Order of Operations

lessonbunny.com

Answer Key & Explanations

Order of Operations · Grade 5 · Worksheet 3

1. A rectangular garden is divided into 4 equal sections. The entire garden measures 12 meters long by 8 meters wide. If you plant flowers in 3 of the 4 sections, what is the total area of the garden that has flowers? Answer: 72 Solution: Area = length × width = 12 m × 8 m = 96 square meters Since there are 4 equal sections and flowers are in 3 sections, that's 3/4 of the garden Area with flowers = total area × fraction with flowers = 96 × 3/4 96 × 3/4 = (96 × 3) ÷ 4 = 288 ÷ 4 = 72 The answer is 72 square meters.
   Full step-by-step solution

   Step 1: Find the total area of the garden Area = length × width = 12 m × 8 m = 96 square meters Step 2: Determine what fraction of the garden has flowers Since there are 4 equal sections and flowers are in 3 sections, that's 3/4 of the garden Step 3: Calculate the area with flowers Area with flowers = total area × fraction with flowers = 96 × 3/4 Step 4: Perform the calculation 96 × 3/4 = (96 × 3) ÷ 4 = 288 ÷ 4 = 72 The answer is 72 square meters.

2. (125 + 75) ÷ 5 × 3 - 40 = ? Answer: 80 Solution: Calculate inside the parentheses: 125 + 75 = 200 Division comes next: 200 ÷ 5 = 40 Multiplication comes next: 40 × 3 = 120 Subtraction comes last: 120 - 40 = 80 The answer is 80.
   Full step-by-step solution

   Step 1: Calculate inside the parentheses: 125 + 75 = 200 Step 2: Division comes next: 200 ÷ 5 = 40 Step 3: Multiplication comes next: 40 × 3 = 120 Step 4: Subtraction comes last: 120 - 40 = 80 The answer is 80.

3. (624 + 376) × 2 - 450 ÷ 3 = ? Answer: 1850 Solution: Solve inside the parentheses: 624 + 376 = 1000 The expression becomes: 1000 × 2 - 450 ÷ 3 Perform multiplication and division from left to right: 1000 × 2 = 2000 and 450 ÷ 3 = 150 The expression becomes: 2000 - 150 Perform subtraction: 2000 - 150 = 1850 The answer is 1850.
   Full step-by-step solution

   Step 1: Solve inside the parentheses: 624 + 376 = 1000 Step 2: The expression becomes: 1000 × 2 - 450 ÷ 3 Step 3: Perform multiplication and division from left to right: 1000 × 2 = 2000 and 450 ÷ 3 = 150 Step 4: The expression becomes: 2000 - 150 Step 5: Perform subtraction: 2000 - 150 = 1850 The answer is 1850.

4. Emma is organizing a school fundraiser and needs to buy supplies. She buys 3 packs of markers for $4.75 each, 2 packs of colored paper for $3.25 each, and 5 packs of stickers for $2.50 each. How much money did Emma spend in total on all the supplies? Answer: 33.25 Solution: Calculate the cost of the markers: 3 packs × $4.75 per pack = $14.25 Calculate the cost of the colored paper: 2 packs × $3.25 per pack = $6.50 Calculate the cost of the stickers: 5 packs × $2.50 per pack = $12.50 Add all the costs together: $14.25 + $6.50 + $12.50 = $33.25 Emma spent $33.25 in…
   Full step-by-step solution

   Step 1: Calculate the cost of the markers: 3 packs × $4.75 per pack = $14.25 Step 2: Calculate the cost of the colored paper: 2 packs × $3.25 per pack = $6.50 Step 3: Calculate the cost of the stickers: 5 packs × $2.50 per pack = $12.50 Step 4: Add all the costs together: $14.25 + $6.50 + $12.50 = $33.25 Emma spent $33.25 in total.

