Mixed Numbers Unlike

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Mixed Numbers Unlike · Grade 5 · Worksheet 2

1. 4 3/5 + 2 7/8 = ? Answer: 7 19/40 Solution: Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Convert 2 7/8 to an improper fraction: (2 × 8 + 7)/8 = (16 + 7)/8 = 23/8 Find a common denominator for 5 and 8, which is 40 Convert 23/5 to fortieths: (23 × 8)/(5 × 8) = 184/40 Convert 23/8 to fortieths: (23 × 5)/(8 × 5) =…
   Full step-by-step solution

   Step 1: Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Step 2: Convert 2 7/8 to an improper fraction: (2 × 8 + 7)/8 = (16 + 7)/8 = 23/8 Step 3: Find a common denominator for 5 and 8, which is 40 Step 4: Convert 23/5 to fortieths: (23 × 8)/(5 × 8) = 184/40 Step 5: Convert 23/8 to fortieths: (23 × 5)/(8 × 5) = 115/40 Step 6: Add the fractions: 184/40 + 115/40 = 299/40 Step 7: Convert 299/40 to a mixed number: 299 ÷ 40 = 7 with remainder 19, so 7 19/40 The answer is 7 19/40.

2. 3 1/2 + 2 3/4 - 1 1/8 = ? Answer: 5 1/8 Solution: Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Convert 2 3/4 to an improper fraction: 2 3/4 = (2 × 4 + 3)/4 = 11/4 Convert 1 1/8 to an improper fraction: 1 1/8 = (1 × 8 + 1)/8 = 9/8 Find a common denominator for 2, 4, and 8, which is 8 Convert 7/2 to eighths: 7/2 = (7 × 4)/(2…
   Full step-by-step solution

   Step 1: Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Step 2: Convert 2 3/4 to an improper fraction: 2 3/4 = (2 × 4 + 3)/4 = 11/4 Step 3: Convert 1 1/8 to an improper fraction: 1 1/8 = (1 × 8 + 1)/8 = 9/8 Step 4: Find a common denominator for 2, 4, and 8, which is 8 Step 5: Convert 7/2 to eighths: 7/2 = (7 × 4)/(2 × 4) = 28/8 Step 6: Convert 11/4 to eighths: 11/4 = (11 × 2)/(4 × 2) = 22/8 Step 7: Now we have: 28/8 + 22/8 - 9/8 Step 8: Add the first two fractions: 28/8 + 22/8 = 50/8 Step 9: Subtract the third fraction: 50/8 - 9/8 = 41/8 Step 10: Convert 41/8 to a mixed number: 41 ÷ 8 = 5 with remainder 1, so 41/8 = 5 1/8 The answer is 5 1/8.

3. 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.

4. Liam is building a bookshelf and needs to cut two pieces of wood. The first piece needs to be 3.75 meters long and the second piece needs to be 2.125 meters long. How many total meters of wood does Liam need to cut for these two pieces? Answer: 5.875 Solution: To find the total meters of wood Liam needs, we add the two given lengths together. Write down the two lengths that need to be added. First piece: 3.75 meters Second piece: 2.125 meters Set up the addition problem.
   Full step-by-step solution

   To find the total meters of wood Liam needs, we add the two given lengths together. Step 1: Write down the two lengths that need to be added. First piece: 3.75 meters Second piece: 2.125 meters Step 2: Set up the addition problem. It is helpful to line up the decimal points to ensure we are adding digits in the correct place value. 3.750 (We can write 3.75 as 3.750 to make it easier to add) + 2.125 Step 3: Add the numbers column by column, starting from the rightmost digit (the thousandths place). - Thousandths place: 0 + 5 = 5. Write down 5. - Hundredths place: 5 + 2 = 7. Write down 7. - Tenths place: 7 + 1 = 8. Write down 8. - Units place: 3 + 2 = 5. Write down 5. - Decimal point: Bring down the decimal point. Step 4: Write the final answer from the addition. The result of adding the columns is 5.875. Therefore, the total meters of wood Liam needs to cut is 5.875 meters.

5. 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.

6. 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.

7. 4 3/5 - 2 2/3 = ? Answer: 1 14/15 Solution: Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Convert 2 2/3 to an improper fraction: (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3 Find a common denominator for 5 and 3, which is 15 Convert 23/5 to fifteenths: (23 × 3)/(5 × 3) = 69/15 Convert 8/3 to fifteenths: (8 × 5)/(3 × 5) =…
   Full step-by-step solution

   Step 1: Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Step 2: Convert 2 2/3 to an improper fraction: (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3 Step 3: Find a common denominator for 5 and 3, which is 15 Step 4: Convert 23/5 to fifteenths: (23 × 3)/(5 × 3) = 69/15 Step 5: Convert 8/3 to fifteenths: (8 × 5)/(3 × 5) = 40/15 Step 6: Subtract the fractions: 69/15 - 40/15 = 29/15 Step 7: Convert 29/15 to a mixed number: 29 ÷ 15 = 1 with remainder 14, so 1 14/15 The answer is 1 14/15.

8. A triangular garden has sides measuring 12.6 meters, 15.8 meters, and 18.4 meters. A fence needs to be installed around the entire perimeter of the garden. What is the total length of fencing needed? Answer: 46.8 Solution: Identify that perimeter is the sum of all side lengths Add the three side lengths: 12.6 + 15.8 + 18.4 First add 12.6 + 15.8 = 28.4 Then add 28.4 + 18.4 = 46.8 The total fencing needed is 46.8 meters
   Full step-by-step solution

   Step 1: Identify that perimeter is the sum of all side lengths Step 2: Add the three side lengths: 12.6 + 15.8 + 18.4 Step 3: First add 12.6 + 15.8 = 28.4 Step 4: Then add 28.4 + 18.4 = 46.8 Step 5: The total fencing needed is 46.8 meters