Divide decimals by whole numbers

Division of a decimal by a whole number is understood as partitioning a quantity into equal groups while preserving place-value relationships; the quotient may be a whole number or a terminating decimal. Accurate reasoning includes estimating the quotient, placing the decimal point according to the value of the dividend, and using multiplication to verify the result. More advanced cases involving nonterminating quotients or general decimal divisors are not included.

Detailed Explanation: Divide decimals by whole numbers

To divide a decimal by a whole number:

Estimate the answer.
Divide as usual, using the place values in the dividend.
Place the decimal point in the quotient directly above the decimal point in the dividend.
Multiply to check your answer.

Example: $8.4 \div 4$

Step 1: Estimate.
Since $8 \div 4=2$ , the answer should be close to $2$ .

Step 2: Divide the whole-number part.
Divide $8$ by $4$ :

8 \div 4=2

Write $2$ in the quotient.

Step 3: Place the decimal point.
Bring the decimal point straight up into the quotient:

\begin{array}{r} \phantom{4}2.\\ 4\overline{)8.4} \end{array}

Step 4: Divide the tenths.
The $4$ in $8.4$ means $4$ tenths. Divide $4$ tenths into $4$ equal groups:

4\text{ tenths}\div4=1\text{ tenth}

Write $1$ in the tenths place. Therefore,

8.4\div4=2.1

Step 5: Check by multiplying.

2.1\times4=8.4

Because the product matches the dividend, the answer is correct.

Learn by doing: Divide decimals by whole numbers

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Long Division - Decimal Dividend 1 x 1

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