Mixed Numbers Unlike

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Answer Key & Explanations

Mixed Numbers Unlike · Grade 5 · Worksheet 1

1. 4 3/8 + 2 2/5 = ? Answer: 6 31/40 Solution: Convert 4 3/8 to an improper fraction: (4 × 8 + 3)/8 = (32 + 3)/8 = 35/8 Convert 2 2/5 to an improper fraction: (2 × 5 + 2)/5 = (10 + 2)/5 = 12/5 Find a common denominator for 8 and 5, which is 40 Convert 35/8 to fortieths: (35 × 5)/(8 × 5) = 175/40 Convert 12/5 to fortieths: (12 × 8)/(5 × 8) =…
   Full step-by-step solution

   Step 1: Convert 4 3/8 to an improper fraction: (4 × 8 + 3)/8 = (32 + 3)/8 = 35/8 Step 2: Convert 2 2/5 to an improper fraction: (2 × 5 + 2)/5 = (10 + 2)/5 = 12/5 Step 3: Find a common denominator for 8 and 5, which is 40 Step 4: Convert 35/8 to fortieths: (35 × 5)/(8 × 5) = 175/40 Step 5: Convert 12/5 to fortieths: (12 × 8)/(5 × 8) = 96/40 Step 6: Add the fractions: 175/40 + 96/40 = 271/40 Step 7: Convert 271/40 to a mixed number: 271 ÷ 40 = 6 with remainder 31, so 6 31/40 The answer is 6 31/40.

2. A rectangular prism-shaped fish tank has a length of 15.2 cm, a width of 8.7 cm, and a height of 12.5 cm. What is the volume of this fish tank in cubic centimeters? Answer: 1653 Solution: Recall that volume of a rectangular prism = length × width × height Multiply the three dimensions: 15.2 × 8.7 × 12.5 First multiply 15.2 × 8.7 = 132.24 Then multiply 132.24 × 12.5 = 1653 The volume is 1653 cubic centimeters The answer is 1653.
   Full step-by-step solution

   Step 1: Recall that volume of a rectangular prism = length × width × height Step 2: Multiply the three dimensions: 15.2 × 8.7 × 12.5 Step 3: First multiply 15.2 × 8.7 = 132.24 Step 4: Then multiply 132.24 × 12.5 = 1653 Step 5: The volume is 1653 cubic centimeters The answer is 1653.

3. Maria 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 sugar 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 3/8 cups used Convert 4 3/8 to decimal for easier subtraction 4 3/8 = 4 + 0.375 = 4.375 cups used 18 - 4.375 = 13.625 cups remaining The answer is 13.625 cups.
   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 improper fraction to mixed number 35/8 = 4 3/8 cups used Step 4: Convert 4 3/8 to decimal for easier subtraction 4 3/8 = 4 + 0.375 = 4.375 cups used Step 5: Subtract from starting amount 18 - 4.375 = 13.625 cups remaining The answer is 13.625 cups.

4. 3 2/5 + 1 3/4 = ? Answer: 5 3/20 Solution: Convert 3 2/5 to an improper fraction: (3 × 5) + 2 = 15 + 2 = 17, so 3 2/5 = 17/5 Convert 1 3/4 to an improper fraction: (1 × 4) + 3 = 4 + 3 = 7, so 1 3/4 = 7/4 Find a common denominator for 5 and 4, which is 20 Convert 17/5 to twentieths: 17/5 = (17 × 4)/(5 × 4) = 68/20 Convert 7/4 to…
   Full step-by-step solution

   Step 1: Convert 3 2/5 to an improper fraction: (3 × 5) + 2 = 15 + 2 = 17, so 3 2/5 = 17/5 Step 2: Convert 1 3/4 to an improper fraction: (1 × 4) + 3 = 4 + 3 = 7, so 1 3/4 = 7/4 Step 3: Find a common denominator for 5 and 4, which is 20 Step 4: Convert 17/5 to twentieths: 17/5 = (17 × 4)/(5 × 4) = 68/20 Step 5: Convert 7/4 to twentieths: 7/4 = (7 × 5)/(4 × 5) = 35/20 Step 6: Add the fractions: 68/20 + 35/20 = 103/20 Step 7: Convert back to a mixed number: 103 ÷ 20 = 5 with remainder 3, so 103/20 = 5 3/20 The answer is 5 3/20.

5. 5 3/4 + 2 2/5 = ? Answer: 8 3/20 Solution: Convert 5 3/4 to an improper fraction: 5 × 4 + 3 = 23/4 Convert 2 2/5 to an improper fraction: 2 × 5 + 2 = 12/5 Find a common denominator for 4 and 5, which is 20 Convert 23/4 to twentieths: 23/4 = 115/20 Convert 12/5 to twentieths: 12/5 = 48/20 Add the fractions: 115/20 + 48/20 = 163/20 Convert…
   Full step-by-step solution

   Step 1: Convert 5 3/4 to an improper fraction: 5 × 4 + 3 = 23/4 Step 2: Convert 2 2/5 to an improper fraction: 2 × 5 + 2 = 12/5 Step 3: Find a common denominator for 4 and 5, which is 20 Step 4: Convert 23/4 to twentieths: 23/4 = 115/20 Step 5: Convert 12/5 to twentieths: 12/5 = 48/20 Step 6: Add the fractions: 115/20 + 48/20 = 163/20 Step 7: Convert back to a mixed number: 163 ÷ 20 = 8 remainder 3, so 8 3/20 The answer is 8 3/20.

6. Isabella is training for a race. On Monday, Isabella ran 5 miles. On Tuesday, Isabella ran 1 miles. How many more miles did Isabella run on Monday than on Tuesday? Answer: 4 Solution: Distance on Monday: 5 miles. Distance on Tuesday: 1 miles. Subtract to find the difference: 5 - 1 = 4.
   Full step-by-step solution

   Step 1: Distance on Monday: 5 miles. Step 2: Distance on Tuesday: 1 miles. Step 3: Subtract to find the difference: 5 - 1 = 4. The answer is 4 miles.

7. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 24 meters long by 18 meters wide. What is the area of one triangular section? Answer: 216 Solution: Area of rectangle = length × width = 24 m × 18 m = 432 square meters A diagonal divides a rectangle into two congruent triangles of equal area Area of one triangle = Total area ÷ 2 = 432 ÷ 2 = 216 square meters The answer is 216.
   Full step-by-step solution

   Step 1: Find the area of the entire rectangular garden Area of rectangle = length × width = 24 m × 18 m = 432 square meters Step 2: Understand how the diagonal divides the rectangle A diagonal divides a rectangle into two congruent triangles of equal area Step 3: Calculate the area of one triangular section Area of one triangle = Total area ÷ 2 = 432 ÷ 2 = 216 square meters The answer is 216.