Area Models

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Answer Key & Explanations

Area Models · Grade 5 · Worksheet 1

1. Liam is baking cookies for a school fundraiser. He needs 3/4 cup of chocolate chips for one batch. If he wants to make 2/3 of a batch, how many cups of chocolate chips should he use? Answer: 1/2 Solution: To find how many cups of chocolate chips Liam needs for 2/3 of a batch, we start with the amount needed for a full batch. A full batch requires 3/4 cup of chocolate chips. To make 2/3 of a batch, multiply 3/4 by 2/3.
   Full step-by-step solution

   To find how many cups of chocolate chips Liam needs for 2/3 of a batch, we start with the amount needed for a full batch. Step 1: A full batch requires 3/4 cup of chocolate chips. Step 2: To make 2/3 of a batch, multiply 3/4 by 2/3. So the calculation is: (3/4) × (2/3) Step 3: Multiply the numerators: 3 × 2 = 6 Step 4: Multiply the denominators: 4 × 3 = 12 This gives: 6/12 Step 5: Simplify 6/12 by dividing numerator and denominator by 6: 6 ÷ 6 = 1 12 ÷ 6 = 2 So 6/12 = 1/2 Answer: Liam needs 1/2 cup of chocolate chips.

2. Lily is baking cookies and uses 3/4 cup of chocolate chips for one batch. She decides to make 2/3 of a batch for a smaller gathering. How many cups of chocolate chips should Lily use for her smaller batch? Answer: 1/2 Solution: To find how many cups of chocolate chips Lily should use for 2/3 of a batch, we start with the fact that a full batch uses 3/4 cup. Write the problem as a multiplication. We need 2/3 of 3/4 cup.
   Full step-by-step solution

   To find how many cups of chocolate chips Lily should use for 2/3 of a batch, we start with the fact that a full batch uses 3/4 cup. Step 1: Write the problem as a multiplication. We need 2/3 of 3/4 cup. That means: (2/3) × (3/4) Step 2: Multiply the numerators together and the denominators together. Numerators: 2 × 3 = 6 Denominators: 3 × 4 = 12 So we have 6/12. Step 3: Simplify the fraction 6/12. Both 6 and 12 can be divided by 6. 6 ÷ 6 = 1 12 ÷ 6 = 2 So 6/12 simplifies to 1/2. Step 4: Conclusion. Lily should use 1/2 cup of chocolate chips for 2/3 of a batch.

3. 4/5 × 3/8 = ? Answer: 3/10 Solution: Multiply the numerators: 4 × 3 = 12 Multiply the denominators: 5 × 8 = 40 Write the resulting fraction: 12/40 Simplify by dividing numerator and denominator by their greatest common factor (4): 12 ÷ 4 = 3, 40 ÷ 4 = 10 Write the simplified fraction: 3/10 The answer is 3/10.
   Full step-by-step solution

   Step 1: Multiply the numerators: 4 × 3 = 12 Step 2: Multiply the denominators: 5 × 8 = 40 Step 3: Write the resulting fraction: 12/40 Step 4: Simplify by dividing numerator and denominator by their greatest common factor (4): 12 ÷ 4 = 3, 40 ÷ 4 = 10 Step 5: Write the simplified fraction: 3/10 The answer is 3/10.

4. Maria is making a quilt for her grandmother. Each quilt square requires 2/3 yard of blue fabric and 3/5 yard of red fabric. Using an area model, what fraction of a yard of fabric is needed for both colors in one quilt square? Answer: 19/15 Solution: Identify the fractions to add: 2/3 (blue fabric) and 3/5 (red fabric) Find a common denominator for 3 and 5, which is 15 Convert 2/3 to have denominator 15: (2 × 5)/(3 × 5) = 10/15 Convert 3/5 to have denominator 15: (3 × 3)/(5 × 3) = 9/15 Add the fractions: 10/15 + 9/15 = 19/15 The total fabric…
   Full step-by-step solution

   Step 1: Identify the fractions to add: 2/3 (blue fabric) and 3/5 (red fabric) Step 2: Find a common denominator for 3 and 5, which is 15 Step 3: Convert 2/3 to have denominator 15: (2 × 5)/(3 × 5) = 10/15 Step 4: Convert 3/5 to have denominator 15: (3 × 3)/(5 × 3) = 9/15 Step 5: Add the fractions: 10/15 + 9/15 = 19/15 Step 6: The total fabric needed is 19/15 yards The answer is 19/15.

