Dividing Decimals by Whole Numbers
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- Dividing Decimals by Whole Numbers - Video - How to Divide a Decimal by a Whole Number Watch
Theory
To divide a decimal by a whole number, use short division and keep the decimal point in the answer straight above the point in the number you are dividing. This Year 7 maths page shows how to divide using place value, when to write a zero, how to add zeros to finish a division, and how to find the better buy.
Think in place value. \(0.9\) is \(9\) tenths, and \(9\) tenths \(\div 3 = 3\) tenths \(= 0.3\).
Short division divides one place at a time from the left, carrying each remainder to the next place. The point in the answer goes straight above the point in the number.
If the divisor does not go into a place, write \(0\) in that place of the answer. If there is still a remainder at the end, add zeros to the number (\(2.4 = 2.40\)) and keep dividing.
Estimate first and check by multiplying: \(9.52 \div 4 \approx 8 \div 4 = 2\), and \(2.38 \times 4 = 9.52\).
Point above point; one place at a time:
How to divide a decimal by a whole number
- Estimate the answer.
- Divide one place at a time from the left, carrying each remainder.
- Put the point in the answer straight above the point in the number.
- Write a 0 when the divisor does not go; add zeros to the number if a remainder is left.
- Check by multiplying the answer by the divisor.
\(8 \div 5\) is \(1\) remainder \(3\); \(36 \div 5\) is \(7\) remainder \(1\); \(15 \div 5\) is \(3\). The answer is \(1.73\). Check: \(1.73 \times 5 = 8.65\).
| \(6 \text{ tenths} \div 3\) | \(=\) | \(2 \text{ tenths}\) |
| \(0.6 \div 3\) | \(=\) | \(0.2\) |
\(0.2\), as in the second diagram.
Estimate \(16 \div 4 = 4\). The answer is \(4.34\). Check: \(4.34 \times 4 = 17.36\).
(i) \(2.142 \div 7\)
(ii) \(3.3 \div 6\)
(i) \(2 \div 7\) does not go (write \(0\)); \(21 \div 7 = 3\); \(4 \div 7\) does not go (write \(0\)); \(42 \div 7 = 6\).
(ii) Add a zero so the division can finish: \(3.3 = 3.30\).
(i) \(0.306\): the \(0\) holds the hundredths place.
(ii) \(0.55\)
Keep the zeros at the front and add two zeros at the end: \(0.00237 \div 4 = 0.0005925\).
| \(5.16 \div 4\) | \(=\) | \(1.29\) |
| \(7.56 \div 6\) | \(=\) | \(1.26\) |
One bar costs \(\$1.29\) or \(\$1.26\). The pack of \(6\) is better value.
Common pitfalls
Frequently asked questions
Where does the decimal point go in short division?
Straight above the decimal point in the number you are dividing.
What do you do if there is a remainder at the end?
Add a zero to the end of the number and keep dividing. \(3.3 = 3.30\), so \(3.3 \div 6 = 0.55\).
Why write a zero in the answer?
When the divisor does not go into a place, the \(0\) holds that place. \(2.142 \div 7 = 0.306\).
How do you check a division?
Multiply the answer by the divisor. \(1.73 \times 5 = 8.65\).
How do you find which pack is better value?
Divide each price by the number of items to get the price of one. The lower price is better value.