Add Unlike Fractions

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Answer Key & Explanations

Add Unlike Fractions · Grade 5 · Worksheet 1

1. 3/8 + 2/5 = ? Answer: 31/40 Solution: Find a common denominator for 8 and 5. The least common multiple is 40.
   Full step-by-step solution

   Step 1: Find a common denominator for 8 and 5. The least common multiple is 40. Step 2: Convert 3/8 to have denominator 40: (3×5)/(8×5) = 15/40 Step 3: Convert 2/5 to have denominator 40: (2×8)/(5×8) = 16/40 Step 4: Add the fractions: 15/40 + 16/40 = 31/40 Step 5: The fraction 31/40 is already in simplest form since 31 and 40 have no common factors. The answer is 31/40.

2. 3/8 + 2/9 = ? Answer: 43/72 Solution: Find a common denominator for 8 and 9. The least common multiple is 72.
   Full step-by-step solution

   Step 1: Find a common denominator for 8 and 9. The least common multiple is 72. Step 2: Convert 3/8 to have denominator 72: (3×9)/(8×9) = 27/72 Step 3: Convert 2/9 to have denominator 72: (2×8)/(9×8) = 16/72 Step 4: Add the fractions: 27/72 + 16/72 = 43/72 Step 5: The fraction 43/72 is already in simplest form since 43 and 72 have no common factors. The answer is 43/72.

3. A rectangular quilt is divided into two colorful sections. The blue section covers 2/5 of the quilt, and the red section covers 1/3 of the quilt. What fraction of the quilt is covered by blue and red sections combined? Answer: 11/15 Solution: Write the addition problem: 2/5 + 1/3 Find a common denominator. The denominators are 5 and 3. The least common multiple of 5 and 3 is 15.
   Full step-by-step solution

   Step 1: Write the addition problem: 2/5 + 1/3 Step 2: Find a common denominator. The denominators are 5 and 3. The least common multiple of 5 and 3 is 15. Step 3: Convert 2/5 to have denominator 15: Multiply numerator and denominator by 3 → (2 × 3)/(5 × 3) = 6/15 Step 4: Convert 1/3 to have denominator 15: Multiply numerator and denominator by 5 → (1 × 5)/(3 × 5) = 5/15 Step 5: Add the fractions: 6/15 + 5/15 = (6 + 5)/15 = 11/15 Step 6: The combined fraction of the quilt covered by blue and red sections is 11/15. Final answer: 11/15

4. 3/10 + 2/15 = ? Answer: 13/30 Solution: Find a common denominator for 10 and 15. The least common multiple is 30.
   Full step-by-step solution

   Step 1: Find a common denominator for 10 and 15. The least common multiple is 30. Step 2: Convert 3/10 to have denominator 30: (3×3)/(10×3) = 9/30 Step 3: Convert 2/15 to have denominator 30: (2×2)/(15×2) = 4/30 Step 4: Add the fractions: 9/30 + 4/30 = 13/30 Step 5: The fraction 13/30 is already in simplest form since 13 and 30 have no common factors. The answer is 13/30.

5. A rectangular garden is divided into two sections. The vegetable section is 3/4 of the garden, and the flower section is 1/6 of the garden. What fraction of the garden is planted with vegetables and flowers combined? Answer: 11/12 Solution: We have a rectangular garden divided into two sections: - Vegetable section = 3/4 of the garden - Flower section = 1/6 of the garden We want the total fraction of the garden planted with vegetables and flowers combined.
   Full step-by-step solution

   Step 1: Understand the problem We have a rectangular garden divided into two sections: - Vegetable section = 3/4 of the garden - Flower section = 1/6 of the garden We want the total fraction of the garden planted with vegetables and flowers combined. Step 2: Add the fractions We need to compute: 3/4 + 1/6 Step 3: Find a common denominator The denominators are 4 and 6. The least common multiple of 4 and 6 is 12. So, the common denominator is 12. Step 4: Convert each fraction For 3/4: Multiply numerator and denominator by 3 to get denominator 12: 3/4 = (3 × 3)/(4 × 3) = 9/12 For 1/6: Multiply numerator and denominator by 2 to get denominator 12: 1/6 = (1 × 2)/(6 × 2) = 2/12 Step 5: Add the fractions Now that both have the same denominator: 9/12 + 2/12 = (9 + 2)/12 = 11/12 Step 6: Interpret the result The combined fraction of the garden planted with vegetables and flowers is 11/12. Final Answer: 11/12

