Subtract Unlike Fractions

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Answer Key & Explanations

Subtract Unlike Fractions · Grade 5 · Worksheet 1

1. Emma is painting a mural on her classroom 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 she use than green paint? Answer: 7/24 Solution: Identify the fractions to subtract: 5/8 - 1/3 Find a common denominator. The denominators are 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. The denominators are 8 and 3. The least common multiple of 8 and 3 is 24. Step 3: Convert 5/8 to have a denominator of 24: (5/8) × (3/3) = 15/24 Step 4: Convert 1/3 to have a denominator of 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.

2. Emma is making a quilt and needs to cut fabric strips. She has a piece of fabric that is 7/8 yard long. She needs to cut a strip that is 3/5 yard long for her project. How much fabric will remain after she cuts the strip? Answer: 11/40 Solution: Start with the original fabric length: 7/8 yard Subtract the strip length: 7/8 - 3/5 Find a common denominator for 8 and 5, which is 40 Convert 7/8 to 35/40 (7 × 5 = 35, 8 × 5 = 40) Convert 3/5 to 24/40 (3 × 8 = 24, 5 × 8 = 40) Subtract: 35/40 - 24/40 = 11/40 The remaining fabric is 11/40 yard
   Full step-by-step solution

   Step 1: Start with the original fabric length: 7/8 yard Step 2: Subtract the strip length: 7/8 - 3/5 Step 3: Find a common denominator for 8 and 5, which is 40 Step 4: Convert 7/8 to 35/40 (7 × 5 = 35, 8 × 5 = 40) Step 5: Convert 3/5 to 24/40 (3 × 8 = 24, 5 × 8 = 40) Step 6: Subtract: 35/40 - 24/40 = 11/40 Step 7: The remaining fabric is 11/40 yard

3. 7/9 - 3/8 = ? Answer: 29/72 Solution: Find a common denominator for 9 and 8. The least common multiple of 9 and 8 is 72.
   Full step-by-step solution

   Step 1: Find a common denominator for 9 and 8. The least common multiple of 9 and 8 is 72. Step 2: Convert 7/9 to have denominator 72: (7 × 8)/(9 × 8) = 56/72 Step 3: Convert 3/8 to have denominator 72: (3 × 9)/(8 × 9) = 27/72 Step 4: Subtract the fractions: 56/72 - 27/72 = 29/72 Step 5: Check if the fraction can be simplified: 29 and 72 have no common factors other than 1, so 29/72 is already in simplest form. The answer is 29/72.

4. Liam is baking cookies and needs 3/4 cup of sugar for the chocolate chip batch and 2/3 cup of sugar for the oatmeal raisin batch. How much more sugar does Liam need for the chocolate chip cookies than for the oatmeal raisin cookies? Answer: 1/12 Solution: To find how much more sugar is needed for the chocolate chip cookies than the oatmeal raisin cookies, we subtract the smaller amount from the larger amount. Identify the amounts of sugar needed. - Chocolate chip cookies: 3/4 cup - Oatmeal raisin cookies: 2/3 cup Write the subtraction problem.
   Full step-by-step solution

   To find how much more sugar is needed for the chocolate chip cookies than the oatmeal raisin cookies, we subtract the smaller amount from the larger amount. Step 1: Identify the amounts of sugar needed. - Chocolate chip cookies: 3/4 cup - Oatmeal raisin cookies: 2/3 cup Step 2: Write the subtraction problem. We need to calculate: 3/4 - 2/3 Step 3: Find a common denominator to subtract the fractions. The denominators are 4 and 3. The smallest number that both 4 and 3 divide into evenly is 12. So, the common denominator is 12. Step 4: Convert each fraction to an equivalent fraction with a denominator of 12. - For 3/4: To change the denominator from 4 to 12, we multiply by 3. So, we multiply both the numerator and denominator by 3. This gives (3 * 3) / (4 * 3) = 9/12. - For 2/3: To change the denominator from 3 to 12, we multiply by 4. So, we multiply both the numerator and denominator by 4. This gives (2 * 4) / (3 * 4) = 8/12. Step 5: Perform the subtraction with the new fractions. Now the calculation is: 9/12 - 8/12 Step 6: Subtract the numerators and keep the denominator. 9/12 - 8/12 = (9 - 8)/12 = 1/12 Step 7: State the final answer. Liam needs 1/12 cup more sugar for the chocolate chip cookies than for the oatmeal raisin cookies.

