12. Use a grid to find the answer. a) The thickness of a quarter is about 1.6 mm. What is the height of a stack of 8 quarters? b) A cow can produce 23.5 L of milk a day. How many l... 12. Use a grid to find the answer. a) The thickness of a quarter is about 1.6 mm. What is the height of a stack of 8 quarters? b) A cow can produce 23.5 L of milk a day. How many litres of milk can a cow produce in a week? c) Each puppy weighs 1.5 kg. How many kilograms do 5 puppies weigh? d) Find the perimeter of a square with a side length of 19.5 m. e) A cheetah can run 33.3 m in 1 second when chasing prey. If the chase only lasts 9 seconds, how far does the cheetah run?
Understand the Problem
The question involves multiple mathematical tasks, including multiplication using grids and finding solutions to real-world problems such as calculating height, weight, and distance based on given information.
Answer
- a) $5.8$ - b) $11.6$ - c) $6.8$ - d) $10.5$ - e) $16.5$ - f) $31.5$ - Height of stack: $12.8$ mm - Weekly milk: $164.5$ L - Puppies weight: $7.5$ kg - Perimeter: $78$ m - Cheetah distance: $299.7$ m
Answer for screen readers
- a) 5.8
- b) 11.6
- c) 6.8
- d) 10.5
- e) 16.5
- f) 31.5
- Height of 8 quarters: 12.8 mm
- Weekly milk production: 164.5 L
- Weight of puppies: 7.5 kg
- Perimeter of the square: 78 m
- Cheetah run distance: 299.7 m
Steps to Solve
-
Multiply Using a Grid for 2.9 × 2
- Set up the grid by breaking down 2.9 into 2 and 0.9.
- Calculate:
- $2 \times 2 = 4$ (for whole numbers)
- $0.9 \times 2 = 1.8$ (for decimal)
- Combine results:
- $4 + 1.8 = 5.8$
-
Multiply Using a Grid for 2.9 × 4
- Break down 2.9 into 2 and 0.9.
- Calculate:
- $4 \times 2 = 8$
- $4 \times 0.9 = 3.6$
- Combine results:
- $8 + 3.6 = 11.6$
-
Multiply Using a Grid for 3.4 × 2
- Break down 3.4 into 3 and 0.4.
- Calculate:
- $3 \times 2 = 6$
- $0.4 \times 2 = 0.8$
- Combine results:
- $6 + 0.8 = 6.8$
-
Multiply Using a Grid for 2.1 × 5
- Break down 2.1 into 2 and 0.1.
- Calculate:
- $2 \times 5 = 10$
- $0.1 \times 5 = 0.5$
- Combine results:
- $10 + 0.5 = 10.5$
-
Multiply Using a Grid for 5.5 × 3
- Break down 5.5 into 5 and 0.5.
- Calculate:
- $5 \times 3 = 15$
- $0.5 \times 3 = 1.5$
- Combine results:
- $15 + 1.5 = 16.5$
-
Multiply Using a Grid for 4.5 × 7
- Break down 4.5 into 4 and 0.5.
- Calculate:
- $4 \times 7 = 28$
- $0.5 \times 7 = 3.5$
- Combine results:
- $28 + 3.5 = 31.5$
-
Calculate Height of a Stack of Quarters
- Thickness of one quarter = 1.6 mm.
- For 8 quarters: [ 1.6 \times 8 = 12.8 \text{ mm} ]
-
Calculate Milk Production in a Week
- Daily milk production = 23.5 L.
- For a week (7 days): [ 23.5 \times 7 = 164.5 \text{ L} ]
-
Calculate Weight of Puppies
- Each puppy weighs 1.5 kg and there are 5 puppies.
- Total weight: [ 1.5 \times 5 = 7.5 \text{ kg} ]
-
Calculate Perimeter of a Square
- Side length = 19.5 m.
- Perimeter: [ 4 \times 19.5 = 78 \text{ m} ]
-
Calculate Cheetah Run Distance
- Cheetah runs 33.3 m in 1 second.
- Distance in 9 seconds: [ 33.3 \times 9 = 299.7 \text{ m} ]
- a) 5.8
- b) 11.6
- c) 6.8
- d) 10.5
- e) 16.5
- f) 31.5
- Height of 8 quarters: 12.8 mm
- Weekly milk production: 164.5 L
- Weight of puppies: 7.5 kg
- Perimeter of the square: 78 m
- Cheetah run distance: 299.7 m
More Information
These calculations utilize grid multiplication for clarity and help illustrate the method of breaking down decimals and integers for easier computation. The real-world context demonstrates practical applications of multiplication in everyday scenarios.
Tips
- Forgetting to include the decimal point in results when multiplying decimals.
- Not regrouping properly when dealing with whole numbers and decimals.
- Miscalculating the total when summing products, particularly with decimals.
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