Mixed Numbers Unlike

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Answer Key & Explanations

Mixed Numbers Unlike · Grade 5 · Worksheet 3

1. Lily is baking cookies. The recipe calls for 5 cups of flour and 2 cups of sugar. How many total cups of dry ingredients does Lily need? Answer: 7 Solution: The recipe needs 5 cups of flour. The recipe needs 2 cups of sugar. Add the amounts: 5 + 2 = 7.
   Full step-by-step solution

   Step 1: The recipe needs 5 cups of flour. Step 2: The recipe needs 2 cups of sugar. Step 3: Add the amounts: 5 + 2 = 7. The answer is 7 cups of dry ingredients.

2. Zoe is baking cookies. The recipe calls for 5 cups of flour and 3 cups of sugar. How many total cups of dry ingredients does Zoe need? Answer: 8 Solution: The recipe needs 5 cups of flour. The recipe needs 3 cups of sugar. Add the amounts: 5 + 3 = 8.
   Full step-by-step solution

   Step 1: The recipe needs 5 cups of flour. Step 2: The recipe needs 3 cups of sugar. Step 3: Add the amounts: 5 + 3 = 8. The answer is 8 cups of dry ingredients.

3. Kai is training for a race. On Monday, Kai ran 2 miles. On Tuesday, Kai ran 1 miles. How many more miles did Kai run on Monday than on Tuesday? Answer: 1 Solution: Distance on Monday: 2 miles. Distance on Tuesday: 1 miles. Subtract to find the difference: 2 - 1 = 1.
   Full step-by-step solution

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

4. A rectangular prism has a length of 15.6 cm, a width of 9.8 cm, and a height of 7.5 cm. What is the volume of this prism? Answer: 1146.6 Solution: Recall the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 15.6 × 9.8 × 7.5 First multiply 15.6 × 9.8 15.6 × 9.8 = 15.6 × (10 - 0.2) = 15.6 × 10 - 15.6 × 0.2 = 156 - 3.12 = 152.88 Now multiply the result by the height: 152.88 ×…
   Full step-by-step solution

   Step 1: Recall the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 15.6 × 9.8 × 7.5 Step 3: First multiply 15.6 × 9.8 15.6 × 9.8 = 15.6 × (10 - 0.2) = 15.6 × 10 - 15.6 × 0.2 = 156 - 3.12 = 152.88 Step 4: Now multiply the result by the height: 152.88 × 7.5 152.88 × 7.5 = 152.88 × (7 + 0.5) = 152.88 × 7 + 152.88 × 0.5 = 1070.16 + 76.44 = 1146.6 Step 5: The volume is 1146.6 cubic centimeters The answer is 1146.6.

5. 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.

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. 7 2/3 - 4 3/5 = ? Answer: 3 1/15 Solution: Convert 7 2/3 to an improper fraction: (7 × 3 + 2)/3 = (21 + 2)/3 = 23/3 Convert 4 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Find a common denominator for 3 and 5, which is 15 Convert 23/3 to fifteenths: (23 × 5)/(3 × 5) = 115/15 Convert 23/5 to fifteenths: (23 × 3)/(5 × 3)…
   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 3/5 to an improper fraction: (4 × 5 + 3)/5 = (20 + 3)/5 = 23/5 Step 3: Find a common denominator for 3 and 5, which is 15 Step 4: Convert 23/3 to fifteenths: (23 × 5)/(3 × 5) = 115/15 Step 5: Convert 23/5 to fifteenths: (23 × 3)/(5 × 3) = 69/15 Step 6: Subtract the fractions: 115/15 - 69/15 = 46/15 Step 7: Convert 46/15 to a mixed number: 46 ÷ 15 = 3 with remainder 1, so 3 1/15 The answer is 3 1/15.