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Mixed Numbers Unlike

Grade 5 · Mathematics · Worksheet 3

  1. 3 2/7 + 4 3/5 = ? Answer: ______________
  2. 2 3/4 + 1 5/6 = ? Answer: ______________
  3. Liam is making a fruit salad. Liam has 6 cups of strawberries and 2 cups of blueberries. How many more cups of strawberries does Liam have than blueberries? Answer: ______________
  4. A rectangular prism has a length of 8.5 cm, a width of 6.2 cm, and a height of 4.3 cm. What is the volume of this prism?
    Answer: ______________
  5. 7 2/5 - 3 1/3 = ? Answer: ______________
  6. Emma is baking cookies for a school fundraiser. She needs 2 3/4 cups of flour for the chocolate chip cookies and 1 5/8 cups of flour for the oatmeal raisin cookies. If she starts with a 5-pound bag of flour that contains approximately 18 cups total, how many cups of flour will she have left after baking both types of cookies? Answer: ______________
  7. 3 2/5 + 1 3/4 - 2 1/10 = ? Answer: ______________
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Answer Key & Explanations

Mixed Numbers Unlike · Grade 5 · Worksheet 3

  1. 3 2/7 + 4 3/5 = ? Answer: 7 31/35 Solution: Convert 3 2/7 to an improper fraction: (3 × 7 + 2)/7 = (21 + 2)/7 = 23/7 Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Find a common denominator for 7 and 5, which is 35 Convert 23/7 to thirty-fifths: (23 × 5)/(7 × 5) = 115/35 Convert 23/5 to thirty-fifths: (23 × 7)/(5…
    Full step-by-step solution

    Step 1: Convert 3 2/7 to an improper fraction: (3 × 7 + 2)/7 = (21 + 2)/7 = 23/7 Step 2: Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Step 3: Find a common denominator for 7 and 5, which is 35 Step 4: Convert 23/7 to thirty-fifths: (23 × 5)/(7 × 5) = 115/35 Step 5: Convert 23/5 to thirty-fifths: (23 × 7)/(5 × 7) = 161/35 Step 6: Add the fractions: 115/35 + 161/35 = 276/35 Step 7: Convert 276/35 to a mixed number: 276 ÷ 35 = 7 with remainder 31, so 7 31/35 The answer is 7 31/35.

  2. 2 3/4 + 1 5/6 = ? Answer: 4 7/12 Solution: Convert 2 3/4 to an improper fraction: (2 × 4 + 3)/4 = 11/4 Convert 1 5/6 to an improper fraction: (1 × 6 + 5)/6 = 11/6 Find a common denominator for 4 and 6, which is 12 Convert 11/4 to twelfths: (11 × 3)/(4 × 3) = 33/12 Convert 11/6 to twelfths: (11 × 2)/(6 × 2) = 22/12 Add the fractions:…
    Full step-by-step solution

    Step 1: Convert 2 3/4 to an improper fraction: (2 × 4 + 3)/4 = 11/4 Step 2: Convert 1 5/6 to an improper fraction: (1 × 6 + 5)/6 = 11/6 Step 3: Find a common denominator for 4 and 6, which is 12 Step 4: Convert 11/4 to twelfths: (11 × 3)/(4 × 3) = 33/12 Step 5: Convert 11/6 to twelfths: (11 × 2)/(6 × 2) = 22/12 Step 6: Add the fractions: 33/12 + 22/12 = 55/12 Step 7: Convert 55/12 to a mixed number: 55 ÷ 12 = 4 with remainder 7, so 4 7/12 The answer is 4 7/12.

  3. Liam is making a fruit salad. Liam has 6 cups of strawberries and 2 cups of blueberries. How many more cups of strawberries does Liam have than blueberries? Answer: 4 Solution: Cups of strawberries: 6. Cups of blueberries: 2. Subtract: 6 - 2 = 4.
    Full step-by-step solution

    Step 1: Cups of strawberries: 6. Step 2: Cups of blueberries: 2. Step 3: Subtract: 6 - 2 = 4. The answer is 4 cups more strawberries.

