, find the greatest common factor of 12 and 16, which is 4. Step 4: Divide both numerator and denominator by 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4. Step 5: The simplified fraction is 3/4. The answer is 3/4.

3. Maria is painting a mural on a wall that is divided into 12 equal sections. She has painted 8 sections so far. What fraction of the whole wall has Maria painted? Write your answer in simplest form. Answer: 2/3 Solution: The wall is divided into 12 equal sections. This means the whole wall is represented by 12/12. Maria has painted 8 of these 12 sections.
   Full step-by-step solution

   Step 1: The wall is divided into 12 equal sections. This means the whole wall is represented by 12/12. Step 2: Maria has painted 8 of these 12 sections. So, the fraction of the wall painted is 8/12. Step 3: To simplify 8/12, find the greatest common factor of 8 and 12. The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The greatest common factor is 4. Step 4: Divide both the numerator and the denominator by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3. Step 5: The simplified fraction is 2/3. The answer is 2/3.

4. Liam is baking cookies for his class party. He has a large rectangular pan that he cuts into 12 equal pieces. He decorates 8 of the pieces with red frosting. What fraction of the whole pan of cookies has red frosting? Write your answer in simplest form. Answer: 2/3 Solution: Liam cuts the rectangular pan into 12 equal pieces. This means the whole pan is represented as 12 pieces, so the whole pan is 12/12. Identify how many pieces have red frosting.
   Full step-by-step solution

   Step 1: Understand the problem. Liam cuts the rectangular pan into 12 equal pieces. This means the whole pan is represented as 12 pieces, so the whole pan is 12/12. Step 2: Identify how many pieces have red frosting. The problem says he decorates 8 of the pieces with red frosting. Step 3: Write the fraction of the pan with red frosting. The fraction is the number of red-frosted pieces over the total pieces: 8/12 Step 4: Simplify the fraction. Both 8 and 12 can be divided by their greatest common factor, which is 4. 8 ÷ 4 = 2 12 ÷ 4 = 3 So, 8/12 simplifies to 2/3. Step 5: Final answer. The fraction of the whole pan with red frosting is 2/3.

5. Lily baked a large rectangular cake for her class party. She cut the cake into 8 equal slices. At the party, 4 slices were eaten. What fraction of the whole cake was eaten? Write your answer in simplest form. Answer: 1/2 Solution: Lily cut the cake into 8 equal slices. Determine how many slices were eaten. At the party, 4 slices were eaten.
   Full step-by-step solution

   Step 1: Understand the cake cutting. Lily cut the cake into 8 equal slices. So, the whole cake is 8 slices. Step 2: Determine how many slices were eaten. At the party, 4 slices were eaten. Step 3: Write the fraction of the cake eaten. The fraction is: (number of slices eaten) / (total slices) = 4/8. Step 4: Simplify the fraction. Both 4 and 8 can be divided by 4. 4 ÷ 4 = 1 8 ÷ 4 = 2 So, 4/8 simplifies to 1/2. Step 5: Conclusion. The fraction of the whole cake that was eaten is 1/2.

6. A rectangular chocolate bar is divided into 12 equal squares. If you break off and eat 4 squares, what fraction of the whole chocolate bar did you eat? Write your answer in simplest form. Answer: 1/3 Solution: The chocolate bar is divided into 12 equal squares, so the whole bar is represented by 12/12. You ate 4 squares out of the 12 total squares, which is the fraction 4/12.
   Full step-by-step solution

   Step 1: The chocolate bar is divided into 12 equal squares, so the whole bar is represented by 12/12. Step 2: You ate 4 squares out of the 12 total squares, which is the fraction 4/12. Step 3: To simplify 4/12, find the greatest common factor of 4 and 12, which is 4. Step 4: Divide both the numerator and denominator by 4: 4 ÷ 4 = 1 and 12 ÷ 4 = 3. Step 5: The simplified fraction is 1/3. The answer is 1/3.

7. Liam is baking cookies for his class party. He has a recipe that makes 24 cookies, but he needs to make 72 cookies total. What fraction of the original recipe should Liam use to get the right amount of cookies? Answer: 3/1 Solution: Liam needs to figure out what fraction of the original recipe he should use. The original recipe makes 24 cookies. Liam needs 72 cookies.
   Full step-by-step solution

   Liam needs to figure out what fraction of the original recipe he should use. Step 1: Understand the problem. The original recipe makes 24 cookies. Liam needs 72 cookies. Step 2: Find the relationship between the number of cookies he needs and the number the recipe makes. We divide the number of cookies he needs by the number the recipe makes. So, we calculate 72 / 24. Step 3: Perform the division. 72 divided by 24 equals 3. We can write this as 72 / 24 = 3. Step 4: Interpret the result. The number 3 means Liam needs to make 3 times the original recipe. In fraction form, "3 times" is written as 3/1. Step 5: State the final answer. Therefore, the fraction of the original recipe Liam should use is 3/1.

8. A rectangular garden is divided into 16 equal square plots. The gardener plants tomatoes in 4 of the plots and carrots in 8 of the plots. What fraction of the garden is planted with carrots? Write your answer in simplest form. Answer: 1/2 Solution: The garden is divided into 16 equal plots, so the whole garden represents 16/16. The gardener plants carrots in 8 plots, so the fraction with carrots is 8/16.
   Full step-by-step solution

   Step 1: The garden is divided into 16 equal plots, so the whole garden represents 16/16. Step 2: The gardener plants carrots in 8 plots, so the fraction with carrots is 8/16. Step 3: Simplify 8/16 by dividing both numerator and denominator by 8. Step 4: 8 ÷ 8 = 1 and 16 ÷ 8 = 2, so 8/16 = 1/2. The answer is 1/2.

9. 2/4 = ?/2 Answer: 1 Solution: 2/4 = ?/2 Simplify the left side. 2/4 = 1/2 1/2 = ?/2 Compare both sides. Since the denominators are the same (both are 2), the numerators must be equal.
   Full step-by-step solution

   We start with the equation: 2/4 = ?/2 Step 1: Simplify the left side. 2/4 = 1/2 So the equation becomes: 1/2 = ?/2 Step 2: Compare both sides. Since the denominators are the same (both are 2), the numerators must be equal. Therefore: ? = 1 Final answer: 1