Division with Decimals worksheet for math practice.

Problem: Division with Decimals

The task involves solving division problems where the divisor or dividend (or both) are decimals. The steps to solve these problems are as follows:

1. Make the divisor a whole number: Move the decimal point in the divisor to the right until it becomes a whole number.
2. Move the decimal point in the dividend: Move the decimal point in the dividend the same number of places to the right as you did for the divisor.
3. Perform the division: Divide the new numbers as if they were whole numbers, placing the decimal point in the quotient directly above the new placement of the decimal point in the dividend.

Let's solve each problem step by step.

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#### Problem a: \( 0.4 \div 1.28 \)

1. Make the divisor a whole number:
- The divisor is \( 0.4 \). To make it a whole number, move the decimal point one place to the right: \( 0.4 \rightarrow 4 \).
- Since we moved the decimal point one place to the right in the divisor, we must do the same in the dividend.

2. Adjust the dividend:
- The dividend is \( 1.28 \). Moving the decimal point one place to the right: \( 1.28 \rightarrow 12.8 \).

3. Perform the division:
- Now, divide \( 12.8 \div 4 \):
\[
12.8 \div 4 = 3.2
\]

- Place the decimal point in the quotient directly above the new placement of the decimal point in the dividend.

Thus, the quotient is:
\[
\boxed{3.2}
\]

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#### Problem b: \( 0.03 \div 0.54 \)

1. Make the divisor a whole number:
- The divisor is \( 0.03 \). To make it a whole number, move the decimal point two places to the right: \( 0.03 \rightarrow 3 \).
- Since we moved the decimal point two places to the right in the divisor, we must do the same in the dividend.

2. Adjust the dividend:
- The dividend is \( 0.54 \). Moving the decimal point two places to the right: \( 0.54 \rightarrow 54 \).

3. Perform the division:
- Now, divide \( 54 \div 3 \):
\[
54 \div 3 = 18
\]

- Place the decimal point in the quotient directly above the new placement of the decimal point in the dividend.

Thus, the quotient is:
\[
\boxed{18}
\]

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#### Problem c: \( 0.9 \div 3.96 \)

1. Make the divisor a whole number:
- The divisor is \( 0.9 \). To make it a whole number, move the decimal point one place to the right: \( 0.9 \rightarrow 9 \).
- Since we moved the decimal point one place to the right in the divisor, we must do the same in the dividend.

2. Adjust the dividend:
- The dividend is \( 3.96 \). Moving the decimal point one place to the right: \( 3.96 \rightarrow 39.6 \).

3. Perform the division:
- Now, divide \( 39.6 \div 9 \):
\[
39.6 \div 9 = 4.4
\]

- Place the decimal point in the quotient directly above the new placement of the decimal point in the dividend.

Thus, the quotient is:
\[
\boxed{4.4}
\]

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#### Problem d: \( 7 \div 39.5 \)

1. Make the divisor a whole number:
- The divisor is \( 39.5 \). To make it a whole number, move the decimal point one place to the right: \( 39.5 \rightarrow 395 \).
- Since we moved the decimal point one place to the right in the divisor, we must do the same in the dividend.

2. Adjust the dividend:
- The dividend is \( 7 \). Moving the decimal point one place to the right: \( 7 \rightarrow 70 \) (add a zero to maintain the value).

3. Perform the division:
- Now, divide \( 70 \div 395 \):
\[
70 \div 395 \approx 0.177
\]

- Place the decimal point in the quotient directly above the new placement of the decimal point in the dividend.

Thus, the quotient is:
\[
\boxed{0.177}
\]

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Final Answers:

\[
\boxed{3.2, 18, 4.4, 0.177}
\]