Multiply decimals by whole numbers

Multiplication of a decimal by a whole number represents a whole-number number of equal groups and can be modeled by an area model, decomposed by place value, or interpreted as scaling a quantity. The standard algorithm preserves this meaning by multiplying the decimal as an integer and accounting for its denominator of 10, 100, or 1,000; estimation helps verify the product’s magnitude, while multiplying two decimal factors or more advanced generalizations is not included.

Detailed Explanation: Multiply decimals by whole numbers

Multiplying a decimal by a whole number means finding a whole-number number of equal groups.

For example, solve:

2.4 \times 3

This means 3 groups of 2.4:

2.4+2.4+2.4

Step 1: Estimate

Since $2.4$ is close to $2$ , estimate:

2 \times 3=6

So the answer should be close to $6$ .

Step 2: Decompose by place value

Break $2.4$ into $2$ ones and $4$ tenths:

2.4=2+0.4

Multiply each part by $3$ :

3(2+0.4)=3\cdot2+3\cdot0.4

=6+1.2

Step 3: Add the products

6+1.2=7.2

Therefore,

\boxed{2.4\times3=7.2}

The answer makes sense because $7.2$ is close to the estimate of $6$ , and $3$ groups of $2.4$ should be greater than $6$ .

Learn by doing: Multiply decimals by whole numbers

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Multiplication - Decimal Tenths by Tens

Earned ?