5. 3/5 × 4/7 = ? Answer: 12/35 Solution: Multiply the numerators: 3 × 4 = 12 Multiply the denominators: 5 × 7 = 35 Write the resulting fraction: 12/35 Check if the fraction can be simplified.
   Full step-by-step solution

   Step 1: Multiply the numerators: 3 × 4 = 12 Step 2: Multiply the denominators: 5 × 7 = 35 Step 3: Write the resulting fraction: 12/35 Step 4: Check if the fraction can be simplified. The greatest common factor of 12 and 35 is 1, so the fraction is already in simplest form. The answer is 12/35.

6. 4/5 × 2/3 = ? Answer: 8/15 Solution: Multiply the numerators: 4 × 2 = 8 Multiply the denominators: 5 × 3 = 15 Combine the results to form the new fraction: 8/15 The answer is 8/15.
   Full step-by-step solution

   Step 1: Multiply the numerators: 4 × 2 = 8 Step 2: Multiply the denominators: 5 × 3 = 15 Step 3: Combine the results to form the new fraction: 8/15 The answer is 8/15.

7. 3/7 × 5/8 = ? Answer: 15/56 Solution: Multiply the numerators: 3 × 5 = 15 Multiply the denominators: 7 × 8 = 56 Write the resulting fraction: 15/56 Check if the fraction can be simplified.
   Full step-by-step solution

   Step 1: Multiply the numerators: 3 × 5 = 15 Step 2: Multiply the denominators: 7 × 8 = 56 Step 3: Write the resulting fraction: 15/56 Step 4: Check if the fraction can be simplified. The greatest common factor of 15 and 56 is 1, so the fraction is already in simplest form. The answer is 15/56.

8. A rectangular garden measures 3/4 of a kilometer in length and 5/8 of a kilometer in width. What fraction of a square kilometer is the area of the garden? Answer: 15/32 Solution: We have a rectangular garden. Length = 3/4 km Width = 5/8 km We need to find the area in square kilometers and express it as a fraction.
   Full step-by-step solution

   Step 1: Understand the problem We have a rectangular garden. Length = 3/4 km Width = 5/8 km We need to find the area in square kilometers and express it as a fraction. Step 2: Recall the area formula for a rectangle Area = length × width Step 3: Substitute the given values Area = (3/4) × (5/8) Step 4: Multiply the fractions To multiply fractions, multiply the numerators together and the denominators together. Numerator: 3 × 5 = 15 Denominator: 4 × 8 = 32 So, Area = 15/32 Step 5: Interpret the result The area is 15/32 of a square kilometer. This is already in simplest form because 15 and 32 have no common factors other than 1. Final Answer: 15/32

9. 2/3 × 3/5 = ? Answer: 2/5 Solution: Multiply the numerators: 2 × 3 = 6 Multiply the denominators: 3 × 5 = 15 Write the resulting fraction: 6/15 Simplify the fraction by dividing numerator and denominator by their greatest common factor (3): 6 ÷ 3 = 2, 15 ÷ 3 = 5 The simplified fraction is 2/5 The answer is 2/5.
   Full step-by-step solution

   Step 1: Multiply the numerators: 2 × 3 = 6 Step 2: Multiply the denominators: 3 × 5 = 15 Step 3: Write the resulting fraction: 6/15 Step 4: Simplify the fraction by dividing numerator and denominator by their greatest common factor (3): 6 ÷ 3 = 2, 15 ÷ 3 = 5 Step 5: The simplified fraction is 2/5 The answer is 2/5.