Subtract Unlike Fractions

lessonbunny.com

Answer Key & Explanations

Subtract Unlike Fractions · Grade 5 · Worksheet 2

1. Liam is baking cookies and needs 3/4 cup of sugar for the first batch and 2/3 cup of sugar for the second batch. How much more sugar does he need for the first batch than for the second batch? Answer: 1/12 Solution: To find how much more sugar Liam needs for the first batch than for the second batch, we subtract the amount for the second batch from the amount for the first batch. Write the subtraction expression. First batch: 3/4 cup Second batch: 2/3 cup Difference = 3/4 - 2/3 To subtract fractions, they…
   Full step-by-step solution

   To find how much more sugar Liam needs for the first batch than for the second batch, we subtract the amount for the second batch from the amount for the first batch. Step 1: Write the subtraction expression. First batch: 3/4 cup Second batch: 2/3 cup Difference = 3/4 - 2/3 Step 2: To subtract fractions, they must have the same denominator. Find a common denominator for 4 and 3. The least common multiple of 4 and 3 is 12. So the common denominator is 12. Step 3: Convert each fraction to an equivalent fraction with a denominator of 12. For 3/4: Multiply the numerator and denominator by 3. (3 * 3)/(4 * 3) = 9/12 For 2/3: Multiply the numerator and denominator by 4. (2 * 4)/(3 * 4) = 8/12 Step 4: Now subtract the fractions with the common denominator. 9/12 - 8/12 = (9 - 8)/12 = 1/12 Step 5: Interpret the result. The difference is 1/12 cup. Therefore, Liam needs 1/12 cup more sugar for the first batch than for the second batch.

2. Maria is making a quilt and needs to cut fabric pieces. She has a strip of fabric that is 7/8 yard long. If she cuts off a piece that is 3/5 yard long for her quilt block, how much fabric remains on the original strip? Answer: 11/40 Solution: Identify the operation: We need to subtract 3/5 from 7/8 to find the remaining fabric. Find a common denominator: The denominators are 8 and 5. The least common multiple of 8 and 5 is 40.
   Full step-by-step solution

   Step 1: Identify the operation: We need to subtract 3/5 from 7/8 to find the remaining fabric. Step 2: Find a common denominator: The denominators are 8 and 5. The least common multiple of 8 and 5 is 40. Step 3: Convert both fractions: 7/8 = (7 × 5)/(8 × 5) = 35/40 and 3/5 = (3 × 8)/(5 × 8) = 24/40. Step 4: Subtract the fractions: 35/40 - 24/40 = (35 - 24)/40 = 11/40. Step 5: The answer is 11/40 yard of fabric remaining.

3. A rectangular garden is divided into two planting sections. The first section takes up 3/8 of the total garden area, and the second section takes up 1/6 of the total garden area. What fraction of the garden is NOT used for planting? Answer: 11/24 Solution: Identify the fractions of the garden used for planting. The first section uses 3/8 of the total area. The second section uses 1/6 of the total area.
   Full step-by-step solution

   Let's solve this step-by-step. Step 1: Identify the fractions of the garden used for planting. The first section uses 3/8 of the total area. The second section uses 1/6 of the total area. Step 2: Add these two fractions to find the total fraction used for planting. To add 3/8 and 1/6, we need a common denominator. The least common multiple of 8 and 6 is 24. Step 3: Convert each fraction to have denominator 24. 3/8 = (3 × 3)/(8 × 3) = 9/24 1/6 = (1 × 4)/(6 × 4) = 4/24 Step 4: Add the fractions. 9/24 + 4/24 = 13/24 So, the total planting area is 13/24 of the garden. Step 5: Find the fraction NOT used for planting. The whole garden is 1, which is 24/24. Fraction not used = 24/24 − 13/24 = 11/24 Final answer: 11/24

4. Maria is painting a mural on her bedroom wall. She used 5/8 of a gallon of blue paint for the sky and 1/3 of a gallon of green paint for the grass. How much more blue paint did Maria use than green paint? Answer: 7/24 Solution: Identify the fractions to subtract: 5/8 - 1/3 Find a common denominator for 8 and 3. The least common multiple of 8 and 3 is 24.
   Full step-by-step solution

   Step 1: Identify the fractions to subtract: 5/8 - 1/3 Step 2: Find a common denominator for 8 and 3. The least common multiple of 8 and 3 is 24. Step 3: Convert 5/8 to have denominator 24: (5/8) × (3/3) = 15/24 Step 4: Convert 1/3 to have denominator 24: (1/3) × (8/8) = 8/24 Step 5: Subtract the fractions: 15/24 - 8/24 = 7/24 Step 6: The answer is 7/24 of a gallon.

