Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 3 · Worksheet 1

1. Matiu is helping his nanny prepare a keke (cake) for a family gathering. He cuts the rectangular cake into 12 equal pieces. He puts icing on 9 of the pieces. His nanny says that the same amount of cake can be shown as 3/4. Is Matiu's nanny correct? Explain using equivalent fractions. Answer: Yes, because 9/12 = 3/4 Solution: The cake is cut into 12 equal pieces. Matiu puts icing on 9 pieces, so the fraction iced is 9/12. To check if 9/12 equals 3/4, imagine dividing the same cake into 4 equal parts instead of 12.
   Full step-by-step solution

   Step 1: The cake is cut into 12 equal pieces. Matiu puts icing on 9 pieces, so the fraction iced is 9/12. Step 2: To check if 9/12 equals 3/4, imagine dividing the same cake into 4 equal parts instead of 12. Each quarter would contain 3 pieces (because 12 divided by 4 is 3). Step 3: Matiu iced 9 pieces. Since each quarter has 3 pieces, 9 pieces make 3 full quarters (because 9 divided by 3 is 3). Step 4: So 3/4 of the cake is the same as 9/12. Therefore, 9/12 = 3/4. Matiu's nanny is correct. The answer is: Yes, because 9/12 = 3/4.

2. Ava is making a fruit salad for her family. She cuts a rectangular watermelon into 6 equal slices. She uses 2 of the slices for the salad. Her brother Noah says she used 1/3 of the watermelon. Ava thinks she used 2/6 of the watermelon. Who is correct? Explain by finding an equivalent fraction. Answer: Both are correct because 2/6 = 1/3 Solution: The watermelon is cut into 6 equal slices. Ava uses 2 slices, so the fraction used is 2/6. To check if 2/6 equals 1/3, think about dividing the same watermelon into 3 equal parts instead of 6.
   Full step-by-step solution

   Step 1: The watermelon is cut into 6 equal slices. Ava uses 2 slices, so the fraction used is 2/6. Step 2: To check if 2/6 equals 1/3, think about dividing the same watermelon into 3 equal parts instead of 6. Each third would contain 2 of the 6 slices (because 6 divided by 3 is 2). Step 3: So 1/3 of the watermelon is the same as 2 slices out of 6, or 2/6. Step 4: Therefore, 2/6 = 1/3. Both Ava and Noah are correct. The answer is: Both are correct because 2/6 = 1/3.

3. Emma is baking cookies and needs to divide the dough into equal parts. She cuts the dough into 8 equal pieces and uses 4 pieces for chocolate chip cookies. What fraction of the whole dough did Emma use for chocolate chip cookies? Write your answer in simplest form. Answer: 1/2 Solution: Emma cuts the dough into 8 equal pieces. So each piece is 1/8 of the whole dough. Determine how many pieces she uses for chocolate chip cookies.
   Full step-by-step solution

   Step 1: Understand the problem. Emma cuts the dough into 8 equal pieces. So each piece is 1/8 of the whole dough. Step 2: Determine how many pieces she uses for chocolate chip cookies. She uses 4 pieces. Step 3: Find the fraction of the whole dough used. If 1 piece = 1/8 of the dough, then 4 pieces = 4 × (1/8) = 4/8 of the dough. Step 4: Simplify the fraction. 4/8 can be simplified by dividing the numerator and denominator by 4: 4 ÷ 4 = 1 8 ÷ 4 = 2 So 4/8 = 1/2. Step 5: Conclusion. Emma used 1/2 of the whole dough for chocolate chip cookies.

