Add Unlike Fractions

lessonbunny.com

Answer Key & Explanations

Add Unlike Fractions · Grade 5 · Worksheet 3

1. Sophia is organizing a craft station for her art club. She has a jar that contains 1/6 of a liter of red paint and another jar that contains 5/6 of a liter of blue paint. She pours both jars into a larger container. What is the total amount of paint, in liters, that Sophia combines? Answer: 1 Solution: Identify the fractions to add: 1/6 and 5/6. Step 2: The denominators are both 6, so they are already the same. Step 3: Add the numerators: 1 + 5 = 6.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 1/6 and 5/6. Step 2: The denominators are both 6, so they are already the same. Step 3: Add the numerators: 1 + 5 = 6. Step 4: Keep the denominator the same: 6/6. Step 5: Simplify 6/6 = 1. The total amount of paint is 1 liter.

2. 3/10 + 2/7 = ? Answer: 41/70 Solution: Find a common denominator for 10 and 7. The least common multiple is 70.
   Full step-by-step solution

   Step 1: Find a common denominator for 10 and 7. The least common multiple is 70. Step 2: Convert 3/10 to have denominator 70: (3×7)/(10×7) = 21/70 Step 3: Convert 2/7 to have denominator 70: (2×10)/(7×10) = 20/70 Step 4: Add the fractions: 21/70 + 20/70 = 41/70 Step 5: The fraction 41/70 is already in simplest form since 41 and 70 have no common factors. The answer is 41/70.

3. Liam is baking cookies and needs 3/4 cup of brown sugar for the first batch and 2/3 cup of brown sugar for the second batch. How many cups of brown sugar does Liam need in total? Answer: 17/12 Solution: To find the total amount of brown sugar Liam needs, we need to add the two fractions: 3/4 and 2/3. Identify the fractions to add. We are adding 3/4 and 2/3.
   Full step-by-step solution

   To find the total amount of brown sugar Liam needs, we need to add the two fractions: 3/4 and 2/3. Step 1: Identify the fractions to add. We are adding 3/4 and 2/3. Step 2: Find a common denominator. 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 3: Convert each fraction to an equivalent fraction with the denominator 12. For 3/4: To change the denominator from 4 to 12, we multiply by 3. To keep the value of the fraction the same, we must also multiply the numerator by 3. 3/4 = (3 * 3) / (4 * 3) = 9/12. For 2/3: To change the denominator from 3 to 12, we multiply by 4. We must also multiply the numerator by 4. 2/3 = (2 * 4) / (3 * 4) = 8/12. Step 4: Add the two fractions. Now that both fractions have the same denominator (12), we can add them by adding the numerators and keeping the denominator the same. 9/12 + 8/12 = (9 + 8)/12 = 17/12. Step 5: Interpret the result. The fraction 17/12 is an improper fraction (the numerator is larger than the denominator). This means Liam needs more than one full cup. The problem asks for the total in cups, and 17/12 is a correct and simplified answer. Therefore, Liam needs 17/12 cups of brown sugar in total.

4. Emma is making a fruit salad for a class party. She uses 3/4 cup of strawberries and 2/5 cup of blueberries. What is the total amount of fruit, in cups, that Emma uses in her fruit salad? Answer: 23/20 Solution: Identify the fractions to add: 3/4 and 2/5 Find a common denominator for 4 and 5.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/4 and 2/5 Step 2: Find a common denominator for 4 and 5. The least common multiple is 20 Step 3: Convert 3/4 to twentieths: (3 × 5)/(4 × 5) = 15/20 Step 4: Convert 2/5 to twentieths: (2 × 4)/(5 × 4) = 8/20 Step 5: Add the fractions: 15/20 + 8/20 = 23/20 Step 6: The answer is 23/20 cups, which can also be written as 1 3/20 cups

