## Multiply and Divide Decimals

Multiplication of Decimals
Multiplication of a decimal number by 10 moves the decimal one place to the right. Multiplication by 10n moves the decimal n places to the right. Division by 10n moves the decimal place n places to the left.

To multiply decimals, multiply as if the numbers were whole numbers. To correctly place the decimal point, first count the total number of decimal places in the factors. The place the decimal point that many places from the right in the product.

Example:

The placement of the decimal point can be explained by using fractions.

Division of Decimals
The division algorithm for dividing a decimal by a whole number is similar to the division algorithm for whole numbers. An example of dividing money can be used to illustrate this.

Divide \$56.34 equally among 6 individuals. How much does each person receive? Think of the \$56.34 as five \$10 bills, six \$1 bills, three dimes, and four pennies.

If the divisor and dividend are multiplied by the same number, the quotient remains the same. If you are dividing apples equally among a group of children and triple both the number of apples and the number of children, then the number of apples per child stays the same. This is the principle used when dividing by a decimal. Use multiples of 10 to convert the division by a decimal into a problem of dividing by a whole number.

23 ÷ 3.2 = 230 ÷ 32
452.893 ÷ 0.23 = 45,289.3 ÷ 23
Multiply by 10.
Multiply by 100.

Such conversions are usually shown as

The quotient of two decimals can always be written as a quotient of whole numbers. For example, the quotient 452.893 ÷ 0.23 = 452,893 ÷ 230 (multiply both the dividend and the divisor by 1,000).

Teaching Model 7.5: Divide Decimals by Decimals