4. A baker has a tray of cookies divided into 8 equal sections. 6 sections have chocolate chip cookies. What fraction of the tray has chocolate chip cookies? Write your answer in simplest form. Answer: 3/4 Solution: The tray is divided into 8 equal sections. 6 of those sections have chocolate chip cookies. Write the fraction of the tray that has chocolate chip cookies.
   Full step-by-step solution

   Step 1: Understand the problem. The tray is divided into 8 equal sections. 6 of those sections have chocolate chip cookies. Step 2: Write the fraction of the tray that has chocolate chip cookies. The fraction is: number of chocolate chip sections / total sections = 6/8. Step 3: Simplify the fraction. Both 6 and 8 can be divided by 2. 6 ÷ 2 = 3 8 ÷ 2 = 4 So, 6/8 simplifies to 3/4. Step 4: Final answer. The fraction of the tray with chocolate chip cookies is 3/4.

5. A school is organizing a field day and needs to divide 120 students into equal teams. The teachers decide to make 8 teams. What fraction of the total students will be on each team? Write your answer in simplest form. Answer: 1/8 Solution: When a whole group is divided into equal parts, the fraction representing one part is 1 divided by the total number of parts. This concept helps us understand fair sharing and division.
6. A rectangular garden is divided into 8 equal sections. If 4 sections are planted with carrots, what fraction of the garden has carrots? Write your answer in simplest form. Answer: 1/2 Solution: The garden is divided into 8 equal sections. 4 of those sections are planted with carrots. Write the fraction of the garden with carrots.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. 4 of those sections are planted with carrots. Step 2: Write the fraction of the garden with carrots. The fraction is the number of sections with carrots over the total number of sections: 4/8 Step 3: Simplify the fraction. Both 4 and 8 can be divided by 4. 4 ÷ 4 = 1 8 ÷ 4 = 2 So, 4/8 = 1/2 Step 4: Conclusion. The fraction of the garden with carrots is 1/2.

7. Liam is baking cookies for his class party. He has a large rectangular pan that he cuts into 12 equal pieces. He puts chocolate chips on 8 of the pieces. What fraction of the whole pan of cookies has chocolate chips? Write your answer in simplest form. Answer: 2/3 Solution: The pan is cut into 12 equal pieces, so the whole pan is represented by 12 pieces. Out of these 12 pieces, 8 have chocolate chips. Write the fraction of pieces with chocolate chips.
   Full step-by-step solution

   Step 1: Understand the problem. The pan is cut into 12 equal pieces, so the whole pan is represented by 12 pieces. Out of these 12 pieces, 8 have chocolate chips. Step 2: Write the fraction of pieces with chocolate chips. The fraction is: number of chocolate chip pieces / total pieces = 8/12. Step 3: Simplify the fraction. Both 8 and 12 can be divided by their greatest common factor, which is 4. Divide the numerator and denominator by 4: 8 ÷ 4 = 2 12 ÷ 4 = 3 Step 4: Write the simplified fraction. The simplified fraction is 2/3. Step 5: Interpret the result. This means 2/3 of the whole pan has chocolate chips. Final answer: 2/3

8. Liam is baking cookies for his class party. He has a recipe that uses 3/4 cup of chocolate chips. If he wants to double the recipe, how many cups of chocolate chips will he need? Write your answer as a fraction. Answer: 1 1/2 Solution: The recipe uses 3/4 cup of chocolate chips. Doubling the recipe means multiplying the amount by 2.
   Full step-by-step solution

   Step 1: Understand the problem The recipe uses 3/4 cup of chocolate chips. Doubling the recipe means multiplying the amount by 2. Step 2: Write the multiplication We need to calculate: 2 × (3/4) Step 3: Multiply the whole number by the fraction 2 × (3/4) = (2 × 3) / 4 = 6/4 Step 4: Simplify the fraction 6/4 can be simplified by dividing the numerator and denominator by 2: 6 ÷ 2 = 3 4 ÷ 2 = 2 So 6/4 = 3/2 Step 5: Convert to a mixed number 3/2 means 3 divided by 2. 2 goes into 3 one whole time (1 × 2 = 2), with remainder 1. So 3/2 = 1 and 1/2. Step 6: Final answer Liam will need 1 1/2 cups of chocolate chips.