8.1 Independent Practice Explained! - Free Printable

Let's solve this step-by-step based on the information provided in the image.

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Problem Summary:

Marie has a small copy of *The Schoolmaster* by René Magritte.
- Copy dimensions: 2 inches by 1.5 inches
- Scale of the copy: 1 inch : 40 cm
This means that 1 inch on the copy represents 40 cm on the original painting.

We are to:
a) Find the dimensions of the original painting (in cm)
b) Find the area of the original painting (in cm²)
c) Convert the original dimensions to inches
d) Find the area of the original painting in square inches

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Step-by-Step Solution

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#### Part a: Find the dimensions of the original painting (in cm)

The scale is 1 inch on the copy = 40 cm on the original.

So, we multiply each dimension of the copy by 40 cm to get the actual size.

- Length:
$ 2 \text{ in} \times 40 \text{ cm/in} = 80 \text{ cm} $

- Width:
$ 1.5 \text{ in} \times 40 \text{ cm/in} = 60 \text{ cm} $

✔ Answer for (a):
Dimensions of the original painting are 80 cm by 60 cm.

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#### Part b: Find the area of the original painting (in cm²)

Area = Length × Width

$$
\text{Area} = 80 \text{ cm} \times 60 \text{ cm} = 4800 \text{ cm}^2
$$

✔ Answer for (b):
Area = 4800 cm²

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#### Part c: Convert the original dimensions to inches

We are told:
1 inch = 2.54 cm, so to convert cm to inches, divide by 2.54.

- Length:
$ 80 \div 2.54 \approx 31.496 \text{ inches} $

- Width:
$ 60 \div 2.54 \approx 23.622 \text{ inches} $

Let’s round to two decimal places:

- Length ≈ 31.50 inches
- Width ≈ 23.62 inches

✔ Answer for (c):
Dimensions in inches: approximately 31.50 in by 23.62 in

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#### Part d: Find the area of the original painting in square inches

Now use the dimensions in inches:

$$
\text{Area} = 31.50 \times 23.62
$$

Let’s calculate:

First, do the multiplication:

$$
31.50 \times 23.62 = ?
$$

Break it down:

- $ 31.50 \times 23.62 = (30 + 1.5) \times 23.62 $
- $ 30 \times 23.62 = 708.6 $
- $ 1.5 \times 23.62 = 35.43 $
- Add: $ 708.6 + 35.43 = 744.03 $

✔ Answer for (d):
Area ≈ 744.03 square inches

Alternatively, you can use the conversion from cm² to in² directly:

We know:
- $ 1 \text{ inch} = 2.54 \text{ cm} $
- So $ 1 \text{ in}^2 = (2.54)^2 = 6.4516 \text{ cm}^2 $

Then:
$$
\text{Area in in}^2 = \frac{4800}{6.4516} \approx 744.03
$$

Same result!

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✔ Final Answers:

a. Dimensions of original painting: 80 cm by 60 cm
b. Area of original painting: 4800 cm²
c. Dimensions in inches: ≈ 31.50 in by 23.62 in
d. Area in square inches: ≈ 744.03 in²

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Let me know if you'd like a visual or diagram explanation!