Subtract Unlike Fractions

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Answer Key & Explanations

Subtract Unlike Fractions · Grade 5 · Worksheet 3

1. Liam is baking cookies and needs 3/4 cup of sugar for the recipe. He already has 1/3 cup of sugar in his bowl. How much more sugar does Liam need to add to have the correct amount? Answer: 5/12 Solution: We need to find how much more sugar Liam needs to add. Identify what is needed and what he already has. The recipe requires 3/4 cup of sugar.
   Full step-by-step solution

   We need to find how much more sugar Liam needs to add. Step 1: Identify what is needed and what he already has. The recipe requires 3/4 cup of sugar. He already has 1/3 cup of sugar. Step 2: Set up the subtraction. Amount needed = Required amount − Current amount Amount needed = 3/4 − 1/3 Step 3: Find a common denominator to subtract. The denominators are 4 and 3. The least common denominator is 12. Step 4: Convert each fraction to have denominator 12. For 3/4: Multiply numerator and denominator by 3 → (3×3)/(4×3) = 9/12 For 1/3: Multiply numerator and denominator by 4 → (1×4)/(3×4) = 4/12 Step 5: Subtract the fractions. 9/12 − 4/12 = (9 − 4)/12 = 5/12 Step 6: Interpret the result. Liam needs to add 5/12 cup of sugar. Final answer: 5/12

2. A scientist needs 7/9 of a liter of chemical A and 5/12 of a liter of chemical B for an experiment. How much more of chemical A is needed than chemical B? Answer: 13/36 Solution: Identify the fractions: 7/9 and 5/12 Find a common denominator. The least common multiple of 9 and 12 is 36.
   Full step-by-step solution

   Step 1: Identify the fractions: 7/9 and 5/12 Step 2: Find a common denominator. The least common multiple of 9 and 12 is 36. Step 3: Convert 7/9 to have denominator 36: (7 × 4)/(9 × 4) = 28/36 Step 4: Convert 5/12 to have denominator 36: (5 × 3)/(12 × 3) = 15/36 Step 5: Subtract the fractions: 28/36 - 15/36 = 13/36 Step 6: The fraction 13/36 is already in simplest form. The answer is 13/36.

3. 4/5 - 3/7 = ? Answer: 13/35 Solution: Find a common denominator for 5 and 7. The least common multiple of 5 and 7 is 35.
   Full step-by-step solution

   Step 1: Find a common denominator for 5 and 7. The least common multiple of 5 and 7 is 35. Step 2: Convert 4/5 to have denominator 35: (4 × 7)/(5 × 7) = 28/35 Step 3: Convert 3/7 to have denominator 35: (3 × 5)/(7 × 5) = 15/35 Step 4: Subtract the fractions: 28/35 - 15/35 = 13/35 Step 5: Check if the fraction can be simplified: 13 and 35 have no common factors other than 1, so 13/35 is already in simplest form. The answer is 13/35.

4. Emma is making a quilt and needs to cut fabric pieces. She has a piece that is 5/6 yard long, but her pattern requires a piece that is 3/4 yard long. How much longer is Emma's current fabric piece than what she needs for the pattern? 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 yard.

5. Noah is building a bookshelf and needs to cut two pieces of wood. The first piece needs to be 5/6 of a meter long, and the second piece needs to be 3/4 of a meter long. How much longer is the first piece of wood than the second piece? Answer: 1/12 Solution: Identify the two lengths: 5/6 meter and 3/4 meter. To find the difference, subtract the smaller fraction from the larger one: 5/6 - 3/4. Find a common denominator for 6 and 4.
   Full step-by-step solution

   Step 1: Identify the two lengths: 5/6 meter and 3/4 meter. Step 2: To find the difference, subtract the smaller fraction from the larger one: 5/6 - 3/4. Step 3: Find a common denominator for 6 and 4. The least common multiple is 12. Step 4: Convert 5/6 to twelfths: (5/6) = (5 x 2)/(6 x 2) = 10/12. Step 5: Convert 3/4 to twelfths: (3/4) = (3 x 3)/(4 x 3) = 9/12. Step 6: Subtract the fractions: 10/12 - 9/12 = 1/12. Step 7: The first piece is 1/12 of a meter longer than the second piece.

6. Emma is making a quilt and needs to cut fabric strips. She has a piece of fabric that is 5/6 yard long. She cuts off a strip that is 3/8 yard long for her first pattern. How much fabric remains after Emma cuts off the first strip? Answer: 11/24 Solution: Identify the fractions to subtract: 5/6 - 3/8 Find a common denominator. The least common multiple of 6 and 8 is 24.
   Full step-by-step solution

   Step 1: Identify the fractions to subtract: 5/6 - 3/8 Step 2: Find a common denominator. The least common multiple of 6 and 8 is 24. Step 3: Convert 5/6 to have denominator 24: (5 × 4)/(6 × 4) = 20/24 Step 4: Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24 Step 5: Subtract the fractions: 20/24 - 9/24 = 11/24 Step 6: The fraction 11/24 is already in simplest form since 11 and 24 share no common factors. The answer is 11/24 yard.

7. Emma and Noah are painting a mural for their school. Emma painted 5/8 of the mural on Monday, and Noah painted 1/3 of the mural on Tuesday. How much more of the mural did Emma paint than Noah? 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.

8. 7/9 - 2/5 = ? Answer: 17/45 Solution: Find a common denominator for 9 and 5. The least common multiple of 9 and 5 is 45.
   Full step-by-step solution

   Step 1: Find a common denominator for 9 and 5. The least common multiple of 9 and 5 is 45. Step 2: Convert 7/9 to have denominator 45: (7 × 5)/(9 × 5) = 35/45 Step 3: Convert 2/5 to have denominator 45: (2 × 9)/(5 × 9) = 18/45 Step 4: Subtract the fractions: 35/45 - 18/45 = 17/45 Step 5: Check if the fraction can be simplified: 17 and 45 have no common factors other than 1, so 17/45 is already in simplest form. The answer is 17/45.

9. 7/10 - 2/3 = ? Answer: 1/30 Solution: Find a common denominator for 10 and 3. The least common multiple of 10 and 3 is 30.
   Full step-by-step solution

   Step 1: Find a common denominator for 10 and 3. The least common multiple of 10 and 3 is 30. Step 2: Convert 7/10 to have denominator 30: (7 × 3)/(10 × 3) = 21/30 Step 3: Convert 2/3 to have denominator 30: (2 × 10)/(3 × 10) = 20/30 Step 4: Subtract the fractions: 21/30 - 20/30 = 1/30 Step 5: Check if the fraction can be simplified: 1 and 30 have no common factors other than 1, so 1/30 is already in simplest form. The answer is 1/30.