How to Multiply and Divide Decimals

How to Multiply or Divide Decimals

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To multiply decimals, multiply as if the numbers were whole numbers. Then count the total number of decimal places in the factors and put that many decimal places in the product.

To divide by a decimal, move the decimal point in both the divisor and the dividend the same number of places until the divisor is a whole number. Then divide normally. Moving both decimals the same way keeps the value of the quotient unchanged.

Examples

Example 1: \(2.3\cdot 0.4\): multiply \(23\cdot 4=92\). There are \(1+1=2\) decimal places, so \(2.3\cdot 0.4=0.92\).

Example 2: \(5.4\div 0.06\): move both decimals two places right to get \(540\div 6=90\).

Practice Exercises

1) Find \(0.6\cdot 4\).

2) Find \(3.2\cdot 0.5\).

3) Find \(1.25\cdot 8\).

4) Find \(4.8\div 6\).

5) Find \(7.2\div 0.9\).

6) Find \(0.04\cdot 0.7\).

7) Find \(12.6\div 0.3\).

8) Find \(3.45\cdot 2.1\).

9) Find \(0.875\div 0.25\).

10) Find \(6.03\cdot 0.04\).

11) Find \(14.4\div 0.12\).

12) Find \(2.75\cdot 3.6\).

13) Find \(0.006\cdot 0.05\).

14) Find \(9.72\div 0.18\).

15) A ribbon is \(2.4\) m long. What is the total length of \(3.5\) such ribbons?

16) A \(5.25\) kg bag is split equally into \(0.75\) kg portions. How many portions are there?

17) Find \(18.9\div 0.07\).

18) Find \(4.125\cdot 0.08\).

19) Find \(0.144\div 0.006\).

20) A car uses \(2.75\) gallons for \(68.75\) miles. How many miles per gallon is that?

Answers

1) Multiply \(6\cdot 4=24\). Since \(0.6\) has one decimal place, place one decimal digit in the product. Answer: \(2.4\).

2) Ignore decimals first: \(32\cdot 5=160\). The factors have \(1+1=2\) decimal places total, so \(160\) becomes \(1.60=1.6\). Answer: \(1.6\).

3) Compute \(125\cdot 8=1000\). Since \(1.25\) has two decimal places, the product is \(10.00=10\). Answer: \(10\).

4) Divide as \(48\div 6=8\). Since \(4.8\) is ten times smaller than \(48\), the quotient is \(0.8\). Answer: \(0.8\).

5) Move both decimals one place right to make the divisor whole: \(7.2\div 0.9=72\div 9=8\). Answer: \(8\).

6) Multiply \(4\cdot 7=28\). The factors have \(2+1=3\) decimal places total, so the product is \(0.028\). Answer: \(0.028\).

7) Move both decimals one place right: \(12.6\div 0.3=126\div 3=42\). Answer: \(42\).

8) Ignore decimals: \(345\cdot 21=7245\). The factors have \(2+1=3\) decimal places total, so \(7245\) becomes \(7.245\). Answer: \(7.245\).

9) Move both decimals two places right: \(0.875\div 0.25=87.5\div 25\). Since \(25\cdot 3.5=87.5\), the quotient is \(3.5\).

10) Multiply \(603\cdot 4=2412\). The factors have \(2+2=4\) decimal places total, so the product is \(0.2412\). Answer: \(0.2412\).

11) Move both decimals two places right: \(14.4\div 0.12=1440\div 12=120\). Answer: \(120\).

12) Ignore decimals: \(275\cdot 36=9900\). The factors have \(2+1=3\) decimal places total, so \(9900\) becomes \(9.900=9.9\). Answer: \(9.9\).

13) Multiply \(6\cdot 5=30\). The factors have \(3+2=5\) decimal places total, so the product is \(0.00030=0.0003\).

14) Move both decimals two places right: \(9.72\div 0.18=972\div 18\). Since \(18\cdot 54=972\), the quotient is \(54\).

15) Multiply \(2.4\cdot 3.5\). Ignore decimals: \(24\cdot 35=840\). There are \(1+1=2\) decimal places, so the total length is \(8.40=8.4\) m.

16) Compute \(5.25\div 0.75\). Move both decimals two places right: \(525\div 75=7\). There are \(7\) portions.

17) Move both decimals two places right: \(18.9\div 0.07=1890\div 7=270\). Answer: \(270\).

18) Ignore decimals: \(4125\cdot 8=33000\). The factors have \(3+2=5\) decimal places total, so the product is \(0.33000=0.33\).

19) Move both decimals three places right: \(0.144\div 0.006=144\div 6=24\). Answer: \(24\).

20) Miles per gallon is miles divided by gallons: \(68.75\div 2.75\). Move decimals two places right: \(6875\div 275=25\). The car gets \(25\) miles per gallon.

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