5. Emma is making a fruit salad for a school picnic. She uses 3/4 cup of strawberries and 2/5 cup of blueberries. What fraction of a cup of berries did Emma use in total for her fruit salad? Answer: 23/20 Solution: Identify the fractions to add: 3/4 and 2/5. Find a common denominator. The denominators are 4 and 5.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/4 and 2/5. Step 2: Find a common denominator. The denominators are 4 and 5. The least common multiple of 4 and 5 is 20. Step 3: Convert 3/4 to have a denominator of 20. Multiply the numerator and denominator by 5: (3 × 5)/(4 × 5) = 15/20. Step 4: Convert 2/5 to have a denominator of 20. Multiply the numerator and denominator by 4: (2 × 4)/(5 × 4) = 8/20. Step 5: Add the fractions with the common denominator: 15/20 + 8/20 = 23/20. Step 6: The fraction 23/20 is the total amount of berries used. The answer is 23/20.

6. 3/8 + 2/7 = ? Answer: 37/56 Solution: Find a common denominator for 8 and 7. The least common multiple is 56.
   Full step-by-step solution

   Step 1: Find a common denominator for 8 and 7. The least common multiple is 56. Step 2: Convert 3/8 to have denominator 56: (3×7)/(8×7) = 21/56 Step 3: Convert 2/7 to have denominator 56: (2×8)/(7×8) = 16/56 Step 4: Add the fractions: 21/56 + 16/56 = 37/56 Step 5: The fraction 37/56 is already in simplest form since 37 and 56 have no common factors. The answer is 37/56.

7. A rectangular garden is divided into two sections. The vegetable section covers 3/8 of the total area, and the flower section covers 2/5 of the total area. What fraction of the garden is used for vegetables and flowers combined? Answer: 31/40 Solution: The vegetable section covers 3/8 of the total area. The flower section covers 2/5 of the total area. We want the combined fraction: vegetables + flowers.
   Full step-by-step solution

   Step 1: Understand the problem. The vegetable section covers 3/8 of the total area. The flower section covers 2/5 of the total area. We want the combined fraction: vegetables + flowers. Step 2: Write the addition. Combined fraction = 3/8 + 2/5 Step 3: Find a common denominator. The denominators are 8 and 5. The least common multiple of 8 and 5 is 40. Step 4: Convert each fraction to have denominator 40. For 3/8: Multiply numerator and denominator by 5 → (3 × 5)/(8 × 5) = 15/40 For 2/5: Multiply numerator and denominator by 8 → (2 × 8)/(5 × 8) = 16/40 Step 5: Add the fractions. 15/40 + 16/40 = (15 + 16)/40 = 31/40 Step 6: Interpret the result. The combined fraction of the garden used for vegetables and flowers is 31/40. Final answer: 31/40

8. 2/5 + 1/3 = ? Answer: 11/15 Solution: Find a common denominator for 5 and 3. The least common multiple is 15.
   Full step-by-step solution

   Step 1: Find a common denominator for 5 and 3. The least common multiple is 15. Step 2: Convert 2/5 to have denominator 15: (2×3)/(5×3) = 6/15 Step 3: Convert 1/3 to have denominator 15: (1×5)/(3×5) = 5/15 Step 4: Add the fractions: 6/15 + 5/15 = 11/15 Step 5: The fraction 11/15 is already in simplest form. The answer is 11/15.

9. Emma is making a quilt and needs different colored fabrics. She uses 3/8 yard of blue fabric for the border and 1/6 yard of red fabric for the center squares. What is the total amount of fabric Emma uses for her quilt? Answer: 13/24 Solution: Identify the fractions to add: 3/8 and 1/6 Find a common denominator.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/8 and 1/6 Step 2: Find a common denominator. The least common multiple of 8 and 6 is 24 Step 3: Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24 Step 4: Convert 1/6 to have denominator 24: (1 × 4)/(6 × 4) = 4/24 Step 5: Add the fractions: 9/24 + 4/24 = 13/24 Step 6: The total fabric used is 13/24 yard