Add/Subtract Mixed Numbers

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Add/Subtract Mixed Numbers · Grade 4 · Worksheet 2

1. A rectangular garden is drawn with a length of 12.5 meters and a width of 8.4 meters. What is the perimeter of the garden? Answer: 41.8 Solution: We have a rectangular garden with length = 12.5 meters and width = 8.4 meters.
   Full step-by-step solution

   Step 1: Understand the problem We have a rectangular garden with length = 12.5 meters and width = 8.4 meters. The perimeter of a rectangle is the total distance around the outside, which can be found using the formula: Perimeter = 2 × (length + width) Step 2: Add length and width Length + width = 12.5 + 8.4 First, add the decimal parts carefully: 12.5 + 8.4 = 12.5 + 8.0 + 0.4 = 20.5 + 0.4 = 20.9 So, length + width = 20.9 meters. Step 3: Multiply by 2 Perimeter = 2 × 20.9 2 × 20.9 = 2 × 20 + 2 × 0.9 = 40 + 1.8 = 41.8 Step 4: Final answer The perimeter of the garden is 41.8 meters.

2. Liam is making a fruit salad for a party. He uses 2 1/4 cups of strawberries and 1 3/4 cups of blueberries. How many total cups of fruit does Liam use in his fruit salad? Answer: 4 cups Solution: Identify the amounts of each fruit. Liam uses 2 1/4 cups of strawberries and 1 3/4 cups of blueberries. Write the total as a sum.
   Full step-by-step solution

   Step 1: Identify the amounts of each fruit. Liam uses 2 1/4 cups of strawberries and 1 3/4 cups of blueberries. Step 2: Write the total as a sum. Total fruit = 2 1/4 + 1 3/4 Step 3: Add the whole numbers first. 2 + 1 = 3 Step 4: Add the fractions. 1/4 + 3/4 = 4/4 Step 5: Simplify 4/4. 4/4 = 1 Step 6: Combine the whole number total and the fraction total. 3 + 1 = 4 Step 7: State the final answer. Liam uses 4 cups of fruit in total.

3. A farmer harvested 3 1/4 bushels of apples in the morning and 2 3/8 bushels in the afternoon. How many bushels of apples did the farmer harvest in total? Answer: 5 5/8 Solution: Write the quantities as mixed numbers. Morning: 3 1/4 bushels Afternoon: 2 3/8 bushels Add the whole numbers first. 3 + 2 = 5 Now add the fractions: 1/4 + 3/8 To add these, we need a common denominator.
   Full step-by-step solution

   Let's add the two amounts step by step. Step 1: Write the quantities as mixed numbers. Morning: 3 1/4 bushels Afternoon: 2 3/8 bushels Step 2: Add the whole numbers first. 3 + 2 = 5 Step 3: Now add the fractions: 1/4 + 3/8 To add these, we need a common denominator. The least common denominator of 4 and 8 is 8. Step 4: Convert 1/4 to eighths. 1/4 = (1 × 2)/(4 × 2) = 2/8 Step 5: Now add the fractions with common denominator: 2/8 + 3/8 = (2 + 3)/8 = 5/8 Step 6: Combine the whole number sum and the fraction sum: 5 + 5/8 = 5 5/8 So, the total harvest is 5 5/8 bushels. Final answer: 5 5/8

4. Mere is drawing a rectangular vegetable patch on grid paper. The length of the patch is 15 3/4 meters and the width is 11 1/4 meters. What is the total perimeter of the vegetable patch? Answer: 54 Solution: The perimeter of a rectangle is the sum of all four sides. Since opposite sides are equal, perimeter = 2 × length + 2 × width. Length = 15 3/4 meters, Width = 11 1/4 meters.
   Full step-by-step solution

   Step 1: The perimeter of a rectangle is the sum of all four sides. Since opposite sides are equal, perimeter = 2 × length + 2 × width. Step 2: Length = 15 3/4 meters, Width = 11 1/4 meters. Step 3: Calculate 2 × length: 2 × 15 3/4 = 2 × (63/4) = 126/4 = 31 2/4. Step 4: Calculate 2 × width: 2 × 11 1/4 = 2 × (45/4) = 90/4 = 22 2/4. Step 5: Add the two results: 31 2/4 + 22 2/4 = 53 4/4 = 54. Step 6: The total perimeter is 54 meters.

5. Emma is drawing a rectangular picture frame on grid paper. The length of the frame is 137 3/5 millimeters and the width is 95 1/5 millimeters. What is the total perimeter of the picture frame? Answer: 465 3/5 Solution: The perimeter of a rectangle is the sum of all four sides. Since opposite sides are equal, perimeter = 2 × length + 2 × width, or 2 × (length + width). Length = 137 3/5 millimeters, Width = 95 1/5 millimeters.
   Full step-by-step solution

   Step 1: The perimeter of a rectangle is the sum of all four sides. Since opposite sides are equal, perimeter = 2 × length + 2 × width, or 2 × (length + width). Step 2: Length = 137 3/5 millimeters, Width = 95 1/5 millimeters. Step 3: Add the length and width: 137 3/5 + 95 1/5 = 232 4/5 (since 137 + 95 = 232 and 3/5 + 1/5 = 4/5). Step 4: Double the sum: 2 × 232 4/5 = 2 × (1164/5) = 2328/5 = 465 3/5 (since 2328 ÷ 5 = 465 remainder 3). Step 5: The total perimeter is 465 3/5 millimeters.

6. Charlotte is reading a book that has 43 pages. Charlotte has already read 15 pages. How many pages does Charlotte have left to read? Answer: 28 Solution: The book has 43 pages in total. Charlotte has read 15 pages so far. Subtract to find how many are left: 43 - 15 = 28 pages.
   Full step-by-step solution

   Step 1: The book has 43 pages in total. Step 2: Charlotte has read 15 pages so far. Step 3: Subtract to find how many are left: 43 - 15 = 28 pages. The answer is 28.

7. A carpenter needs to cut a board that is 4 3/4 feet long. She already has a piece that is 2 1/2 feet long. How many more feet does she need to cut to reach the required length? Answer: 2.25 Solution: Write the problem as a subtraction: 4 3/4 - 2 1/2 Convert mixed numbers to improper fractions: 4 3/4 = 19/4 and 2 1/2 = 5/2 Find a common denominator to subtract: 5/2 = 10/4 Subtract the fractions: 19/4 - 10/4 = 9/4 Convert back to a mixed number: 9/4 = 2 1/4 Convert to decimal: 2 1/4 = 2.25 The…
   Full step-by-step solution

   Step 1: Write the problem as a subtraction: 4 3/4 - 2 1/2 Step 2: Convert mixed numbers to improper fractions: 4 3/4 = 19/4 and 2 1/2 = 5/2 Step 3: Find a common denominator to subtract: 5/2 = 10/4 Step 4: Subtract the fractions: 19/4 - 10/4 = 9/4 Step 5: Convert back to a mixed number: 9/4 = 2 1/4 Step 6: Convert to decimal: 2 1/4 = 2.25 The answer is 2.25.