Multiplying and Dividing Decimals

Grade 5 · Math · Study Guide

Learn the steps for multiplying and dividing decimal numbers accurately.

Decimals are numbers that use a decimal point to show values less than one. Multiplying and dividing decimals follows rules based on place value.

To multiply decimals, ignore the decimal points at first and multiply as if the numbers are whole numbers. Then count the total number of decimal places in both factors. Place the decimal point in the product so it has that same total number of decimal places. For example, 2.3 x 1.4: multiply 23 x 14 = 322, then place 2 decimal places to get 3.22.

To divide a decimal by a whole number, place the decimal point in the quotient directly above the decimal point in the dividend, then divide as usual. For example, 4.8 ÷ 4 = 1.2.

To divide by a decimal, multiply both the divisor and dividend by a power of 10 to make the divisor a whole number. For example, 3.6 ÷ 0.4: multiply both by 10 to get 36 ÷ 4 = 9.

Estimating helps you check your work. Round each number to its greatest non-zero place, then multiply or divide the rounded numbers to see if your answer is reasonable.

Key terms

Decimal point
A dot that separates the whole number part from the fractional part of a decimal number
Decimal places
The number of digits to the right of the decimal point
Product
The answer to a multiplication problem
Quotient
The answer to a division problem
Dividend
The number being divided in a division problem
Divisor
The number you are dividing by in a division problem

Flashcards

0.6 x 0.5
0.30 = 0.3; multiply 6 x 5 = 30, then place 2 decimal places
2.5 x 3
7.5; multiply 25 x 3 = 75, then place 1 decimal place
8.4 ÷ 2
4.2; place decimal above the one in dividend, divide normally
0.72 ÷ 0.9
0.8; multiply both by 10 to get 7.2 ÷ 9 = 0.8
Counting decimal places in a product
Add the decimal places in each factor: 1.23 (2 places) x 4.5 (1 place) = 3 decimal places in product
1.23 x 4.5
5.535; multiply 123 x 45 = 5535, then place 3 decimal places
Why multiply both numbers by 10 when dividing by a decimal?
Multiplying both by the same power of 10 keeps the ratio the same but makes the divisor a whole number

Questions

  1. What is 0.4 x 0.3?

    1. 1.2
    2. 0.12
    3. 0.012
    4. 12
    Show answer

    Answer: 0.12

    0.4 x 0.3: multiply 4 x 3 = 12, then count 2 total decimal places to place the decimal: 0.12.

  2. 6.4 ÷ 8 = ___

    Show answer

    Answer: 0.8

    Place the decimal point in the quotient above the one in 6.4, then divide 64 ÷ 8 = 8, giving 0.8.

  3. When multiplying 1.5 x 2.4, the product should have 2 decimal places.

    Show answer

    Answer: True

    1.5 has 1 decimal place and 2.4 has 1 decimal place. 1 + 1 = 2 total decimal places in the product.

  4. To divide 4.5 ÷ 0.9, you can rewrite the problem as:

    1. 45 ÷ 9
    2. 4.5 ÷ 9
    3. 0.45 ÷ 9
    4. 4.5 ÷ 90
    Show answer

    Answer: 45 ÷ 9

    Multiply both 4.5 and 0.9 by 10 to eliminate the decimal in the divisor: 45 ÷ 9 = 5.

  5. 3.6 x 4 = ___

    Show answer

    Answer: 14.4

    Multiply 36 x 4 = 144, then place 1 decimal place from the factor 3.6, giving 14.4.

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