Mixed Numbers Unlike

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Answer Key & Explanations

Mixed Numbers Unlike · Grade 5 · Worksheet 1

1. Mere is drawing a rectangular garden on grid paper. The length of the garden is 10 3/5 cm and the width is 6 2/3 cm. What is the perimeter of Mere's garden rectangle? (Express your answer as a mixed number in simplest form.) Answer: 34 8/15 cm Solution: The perimeter of a rectangle is twice the sum of its length and width: P = 2 × (length + width). Length = 10 3/5, Width = 6 2/3. First, find a common denominator for 3/5 and 2/3.
   Full step-by-step solution

   Step 1: The perimeter of a rectangle is twice the sum of its length and width: P = 2 × (length + width). Step 2: Length = 10 3/5, Width = 6 2/3. First, find a common denominator for 3/5 and 2/3. The least common multiple of 5 and 3 is 15. Step 3: Convert the fractions: 3/5 = (3×3)/(5×3) = 9/15. 2/3 = (2×5)/(3×5) = 10/15. Step 4: Add the whole numbers: 10 + 6 = 16. Add the fractions: 9/15 + 10/15 = 19/15. So the sum is 16 + 19/15 = 16 + 1 4/15 = 17 4/15. Step 5: Now double the sum: 2 × 17 4/15 = 34 + 8/15 = 34 8/15. The perimeter of Mere's garden rectangle is 34 8/15 cm.

2. 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.

3. 4 2/5 + 3 3/4 = ? Answer: 8 3/20 Solution: Convert 4 2/5 to an improper fraction: (4 × 5 + 2)/5 = (20 + 2)/5 = 22/5 Convert 3 3/4 to an improper fraction: (3 × 4 + 3)/4 = (12 + 3)/4 = 15/4 Find a common denominator for 5 and 4, which is 20 Convert 22/5 to twentieths: (22 × 4)/(5 × 4) = 88/20 Convert 15/4 to twentieths: (15 × 5)/(4 × 5) =…
   Full step-by-step solution

   Step 1: Convert 4 2/5 to an improper fraction: (4 × 5 + 2)/5 = (20 + 2)/5 = 22/5 Step 2: Convert 3 3/4 to an improper fraction: (3 × 4 + 3)/4 = (12 + 3)/4 = 15/4 Step 3: Find a common denominator for 5 and 4, which is 20 Step 4: Convert 22/5 to twentieths: (22 × 4)/(5 × 4) = 88/20 Step 5: Convert 15/4 to twentieths: (15 × 5)/(4 × 5) = 75/20 Step 6: Add the fractions: 88/20 + 75/20 = 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.

4. 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 the fish tank in cubic centimeters? Answer: 1653 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 15.2 cm × 8.7 cm × 12.5 cm First multiply 15.2 × 8.7: 15.2 × 8 = 121.6 15.2 × 0.7 = 10.64 121.6 + 10.64 = 132.24 Now multiply 132.24 × 12.5: 132.24 × 10 = 1322.4 132.24…
   Full step-by-step solution

   Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 15.2 cm × 8.7 cm × 12.5 cm Step 3: First multiply 15.2 × 8.7: 15.2 × 8 = 121.6 15.2 × 0.7 = 10.64 121.6 + 10.64 = 132.24 Step 4: Now multiply 132.24 × 12.5: 132.24 × 10 = 1322.4 132.24 × 2 = 264.48 132.24 × 0.5 = 66.12 1322.4 + 264.48 = 1586.88 1586.88 + 66.12 = 1653 Step 5: The volume is 1653 cubic centimeters.

5. Noah is drawing a scale model of a rectangular playground. On his grid paper, the length of the playground is 8 5/6 cm and the width is 6 3/4 cm. What is the perimeter of Noah's playground model? (Express your answer as a mixed number in simplest form.) Answer: 31 1/6 cm Solution: The perimeter of a rectangle is twice the sum of its length and width: P = 2 × (length + width). Length = 8 5/6, Width = 6 3/4. First, find a common denominator for 5/6 and 3/4.
   Full step-by-step solution

   Step 1: The perimeter of a rectangle is twice the sum of its length and width: P = 2 × (length + width). Step 2: Length = 8 5/6, Width = 6 3/4. First, find a common denominator for 5/6 and 3/4. The least common multiple of 6 and 4 is 12. Step 3: Convert the fractions: 5/6 = (5×2)/(6×2) = 10/12. 3/4 = (3×3)/(4×3) = 9/12. Step 4: Add the whole numbers: 8 + 6 = 14. Add the fractions: 10/12 + 9/12 = 19/12 = 1 7/12. So the sum is 14 + 1 7/12 = 15 7/12. Step 5: Now double the sum: 2 × 15 7/12 = 30 + 14/12 = 30 + 1 2/12 = 31 2/12. Simplify 2/12 to 1/6. The perimeter of Noah's playground model is 31 1/6 cm.

6. 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.

7. 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. If he starts with an 8-meter board, how many meters of wood will he have left after making the two cuts? Answer: 2.125 Solution: Liam starts with an 8-meter board. - First piece = 3.75 meters - Second piece = 2.125 meters We need to find the remaining length after cutting both pieces from the 8-meter board. 3.75 + 2.125 = ?
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the problem** Liam starts with an 8-meter board. He cuts two pieces: - First piece = 3.75 meters - Second piece = 2.125 meters We need to find the remaining length after cutting both pieces from the 8-meter board. --- **Step 2: Add the lengths of the two pieces** 3.75 + 2.125 = ? First, add the whole numbers: 3 + 2 = 5 Now add the decimals: 0.75 + 0.125 = 0.875 So total length used = 5 + 0.875 = 5.875 meters --- **Step 3: Subtract from the original board** Original board length = 8 meters Remaining wood = 8 - 5.875 We can subtract step by step: 8.000 - 5.875 First, subtract thousandths: 8.000 - 5.875 = (8.000 - 5.000) - 0.875 = 3.000 - 0.875 Now, 3.000 - 0.875 = 2.125 --- **Step 4: Conclusion** After cutting the two pieces, Liam will have **2.125 meters** of wood left. --- **Final Answer:** 2.125