6. A rectangular mural is divided into two colored sections. The blue section covers 2/3 of the mural, and the yellow section covers 3/8 of the mural. What fraction of the mural is covered by blue and yellow combined? Answer: 25/24 Solution: The blue section covers 2/3 of the mural. The yellow section covers 3/8 of the mural. We want the combined fraction: blue + yellow.
   Full step-by-step solution

   Step 1: Understand the problem. The blue section covers 2/3 of the mural. The yellow section covers 3/8 of the mural. We want the combined fraction: blue + yellow. Step 2: Write the addition. Combined fraction = 2/3 + 3/8 Step 3: Find a common denominator. The denominators are 3 and 8. The least common multiple of 3 and 8 is 24. Step 4: Convert each fraction to have denominator 24. For 2/3: Multiply numerator and denominator by 8 → (2 × 8)/(3 × 8) = 16/24 For 3/8: Multiply numerator and denominator by 3 → (3 × 3)/(8 × 3) = 9/24 Step 5: Add the fractions. 16/24 + 9/24 = (16 + 9)/24 = 25/24 Step 6: Interpret the result. The combined fraction of the mural covered by blue and yellow is 25/24. Final answer: 25/24

7. 2/3 + 1/4 = ? Answer: 11/12 Solution: To add the fractions 2/3 and 1/4, we need a common denominator because the denominators (the bottom numbers) are different. Find a common denominator. The denominators are 3 and 4.
   Full step-by-step solution

   To add the fractions 2/3 and 1/4, we need a common denominator because the denominators (the bottom numbers) are different. Step 1: Find a common denominator. The denominators are 3 and 4. The smallest number that both 3 and 4 divide into evenly is 12. So, the common denominator is 12. Step 2: Convert the first fraction, 2/3, to have a denominator of 12. To change the denominator from 3 to 12, we multiply it by 4. To keep the value of the fraction the same, we must also multiply the numerator (the top number) by the same amount. So, 2/3 = (2 * 4) / (3 * 4) = 8/12. Step 3: Convert the second fraction, 1/4, to have a denominator of 12. To change the denominator from 4 to 12, we multiply it by 3. We must also multiply the numerator by 3. So, 1/4 = (1 * 3) / (4 * 3) = 3/12. Step 4: Now add the two fractions that have the same denominator. Since both fractions now have a denominator of 12, we add the numerators and keep the denominator. 8/12 + 3/12 = (8 + 3)/12 = 11/12. Step 5: Check if the answer can be simplified. The fraction 11/12 is already in its simplest form because 11 and 12 have no common factors other than 1. Therefore, the final answer is 11/12.

8. Emma is making a fruit salad for a class party. 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 answer is 23/20 cups, which can also be written as 1 3/20 cups.

9. Liam is baking cookies and needs 3/4 cup of flour for the chocolate chip batch and 2/3 cup of flour for the oatmeal raisin batch. What is the total amount of flour Liam needs for both batches of cookies? Answer: 17/12 or 1 5/12 Solution: To find the total amount of flour Liam needs, we need to add the two amounts: 3/4 cup and 2/3 cup. Identify the fractions to be added. We are adding 3/4 and 2/3.
   Full step-by-step solution

   To find the total amount of flour Liam needs, we need to add the two amounts: 3/4 cup and 2/3 cup. Step 1: Identify the fractions to be added. 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 a denominator of 12. - For 3/4: To change the denominator from 4 to 12, we multiply by 3. So we must also multiply the numerator by 3. This gives us (3 * 3) / (4 * 3) = 9/12. - For 2/3: To change the denominator from 3 to 12, we multiply by 4. So we must also multiply the numerator by 4. This gives us (2 * 4) / (3 * 4) = 8/12. Step 4: Add the converted fractions. Now we add the two fractions that have the same denominator: 9/12 + 8/12. When adding fractions with the same denominator, we keep the denominator and add the numerators. So, 9/12 + 8/12 = (9 + 8)/12 = 17/12. Step 5: Simplify the result, if possible. The fraction 17/12 is an improper fraction (the numerator is larger than the denominator). We can also express this as a mixed number. To convert 17/12 to a mixed number, we see how many whole groups of 12/12 are in 17/12. 12/12 is 1 whole. 17/12 is 12/12 + 5/12, which is 1 + 5/12, or 1 5/12. Therefore, the total amount of flour Liam needs is 17/12 cups or 1 5/12 cups.