Solved on Dec 10, 2023

Simplify $0.4 \times 8.7$ and choose the equivalent expression.

STEP 1

Assumptions
1. We need to find an expression equivalent to $0.4 \times 8.7$ .
2. We are given four options (A), (B), (C), and (D) to choose from.

STEP 2

First, let's express $0.4$ and $8.7$ in terms of whole numbers and powers of $10$ to make the multiplication easier.
$0.4 = \frac{4}{10} = 4 \times 0.1$ $8.7 = \frac{87}{10} = 87 \times 0.1$

STEP 3

Now, we can rewrite the original expression using these new representations.
$0.4 \times 8.7 = (4 \times 0.1) \times (87 \times 0.1)$

STEP 4

Using the associative property of multiplication, we can group the whole numbers together and the decimal parts together.
$0.4 \times 8.7 = (4 \times 87) \times (0.1 \times 0.1)$

STEP 5

Now let's compare the expression we have with the given options.
The expression we derived is $(4 \times 87) \times (0.1 \times 0.1)$ .

STEP 6

We can see that option (D) matches our derived expression.
$\text{(D)}\ (4 \times 87) \times (0.1 \times 0.1)$

STEP 7

Therefore, the equivalent expression to $0.4 \times 8.7$ is option (D).
The correct answer is (D) $(4 \times 87) \times (0.1 \times 0.1)$ .

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Simplify $0.4 \times 8.7$ and choose the equivalent expression.

STEP 1

Assumptions
1. We need to find an expression equivalent to $0.4 \times 8.7$ .
2. We are given four options (A), (B), (C), and (D) to choose from.

STEP 2

First, let's express $0.4$ and $8.7$ in terms of whole numbers and powers of $10$ to make the multiplication easier.
$0.4 = \frac{4}{10} = 4 \times 0.1$ $8.7 = \frac{87}{10} = 87 \times 0.1$

STEP 3

Now, we can rewrite the original expression using these new representations.
$0.4 \times 8.7 = (4 \times 0.1) \times (87 \times 0.1)$

STEP 4

Using the associative property of multiplication, we can group the whole numbers together and the decimal parts together.
$0.4 \times 8.7 = (4 \times 87) \times (0.1 \times 0.1)$

STEP 5

Now let's compare the expression we have with the given options.
The expression we derived is $(4 \times 87) \times (0.1 \times 0.1)$ .

STEP 6

We can see that option (D) matches our derived expression.
$\text{(D)}\ (4 \times 87) \times (0.1 \times 0.1)$

STEP 7

Therefore, the equivalent expression to $0.4 \times 8.7$ is option (D).
The correct answer is (D) $(4 \times 87) \times (0.1 \times 0.1)$ .

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Simplify 0.4×8.70.4 \times 8.70.4×8.7 and choose the equivalent expression.

STEP 1

Assumptions1. We need to find an expression equivalent to 0.4×8.70.4 \times 8.70.4×8.7.2. We are given four options (A), (B), (C), and (D) to choose from.

STEP 2

First, let's express 0.40.40.4 and 8.78.78.7 in terms of whole numbers and powers of 101010 to make the multiplication easier.0.4=410=4×0.10.4 = \frac{4}{10} = 4 \times 0.10.4=104​=4×0.1 8.7=8710=87×0.18.7 = \frac{87}{10} = 87 \times 0.18.7=1087​=87×0.1

STEP 3

Now, we can rewrite the original expression using these new representations.0.4×8.7=(4×0.1)×(87×0.1)0.4 \times 8.7 = (4 \times 0.1) \times (87 \times 0.1)0.4×8.7=(4×0.1)×(87×0.1)

STEP 4

Using the associative property of multiplication, we can group the whole numbers together and the decimal parts together.0.4×8.7=(4×87)×(0.1×0.1)0.4 \times 8.7 = (4 \times 87) \times (0.1 \times 0.1)0.4×8.7=(4×87)×(0.1×0.1)

STEP 5

Now let's compare the expression we have with the given options.The expression we derived is (4×87)×(0.1×0.1)(4 \times 87) \times (0.1 \times 0.1)(4×87)×(0.1×0.1).

STEP 6

We can see that option (D) matches our derived expression.(D) (4×87)×(0.1×0.1)\text{(D)}\ (4 \times 87) \times (0.1 \times 0.1)(D) (4×87)×(0.1×0.1)

STEP 7

Therefore, the equivalent expression to 0.4×8.70.4 \times 8.70.4×8.7 is option (D).The correct answer is (D) (4×87)×(0.1×0.1)(4 \times 87) \times (0.1 \times 0.1)(4×87)×(0.1×0.1).

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Simplify $0.4 \times 8.7$ and choose the equivalent expression.

Assumptions
1. We need to find an expression equivalent to $0.4 \times 8.7$ .
2. We are given four options (A), (B), (C), and (D) to choose from.

First, let's express $0.4$ and $8.7$ in terms of whole numbers and powers of $10$ to make the multiplication easier.
$0.4 = \frac{4}{10} = 4 \times 0.1$ $8.7 = \frac{87}{10} = 87 \times 0.1$

Now, we can rewrite the original expression using these new representations.
$0.4 \times 8.7 = (4 \times 0.1) \times (87 \times 0.1)$

Using the associative property of multiplication, we can group the whole numbers together and the decimal parts together.
$0.4 \times 8.7 = (4 \times 87) \times (0.1 \times 0.1)$

Now let's compare the expression we have with the given options.
The expression we derived is $(4 \times 87) \times (0.1 \times 0.1)$ .

We can see that option (D) matches our derived expression.
$\text{(D)}\ (4 \times 87) \times (0.1 \times 0.1)$

Therefore, the equivalent expression to $0.4 \times 8.7$ is option (D).
The correct answer is (D) $(4 \times 87) \times (0.1 \times 0.1)$ .