Add Unlike Fractions

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Answer Key & Explanations

Add Unlike Fractions · Grade 5 · Worksheet 2

1. A construction crew needs to add two different lengths of pipe for a plumbing project. The first pipe measures 7/8 of a meter and the second pipe measures 5/6 of a meter. What is the total length when these two pipes are connected together? Answer: 41/24 Solution: To find the total length when the two pipes are connected, we need to add the two fractions: 7/8 and 5/6. Identify the fractions to add. We are adding 7/8 and 5/6.
   Full step-by-step solution

   To find the total length when the two pipes are connected, we need to add the two fractions: 7/8 and 5/6. Step 1: Identify the fractions to add. We are adding 7/8 and 5/6. Step 2: Find a common denominator. The denominators are 8 and 6. We need the smallest number that both 8 and 6 divide into evenly. This is the Least Common Multiple (LCM). - The multiples of 8 are: 8, 16, 24, 32... - The multiples of 6 are: 6, 12, 18, 24, 30... The smallest common multiple is 24. So, our common denominator is 24. Step 3: Convert each fraction to an equivalent fraction with the denominator 24. - For 7/8: To change the denominator 8 into 24, we multiply by 3 (because 8 * 3 = 24). To keep the value of the fraction the same, we must also multiply the numerator by 3. So, (7 * 3) / (8 * 3) = 21/24. - For 5/6: To change the denominator 6 into 24, we multiply by 4 (because 6 * 4 = 24). We must also multiply the numerator by 4. So, (5 * 4) / (6 * 4) = 20/24. Step 4: Add the converted fractions. Now we add the two fractions that have the same denominator: 21/24 + 20/24. When adding fractions with the same denominator, we add the numerators and keep the denominator. So, (21 + 20) / 24 = 41/24. Step 5: Simplify the result (if possible). We check if the fraction 41/24 can be simplified. The number 41 is a prime number (its only factors are 1 and 41). The number 24 has factors like 2, 3, 4, 6, 8, 12. Since 41 and 24 share no common factors other than 1, the fraction 41/24 is already in its simplest form. Therefore, the total length of the connected pipes is 41/24 meters.

2. A construction crew needs to mix concrete using 3/4 ton of sand and 5/8 ton of gravel. What is the total weight of these two materials combined? Answer: 11/8 Solution: We are adding 3/4 ton of sand and 5/8 ton of gravel. Write the problem as an addition of fractions. Total weight = 3/4 + 5/8 To add fractions, they must have the same denominator.
   Full step-by-step solution

   We are adding 3/4 ton of sand and 5/8 ton of gravel. Step 1: Write the problem as an addition of fractions. Total weight = 3/4 + 5/8 Step 2: To add fractions, they must have the same denominator. The denominators are 4 and 8. The least common denominator is 8. Step 3: Convert 3/4 to a fraction with denominator 8. Since 4 × 2 = 8, multiply numerator and denominator by 2: 3/4 = (3 × 2)/(4 × 2) = 6/8 Step 4: Now both fractions have denominator 8. 6/8 + 5/8 Step 5: Add the numerators and keep the denominator. (6 + 5)/8 = 11/8 Step 6: The result is 11/8 tons. Final answer: 11/8

3. 3/7 + 2/9 = ? Answer: 41/63 Solution: Find a common denominator for 7 and 9. The least common multiple is 63.
   Full step-by-step solution

   Step 1: Find a common denominator for 7 and 9. The least common multiple is 63. Step 2: Convert 3/7 to have denominator 63: (3×9)/(7×9) = 27/63 Step 3: Convert 2/9 to have denominator 63: (2×7)/(9×7) = 14/63 Step 4: Add the fractions: 27/63 + 14/63 = 41/63 Step 5: The fraction 41/63 is already in simplest form since 41 and 63 have no common factors. The answer is 41/63.

4. A rectangular garden is divided into two triangular flower beds by a diagonal path. The garden measures 12 meters long and 5 meters wide. What is the area of one of the triangular flower beds? Answer: 30 Solution: We have a rectangular garden that is 12 meters long and 5 meters wide. A diagonal divides it into two equal triangles. We need the area of one triangular flower bed.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular garden that is 12 meters long and 5 meters wide. A diagonal divides it into two equal triangles. We need the area of one triangular flower bed. Step 2: Recall the area of a rectangle. Area of rectangle = length × width So, Area = 12 × 5 = 60 square meters. Step 3: Understand the diagonal's effect. A diagonal of a rectangle splits it into two congruent (identical) triangles. So, each triangle has half the area of the rectangle. Step 4: Calculate the area of one triangle. Area of one triangle = (Area of rectangle) / 2 = 60 / 2 = 30 square meters. Step 5: Final answer. The area of one triangular flower bed is 30 square meters.

5. A rectangular garden is divided into two sections for different vegetables. The first section is 3/4 of the total area and is planted with tomatoes. The second section is 1/6 of the total area and is planted with carrots. What fraction of the garden is planted with vegetables? Answer: 11/12 Solution: Identify the fractions given in the problem. The first section for tomatoes is 3/4 of the total garden area. The second section for carrots is 1/6 of the total garden area.
   Full step-by-step solution

   Let's go step-by-step. Step 1: Identify the fractions given in the problem. The first section for tomatoes is 3/4 of the total garden area. The second section for carrots is 1/6 of the total garden area. Step 2: Understand what is being asked. We need the total fraction of the garden planted with vegetables. That means we add the two fractions: 3/4 + 1/6. Step 3: Find a common denominator to add the fractions. The denominators are 4 and 6. The least common multiple of 4 and 6 is 12. Step 4: Convert each fraction to have denominator 12. 3/4 = (3 × 3) / (4 × 3) = 9/12 1/6 = (1 × 2) / (6 × 2) = 2/12 Step 5: Add the fractions. 9/12 + 2/12 = (9 + 2)/12 = 11/12 Step 6: Interpret the result. 11/12 of the total garden area is planted with vegetables. Final answer: 11/12

6. 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? Answer: 23/20 Solution: Identify the fractions to add: 3/4 and 2/5 Find a common denominator. The denominators are 4 and 5. The least common multiple of 4 and 5 is 20.
   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 denominator 20: 3/4 = (3 × 5)/(4 × 5) = 15/20 Step 4: Convert 2/5 to have denominator 20: 2/5 = (2 × 4)/(5 × 4) = 8/20 Step 5: Add the fractions: 15/20 + 8/20 = 23/20 Step 6: The fraction 23/20 is already in simplest form. The total amount of berries Emma used is 23/20 cups.

7. Emma is making a fruit salad for a school picnic. 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 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. The least common multiple of 4 and 5 is 20.
   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 denominator 20: (3 × 5)/(4 × 5) = 15/20 Step 4: Convert 2/5 to have denominator 20: (2 × 4)/(5 × 4) = 8/20 Step 5: Add the fractions: 15/20 + 8/20 = 23/20 Step 6: The fraction 23/20 is the total amount of fruit in cups. The answer is 23/20.