Mixed Numbers Unlike

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Answer Key & Explanations

Mixed Numbers Unlike · Grade 5 · Worksheet 2

1. A rectangular prism has a length of 12.5 cm, a width of 8.4 cm, and a height of 6.3 cm. What is the volume of this prism? Answer: 661.5 Solution: To find the volume of a rectangular prism, we multiply its length by its width by its height. Write down the formula for volume. Volume = length × width × height Substitute the given values into the formula.
   Full step-by-step solution

   To find the volume of a rectangular prism, we multiply its length by its width by its height. Step 1: Write down the formula for volume. Volume = length × width × height Step 2: Substitute the given values into the formula. Volume = 12.5 cm × 8.4 cm × 6.3 cm Step 3: First, multiply the length and the width. 12.5 × 8.4 We can calculate this step-by-step. First, 12.5 × 8 = 100 Next, 12.5 × 0.4 = 5 Now, add the two results: 100 + 5 = 105 So, 12.5 × 8.4 = 105 Step 4: Now multiply this result by the height. 105 × 6.3 We can calculate this step-by-step. First, 105 × 6 = 630 Next, 105 × 0.3 = 31.5 Now, add the two results: 630 + 31.5 = 661.5 Step 5: State the final answer with the correct units. The volume is 661.5 cubic centimeters. Therefore, the volume of the rectangular prism is 661.5.

2. 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.

3. A construction worker needs to install two pipes. The first pipe measures 7 3/8 feet long and the second pipe measures 5 5/6 feet long. What is the total length of the two pipes combined? Answer: 13 5/24 Solution: Convert 7 3/8 to an improper fraction: (7 × 8 + 3)/8 = (56 + 3)/8 = 59/8 Convert 5 5/6 to an improper fraction: (5 × 6 + 5)/6 = (30 + 5)/6 = 35/6 Find a common denominator for 8 and 6, which is 24 Convert 59/8 to have denominator 24: (59 × 3)/(8 × 3) = 177/24 Convert 35/6 to have denominator 24:…
   Full step-by-step solution

   Step 1: Convert 7 3/8 to an improper fraction: (7 × 8 + 3)/8 = (56 + 3)/8 = 59/8 Step 2: Convert 5 5/6 to an improper fraction: (5 × 6 + 5)/6 = (30 + 5)/6 = 35/6 Step 3: Find a common denominator for 8 and 6, which is 24 Step 4: Convert 59/8 to have denominator 24: (59 × 3)/(8 × 3) = 177/24 Step 5: Convert 35/6 to have denominator 24: (35 × 4)/(6 × 4) = 140/24 Step 6: Add the fractions: 177/24 + 140/24 = 317/24 Step 7: Convert back to a mixed number: 317 ÷ 24 = 13 with remainder 5, so 13 5/24 The answer is 13 5/24.

4. 7 2/3 - 4 3/8 = ? Answer: 3 7/24 Solution: Convert 7 2/3 to an improper fraction: (7 × 3 + 2)/3 = (21 + 2)/3 = 23/3 Convert 4 3/8 to an improper fraction: (4 × 8 + 3)/8 = (32 + 3)/8 = 35/8 Find a common denominator for 3 and 8, which is 24 Convert 23/3 to twenty-fourths: (23 × 8)/(3 × 8) = 184/24 Convert 35/8 to twenty-fourths: (35 ×…
   Full step-by-step solution

   Step 1: Convert 7 2/3 to an improper fraction: (7 × 3 + 2)/3 = (21 + 2)/3 = 23/3 Step 2: Convert 4 3/8 to an improper fraction: (4 × 8 + 3)/8 = (32 + 3)/8 = 35/8 Step 3: Find a common denominator for 3 and 8, which is 24 Step 4: Convert 23/3 to twenty-fourths: (23 × 8)/(3 × 8) = 184/24 Step 5: Convert 35/8 to twenty-fourths: (35 × 3)/(8 × 3) = 105/24 Step 6: Subtract the fractions: 184/24 - 105/24 = 79/24 Step 7: Convert 79/24 to a mixed number: 79 ÷ 24 = 3 with remainder 7, so 3 7/24 The answer is 3 7/24.

5. 3 2/7 + 1 3/4 = ? Answer: 5 1/28 Solution: Convert 3 2/7 to an improper fraction: (3 × 7 + 2)/7 = (21 + 2)/7 = 23/7 Convert 1 3/4 to an improper fraction: (1 × 4 + 3)/4 = (4 + 3)/4 = 7/4 Find a common denominator for 7 and 4, which is 28 Convert 23/7 to twenty-eighths: (23 × 4)/(7 × 4) = 92/28 Convert 7/4 to twenty-eighths: (7 × 7)/(4 ×…
   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 1 3/4 to an improper fraction: (1 × 4 + 3)/4 = (4 + 3)/4 = 7/4 Step 3: Find a common denominator for 7 and 4, which is 28 Step 4: Convert 23/7 to twenty-eighths: (23 × 4)/(7 × 4) = 92/28 Step 5: Convert 7/4 to twenty-eighths: (7 × 7)/(4 × 7) = 49/28 Step 6: Add the fractions: 92/28 + 49/28 = 141/28 Step 7: Convert 141/28 to a mixed number: 141 ÷ 28 = 5 with remainder 1, so 5 1/28 The answer is 5 1/28.

6. A rectangular prism has a length of 12.5 cm, a width of 8.4 cm, and a height of 6.3 cm. What is the volume of this rectangular prism? Answer: 661.5 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Length = 12.5 cm Width = 8.4 cm Height = 6.3 cm 12.5 × 8.4 First, multiply 125 × 84 for easier calculation (ignoring decimals for now): 125 × 84 = 125 × (80 + 4) = 125 × 80 + 125 × 4 125 × 80 = 10,000…
   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 = 12.5 cm Width = 8.4 cm Height = 6.3 cm Step 2: Multiply the length and width first: 12.5 × 8.4 First, multiply 125 × 84 for easier calculation (ignoring decimals for now): 125 × 84 = 125 × (80 + 4) = 125 × 80 + 125 × 4 125 × 80 = 10,000 125 × 4 = 500 10,000 + 500 = 10,500 Now, since we ignored two decimal places (one from 12.5 and one from 8.4), we put back two decimal places: 10,500 becomes 105.00 So, 12.5 × 8.4 = 105.0 Step 3: Multiply the result by the height: 105.0 × 6.3 Multiply 105 × 63 (ignoring decimals for now): 105 × 63 = 105 × (60 + 3) = 105 × 60 + 105 × 3 105 × 60 = 6,300 105 × 3 = 315 6,300 + 315 = 6,615 Now, since we ignored one decimal place from 6.3, we put back one decimal place: 6,615 becomes 661.5 Step 4: Final answer: Volume = 661.5 cubic centimeters Answer: 661.5