Add/Subtract Mixed Numbers

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Answer Key & Explanations

Add/Subtract Mixed Numbers · Grade 4 · Worksheet 1

1. Hana is drawing a rectangular hiking trail map on grid paper. The length of the trail map is 110 3/9 meters and the width is 95 2/9 meters. What is the total perimeter of the trail map? Answer: 411 1/9 Solution: The perimeter of a rectangle is the sum of all four sides. Since opposite sides are equal, perimeter = 2 × length + 2 × width. Length = 110 3/9 meters, Width = 95 2/9 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 = 110 3/9 meters, Width = 95 2/9 meters. Step 3: Calculate 2 × length: 2 × 110 3/9 = 2 × (993/9) = 1986/9 = 220 6/9. Step 4: Calculate 2 × width: 2 × 95 2/9 = 2 × (857/9) = 1714/9 = 190 4/9. Step 5: Add the two results: 220 6/9 + 190 4/9 = 410 10/9 = 410 + 1 1/9 = 411 1/9. Step 6: Simplify the fraction: 1/9 is already in simplest form. Step 7: The total perimeter is 411 1/9 meters.

2. Oliver is reading a book that has 40 pages. Oliver has already read 22 pages. How many pages does Oliver have left to read? Answer: 18 Solution: The book has 40 pages in total. Oliver has read 22 pages so far. Subtract to find how many are left: 40 - 22 = 18 pages.
   Full step-by-step solution

   Step 1: The book has 40 pages in total. Step 2: Oliver has read 22 pages so far. Step 3: Subtract to find how many are left: 40 - 22 = 18 pages. The answer is 18.

3. Nikau has 10 stickers in a collection. Nikau's friend gives them 9 more stickers. How many stickers does Nikau have now? Answer: 19 Solution: Nikau starts with 10 stickers. The friend gives 9 more stickers. Add to find the new total: 10 + 9 = 19 stickers.
   Full step-by-step solution

   Step 1: Nikau starts with 10 stickers. Step 2: The friend gives 9 more stickers. Step 3: Add to find the new total: 10 + 9 = 19 stickers. The answer is 19.

4. A rectangular garden is drawn with a length of 12.5 meters and a width of 8.25 meters. What is the total perimeter of the garden? Answer: 41.5 Solution: We are given a rectangular garden with length 12.5 meters and width 8.25 meters.
   Full step-by-step solution

   Step 1: Understand the problem We are given a rectangular garden with length 12.5 meters and width 8.25 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: Write down the formula with the given numbers Length = 12.5 Width = 8.25 Perimeter = 2 × (12.5 + 8.25) Step 3: Add the length and width 12.5 + 8.25 = 20.75 Step 4: Multiply the sum by 2 2 × 20.75 = 41.50 Step 5: Write the final answer The total perimeter is 41.5 meters.

5. 2 3/8 + 1 5/8 = ? Answer: 4 Solution: Add the whole numbers: 2 + 1 = 3 Add the fractions: 3/8 + 5/8 = 8/8 Simplify the fraction: 8/8 = 1 Combine the results: 3 + 1 = 4 The answer is 4.
   Full step-by-step solution

   Step 1: Add the whole numbers: 2 + 1 = 3 Step 2: Add the fractions: 3/8 + 5/8 = 8/8 Step 3: Simplify the fraction: 8/8 = 1 Step 4: Combine the results: 3 + 1 = 4 The answer is 4.

6. A rectangular classroom floor is drawn with a length of 12.75 meters and a width of 9.25 meters. What is the total perimeter of the classroom floor? Answer: 44 Solution: The formula for perimeter of a rectangle is: Perimeter = 2 × length + 2 × width Substitute the given values: Perimeter = 2 × 12.75 + 2 × 9.25 Calculate 2 × 12.75 = 25.5 Calculate 2 × 9.25 = 18.5 Add the results: 25.5 + 18.5 = 44 The total perimeter is 44 meters.
   Full step-by-step solution

   Step 1: The formula for perimeter of a rectangle is: Perimeter = 2 × length + 2 × width Step 2: Substitute the given values: Perimeter = 2 × 12.75 + 2 × 9.25 Step 3: Calculate 2 × 12.75 = 25.5 Step 4: Calculate 2 × 9.25 = 18.5 Step 5: Add the results: 25.5 + 18.5 = 44 Step 6: The total perimeter is 44 meters.