5. 7/10 - 2/9 = ? Answer: 43/90 Solution: Find a common denominator for 10 and 9. The least common multiple of 10 and 9 is 90.
   Full step-by-step solution

   Step 1: Find a common denominator for 10 and 9. The least common multiple of 10 and 9 is 90. Step 2: Convert 7/10 to have denominator 90: (7 × 9)/(10 × 9) = 63/90 Step 3: Convert 2/9 to have denominator 90: (2 × 10)/(9 × 10) = 20/90 Step 4: Subtract the fractions: 63/90 - 20/90 = 43/90 Step 5: Check if the fraction can be simplified: 43 and 90 have no common factors other than 1, so 43/90 is already in simplest form. The answer is 43/90.

6. Maria is painting two walls in her room. She used 5/6 of a can of blue paint on the first wall and 3/4 of a can on the second wall. How much more blue paint did Maria use on the first wall than on the second wall? Answer: 1/12 Solution: Identify the fractions to subtract: 5/6 - 3/4 Find a common denominator for 6 and 4. The least common multiple is 12.
   Full step-by-step solution

   Step 1: Identify the fractions to subtract: 5/6 - 3/4 Step 2: Find a common denominator for 6 and 4. The least common multiple is 12. Step 3: Convert 5/6 to twelfths: 5/6 = 10/12 (multiply numerator and denominator by 2) Step 4: Convert 3/4 to twelfths: 3/4 = 9/12 (multiply numerator and denominator by 3) Step 5: Subtract the fractions: 10/12 - 9/12 = 1/12 Step 6: The answer is 1/12 of a can.

7. A rectangular garden is divided into three planting sections. The vegetable section takes up 3/5 of the total area, the flower section takes up 1/4 of the total area, and the herb section takes up the remaining space. What fraction of the garden is planted with herbs? Answer: 3/20 Solution: The vegetable section is 3/5 of the garden. The flower section is 1/4 of the garden. To find the total used by vegetables and flowers, add 3/5 and 1/4.
   Full step-by-step solution

   Step 1: The vegetable section is 3/5 of the garden. Step 2: The flower section is 1/4 of the garden. Step 3: To find the total used by vegetables and flowers, add 3/5 and 1/4. Step 4: Find a common denominator for 5 and 4, which is 20. Step 5: Convert 3/5 to 12/20 (since 3/5 = 12/20). Step 6: Convert 1/4 to 5/20 (since 1/4 = 5/20). Step 7: Add the fractions: 12/20 + 5/20 = 17/20. Step 8: The herb section is the remaining part: 1 - 17/20 = 20/20 - 17/20 = 3/20. The answer is 3/20.

8. 7/8 - 3/5 = ? Answer: 11/40 Solution: Find a common denominator for 8 and 5. The least common multiple of 8 and 5 is 40.
   Full step-by-step solution

   Step 1: Find a common denominator for 8 and 5. The least common multiple of 8 and 5 is 40. Step 2: Convert 7/8 to have denominator 40: (7 × 5)/(8 × 5) = 35/40 Step 3: Convert 3/5 to have denominator 40: (3 × 8)/(5 × 8) = 24/40 Step 4: Subtract the fractions: 35/40 - 24/40 = 11/40 Step 5: Check if the fraction can be simplified: 11 and 40 have no common factors other than 1, so 11/40 is already in simplest form. The answer is 11/40.

9. 7/12 - 3/8 = ? Answer: 5/24 Solution: Find a common denominator for 12 and 8. The least common multiple of 12 and 8 is 24.
   Full step-by-step solution

   Step 1: Find a common denominator for 12 and 8. The least common multiple of 12 and 8 is 24. Step 2: Convert 7/12 to have denominator 24: (7 × 2)/(12 × 2) = 14/24 Step 3: Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24 Step 4: Subtract the fractions: 14/24 - 9/24 = 5/24 Step 5: Check if the fraction can be simplified: 5 and 24 have no common factors other than 1, so 5/24 is already in simplest form. The answer is 5/24.