  4. A rectangular prism has a length of 8.5 cm, a width of 6.2 cm, and a height of 4.3 cm. What is the volume of this prism? Answer: 226.61 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given dimensions. Length = 8.5 cm Width = 6.2 cm Height = 4.3 cm Substitute the values into the formula.
    Full step-by-step solution

    To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given dimensions. Length = 8.5 cm Width = 6.2 cm Height = 4.3 cm Step 2: Substitute the values into the formula. Volume = 8.5 × 6.2 × 4.3 Step 3: Perform the multiplication step-by-step. First, multiply the length and the width. 8.5 × 6.2 To do this, we can calculate 85 × 62 and then divide by 100 because both numbers have one decimal place. 85 × 62 = 85 × (60 + 2) = (85 × 60) + (85 × 2) = 5100 + 170 = 5270 Since we had one decimal place in each original number, the product has two decimal places. So, 8.5 × 6.2 = 52.70 Step 4: Now multiply this result by the height. 52.70 × 4.3 To do this, we can calculate 5270 × 43 and then divide by 1000 because 52.70 has two decimal places and 4.3 has one decimal place, for a total of three decimal places. 5270 × 43 = 5270 × (40 + 3) = (5270 × 40) + (5270 × 3) = 210800 + 15810 = 226610 Now, since we need three decimal places, we divide by 1000: 226610 / 1000 = 226.610 Step 5: Write the final answer with the correct number of decimal places. The problem's correct answer is given as 226.61, which is the result rounded to two decimal places. Therefore, the volume of the rectangular prism is 226.61 cubic centimeters.

  5. 7 2/5 - 3 1/3 = ? Answer: 4 1/15 Solution: Convert 7 2/5 to an improper fraction: (7 × 5 + 2)/5 = (35 + 2)/5 = 37/5 Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Find a common denominator for 5 and 3, which is 15 Convert 37/5 to fifteenths: (37 × 3)/(5 × 3) = 111/15 Convert 10/3 to fifteenths: (10 × 5)/(3 × 5) =…
    Full step-by-step solution

    Step 1: Convert 7 2/5 to an improper fraction: (7 × 5 + 2)/5 = (35 + 2)/5 = 37/5 Step 2: Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Step 3: Find a common denominator for 5 and 3, which is 15 Step 4: Convert 37/5 to fifteenths: (37 × 3)/(5 × 3) = 111/15 Step 5: Convert 10/3 to fifteenths: (10 × 5)/(3 × 5) = 50/15 Step 6: Subtract the fractions: 111/15 - 50/15 = 61/15 Step 7: Convert 61/15 to a mixed number: 61 ÷ 15 = 4 with remainder 1, so 4 1/15 The answer is 4 1/15.

  6. Emma is baking cookies for a school fundraiser. She needs 2 3/4 cups of flour for the chocolate chip cookies and 1 5/8 cups of flour for the oatmeal raisin cookies. If she starts with a 5-pound bag of flour that contains approximately 18 cups total, how many cups of flour will she have left after baking both types of cookies? Answer: 13.625 Solution: 2 3/4 + 1 5/8 = 11/4 + 13/8 Convert to common denominator (8) 11/4 = 22/8 22/8 + 13/8 = 35/8 35/8 = 4.375 cups used 18 - 4.375 = 13.625 cups remaining The answer is 13.625.
    Full step-by-step solution

    Step 1: Find the total flour used for both cookie types 2 3/4 + 1 5/8 = 11/4 + 13/8 Step 2: Convert to common denominator (8) 11/4 = 22/8 22/8 + 13/8 = 35/8 Step 3: Convert to decimal 35/8 = 4.375 cups used Step 4: Subtract from starting amount 18 - 4.375 = 13.625 cups remaining The answer is 13.625.

  7. 3 2/5 + 1 3/4 - 2 1/10 = ? Answer: 3 1/20 Solution: 3 2/5 = (3 × 5 + 2)/5 = 17/5 1 3/4 = (1 × 4 + 3)/4 = 7/4 2 1/10 = (2 × 10 + 1)/10 = 21/10 Find a common denominator for 5, 4, and 10 The least common multiple is 20 Convert all fractions to have denominator 20 17/5 = (17 × 4)/(5 × 4) = 68/20 7/4 = (7 × 5)/(4 × 5) = 35/20 21/10 = (21 × 2)/(10 ×…
    Full step-by-step solution

    Step 1: Convert all mixed numbers to improper fractions 3 2/5 = (3 × 5 + 2)/5 = 17/5 1 3/4 = (1 × 4 + 3)/4 = 7/4 2 1/10 = (2 × 10 + 1)/10 = 21/10 Step 2: Find a common denominator for 5, 4, and 10 The least common multiple is 20 Step 3: Convert all fractions to have denominator 20 17/5 = (17 × 4)/(5 × 4) = 68/20 7/4 = (7 × 5)/(4 × 5) = 35/20 21/10 = (21 × 2)/(10 × 2) = 42/20 Step 4: Perform the operations from left to right 68/20 + 35/20 - 42/20 = (68 + 35)/20 - 42/20 = 103/20 - 42/20 Step 5: Complete the subtraction 103/20 - 42/20 = 61/20 Step 6: Convert back to a mixed number 61/20 = 3 1/20 The answer is 3 1/20.