5. A rectangular garden is divided into two sections. The vegetable section takes up 3/4 of the garden, and the flower section takes up the remaining space. If the flower section is further divided into equal parts for roses and tulips, what fraction of the entire garden is planted with tulips? Answer: 1/8 Solution: 1. The vegetable section takes up 3/4 of the garden. 1 - 3/4 = 1/4 of the garden.
   Full step-by-step solution

   Let's go step by step. 1. The vegetable section takes up 3/4 of the garden. That means the remaining flower section is: 1 - 3/4 = 1/4 of the garden. 2. The flower section (1/4 of the garden) is divided equally between roses and tulips. So, each part is: (1/4) ÷ 2 = 1/4 × 1/2 = 1/8 of the garden. 3. Therefore, the fraction of the entire garden planted with tulips is 1/8. Final answer: 1/8

6. Maria is painting a mural on her bedroom wall. On Monday, she painted 5/8 of the wall. On Tuesday, she painted another 1/3 of the wall. What fraction more of the wall did Maria paint on Monday than on Tuesday? Answer: 7/24 Solution: Identify the fractions to subtract: 5/8 - 1/3 Find a common denominator for 8 and 3. The least common multiple is 24.
   Full step-by-step solution

   Step 1: Identify the fractions to subtract: 5/8 - 1/3 Step 2: Find a common denominator for 8 and 3. The least common multiple is 24. Step 3: Convert 5/8 to have denominator 24: (5 × 3)/(8 × 3) = 15/24 Step 4: Convert 1/3 to have denominator 24: (1 × 8)/(3 × 8) = 8/24 Step 5: Subtract the fractions: 15/24 - 8/24 = 7/24 Step 6: The answer is 7/24, which cannot be simplified further.

7. A construction company needs 7/8 of a ton of concrete for a foundation and 2/3 of a ton for a patio. How much more concrete is needed for the foundation than for the patio? Answer: 5/24 Solution: We are asked: "How much more concrete is needed for the foundation than for the patio?" Identify the amounts. Foundation: 7/8 ton Patio: 2/3 ton The phrase "how much more for the foundation than the patio" means we subtract the patio amount from the foundation amount: Difference = Foundation −…
   Full step-by-step solution

   We are asked: "How much more concrete is needed for the foundation than for the patio?" Step 1: Identify the amounts. Foundation: 7/8 ton Patio: 2/3 ton Step 2: The phrase "how much more for the foundation than the patio" means we subtract the patio amount from the foundation amount: Difference = Foundation − Patio = 7/8 − 2/3 Step 3: To subtract fractions, they must have the same denominator. Find a common denominator for 8 and 3. The least common multiple of 8 and 3 is 24. Step 4: Convert each fraction to have denominator 24. For 7/8: Multiply numerator and denominator by 3: (7×3)/(8×3) = 21/24 For 2/3: Multiply numerator and denominator by 8: (2×8)/(3×8) = 16/24 Step 5: Now subtract: 21/24 − 16/24 = (21 − 16)/24 = 5/24 Step 6: Interpret the result: The foundation needs 5/24 ton more concrete than the patio. Final answer: 5/24

8. 3/4 - 1/6 = ? Answer: 7/12 Solution: To subtract fractions, they must have the same denominator (the bottom number). The denominators are 4 and 6. The smallest number that both 4 and 6 divide into is 12.
   Full step-by-step solution

   To subtract fractions, they must have the same denominator (the bottom number). Here is the step-by-step process: Step 1: Find a common denominator. The denominators are 4 and 6. The smallest number that both 4 and 6 divide into is 12. So, the common denominator is 12. Step 2: Convert the first fraction, 3/4, to have a denominator of 12. To change 4 into 12, you multiply by 3. You must do the same to the numerator (the top number) to keep the value of the fraction the same. So, (3 * 3) / (4 * 3) = 9/12. Step 3: Convert the second fraction, 1/6, to have a denominator of 12. To change 6 into 12, you multiply by 2. You must do the same to the numerator. So, (1 * 2) / (6 * 2) = 2/12. Step 4: Now subtract the new fractions. Since both fractions now have the same denominator (12), you subtract the numerators and keep the denominator. So, 9/12 - 2/12 = (9 - 2)/12 = 7/12. Step 5: Check if the answer can be simplified. The fraction 7/12 is already in its simplest form because 7 and 12 have no common factors other than 1. Therefore, the final answer is 7/12.

9. 7/10 - 2/5 = ? Answer: 3/10 Solution: Find a common denominator for 10 and 5. The least common multiple of 10 and 5 is 10. Convert 7/10 to have denominator 10: 7/10 already has denominator 10, so it remains 7/10.
   Full step-by-step solution

   Step 1: Find a common denominator for 10 and 5. The least common multiple of 10 and 5 is 10. Step 2: Convert 7/10 to have denominator 10: 7/10 already has denominator 10, so it remains 7/10. Step 3: Convert 2/5 to have denominator 10: (2 × 2)/(5 × 2) = 4/10. Step 4: Subtract the fractions: 7/10 - 4/10 = 3/10. Step 5: Check if the fraction can be simplified: 3 and 10 have no common factors other than 1, so 3/10 is already in simplest form. The answer is 3/10.