Emma draws a square on a coordinate grid. The corners of the square are at (3, 1), (7, 1), (7, 5), and (3, 5). She then shades a smaller square inside it, where each side of the smaller square is half the length of the larger square's side. What is the area of the shaded smaller square? Write your answer as an expression with an exponent, then evaluate it.Answer: ______________
Kaia is designing a square mosaic tile for an art project. She draws a square on a coordinate grid with corners at (10, 12), (19, 12), (19, 21), and (10, 21). Inside the square, she paints a circular pattern with a radius of 3 units. What is the area of the square that is NOT covered by the circle? Use π = 3.14.Answer: ______________
(-18 + 12) × 5 ÷ (-2) = ?Answer: ______________
Aroha is helping her school organize a book donation drive. She arranges the donated books into a large cube-shaped display for a photo. The display has 9 books along each edge. How many total books are in the display?Answer: ______________
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Answer Key & Explanations
Expressions with Exponents · Grade 6 · Worksheet 2
(-3)² × (5 + 15 ÷ 3) - 18 = ?Answer: 72 Solution: Evaluate inside the parentheses: 5 + 15 ÷ 3 Division first: 15 ÷ 3 = 5 Then addition: 5 + 5 = 10 Now we have (-3)² × 10 - 18 Evaluate the exponent: (-3)² = 9 Now we have 9 × 10 - 18 Multiplication next: 9 × 10 = 90 Finally subtraction: 90 - 18 = 72 The answer is 72.Full step-by-step solution
Step 1: Evaluate inside the parentheses: 5 + 15 ÷ 3
Step 2: Division first: 15 ÷ 3 = 5
Step 3: Then addition: 5 + 5 = 10
Step 4: Now we have (-3)² × 10 - 18
Step 5: Evaluate the exponent: (-3)² = 9
Step 6: Now we have 9 × 10 - 18
Step 7: Multiplication next: 9 × 10 = 90
Step 8: Finally subtraction: 90 - 18 = 72
The answer is 72.
(-3)² + 2 × (15 - 20) ÷ 5 = ?Answer: 7 Solution: Solve inside the parentheses: (15 - 20) = -5 Apply the exponent: (-3)² = 9 Perform multiplication and division from left to right: 2 × (-5) = -10, then -10 ÷ 5 = -2 Add the results: 9 + (-2) = 7 The answer is 7.Full step-by-step solution
Step 1: Solve inside the parentheses: (15 - 20) = -5
Step 2: Apply the exponent: (-3)² = 9
Step 3: Perform multiplication and division from left to right: 2 × (-5) = -10, then -10 ÷ 5 = -2
Step 4: Add the results: 9 + (-2) = 7
The answer is 7.
Emma draws a square on a coordinate grid. The corners of the square are at (3, 1), (7, 1), (7, 5), and (3, 5). She then shades a smaller square inside it, where each side of the smaller square is half the length of the larger square's side. What is the area of the shaded smaller square? Write your answer as an expression with an exponent, then evaluate it.Answer: 4 squared = 16 Solution: Find the side length of the large square. From x = 3 to x = 7, the length is 7 - 3 = 4 units. From y = 1 to y = 7, the length is 5 - 1 = 4 units.Full step-by-step solution
Step 1: Find the side length of the large square. From x = 3 to x = 7, the length is 7 - 3 = 4 units. From y = 1 to y = 7, the length is 5 - 1 = 4 units. So the large square has side length 4 units. Step 2: The small square's side is half of 4, so 4 ÷ 2 = 2 units. Step 3: The area of a square is side length squared, so area = 2 squared = 2^2 = 4 square units. Final answer: 2^2 = 4.
Kaia is designing a square mosaic tile for an art project. She draws a square on a coordinate grid with corners at (10, 12), (19, 12), (19, 21), and (10, 21). Inside the square, she paints a circular pattern with a radius of 3 units. What is the area of the square that is NOT covered by the circle? Use π = 3.14.Answer: 52.74 Solution: Find the side length of the square. The corners are at (10, 12), (19, 12), (19, 21), and (10, 21). The horizontal distance from x = 10 to x = 19 is 19 - 10 = 9 units.Full step-by-step solution
Step 1: Find the side length of the square. The corners are at (10, 12), (19, 12), (19, 21), and (10, 21). The horizontal distance from x = 10 to x = 19 is 19 - 10 = 9 units. So side length = 9 units.
Step 2: Find the area of the square. Area = side × side = 9 × 9 = 81 square units.
Step 3: Find the area of the circle. Radius r = 3 units. Area of circle = π × r^2 = 3.14 × (3)^2 = 3.14 × 9 = 28.26 square units.
Step 4: Find the area not covered by the circle. Uncovered area = Area of square - Area of circle = 81 - 28.26 = 52.74 square units.
The answer is 52.74.
(-18 + 12) × 5 ÷ (-2) = ?Answer: 15 Solution: First, solve the operation inside the parentheses: -18 + 12 = -6 Now the expression is -6 × 5 ÷ (-2) Perform multiplication and division from left to right: -6 × 5 = -30 Now we have -30 ÷ (-2) = 15 When dividing two negative numbers, the result is positive -30 ÷ (-2) = 15 The answer is 15.Full step-by-step solution
Step 1: First, solve the operation inside the parentheses: -18 + 12 = -6
Step 2: Now the expression is -6 × 5 ÷ (-2)
Step 3: Perform multiplication and division from left to right: -6 × 5 = -30
Step 4: Now we have -30 ÷ (-2) = 15
Step 5: When dividing two negative numbers, the result is positive
Step 6: -30 ÷ (-2) = 15
The answer is 15.
Aroha is helping her school organize a book donation drive. She arranges the donated books into a large cube-shaped display for a photo. The display has 9 books along each edge. How many total books are in the display?Answer: 729 Solution: The display is a cube, so the number of books along the length, width, and height are all the same: 9 books. To find the total number of books, multiply the three dimensions: 9 × 9 × 9.Full step-by-step solution
Step 1: The display is a cube, so the number of books along the length, width, and height are all the same: 9 books.
Step 2: To find the total number of books, multiply the three dimensions: 9 × 9 × 9.
Step 3: Write this as an exponent: 9 × 9 × 9 = 9^3.
Step 4: Calculate 9^3: 9 × 9 = 81, then 81 × 9 = 729.
The total number of books in the display is 729.
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