5. (850 - 125) × 3 + 600 ÷ 5 = ? Answer: 2295 Solution: Solve inside the parentheses: 850 - 125 = 725 The expression becomes: 725 × 3 + 600 ÷ 5 Perform multiplication and division from left to right: 725 × 3 = 2175 and 600 ÷ 5 = 120 The expression becomes: 2175 + 120 Perform addition: 2175 + 120 = 2295 The answer is 2295.
   Full step-by-step solution

   Step 1: Solve inside the parentheses: 850 - 125 = 725 Step 2: The expression becomes: 725 × 3 + 600 ÷ 5 Step 3: Perform multiplication and division from left to right: 725 × 3 = 2175 and 600 ÷ 5 = 120 Step 4: The expression becomes: 2175 + 120 Step 5: Perform addition: 2175 + 120 = 2295 The answer is 2295.

6. (720 + 280) ÷ 5 × 4 - 150 = ? Answer: 650 Solution: Solve inside the parentheses: 720 + 280 = 1000 The expression becomes: 1000 ÷ 5 × 4 - 150 Perform division and multiplication from left to right: 1000 ÷ 5 = 200 The expression becomes: 200 × 4 - 150 Continue with multiplication: 200 × 4 = 800 The expression becomes: 800 - 150 Perform…
   Full step-by-step solution

   Step 1: Solve inside the parentheses: 720 + 280 = 1000 The expression becomes: 1000 ÷ 5 × 4 - 150 Step 2: Perform division and multiplication from left to right: 1000 ÷ 5 = 200 The expression becomes: 200 × 4 - 150 Step 3: Continue with multiplication: 200 × 4 = 800 The expression becomes: 800 - 150 Step 4: Perform subtraction: 800 - 150 = 650 The answer is 650.

7. Hana is drawing a rectangular grid of squares on a piece of paper. The grid has 6 rows and 8 columns of squares. She then divides the entire grid into 4 equal rectangular sections by drawing one vertical line and one horizontal line through the middle. What is the total number of squares in 3 of those 4 equal sections combined? Answer: 36 Solution: Find the total number of squares in the grid. Total squares = rows × columns = 6 × 8 = 48 squares. The grid is divided into 4 equal rectangular sections.
   Full step-by-step solution

   Step 1: Find the total number of squares in the grid. Total squares = rows × columns = 6 × 8 = 48 squares. Step 2: The grid is divided into 4 equal rectangular sections. Find the number of squares in one section. Squares per section = total squares ÷ 4 = 48 ÷ 4 = 12 squares. Step 3: Find the number of squares in 3 sections. Squares in 3 sections = 12 × 3 = 36 squares. The answer is 36.

8. (516 + 284) × 2 - 150 ÷ 3 = ? Answer: 1550 Solution: Solve inside the parentheses: 516 + 284 = 800 The expression becomes: 800 × 2 - 150 ÷ 3 Perform multiplication and division from left to right: 800 × 2 = 1600 and 150 ÷ 3 = 50 The expression becomes: 1600 - 50 Perform subtraction: 1600 - 50 = 1550 The answer is 1550.
   Full step-by-step solution

   Step 1: Solve inside the parentheses: 516 + 284 = 800 Step 2: The expression becomes: 800 × 2 - 150 ÷ 3 Step 3: Perform multiplication and division from left to right: 800 × 2 = 1600 and 150 ÷ 3 = 50 Step 4: The expression becomes: 1600 - 50 Step 5: Perform subtraction: 1600 - 50 = 1550 The answer is 1550.

9. A rectangular garden is divided into a grid with 8 rows and 12 columns of equal-sized square plots. Each square plot has a side length of 2.5 meters. What is the total area of the garden in square meters? Answer: 600 Solution: Find the total number of square plots: 8 rows × 12 columns = 96 plots Calculate the area of one square plot: side × side = 2.5 m × 2.5 m = 6.25 square meters Calculate the total area: 96 plots × 6.25 square meters per plot = 600 square meters The answer is 600.
   Full step-by-step solution

   Step 1: Find the total number of square plots: 8 rows × 12 columns = 96 plots Step 2: Calculate the area of one square plot: side × side = 2.5 m × 2.5 m = 6.25 square meters Step 3: Calculate the total area: 96 plots × 6.25 square meters per plot = 600 square meters The answer is 600.