How to Divide Decimals by Whole Numbers?
Divide a decimal by a nonzero whole number using long division, keeping the place values aligned. Check the quotient by multiplying it by the divisor.
TL;DR: Dividing a decimal by a whole number sounds tricky, but there's one move that makes it easy: set up long division like normal, then drop the decimal point straight up into the quotient, right above where it sits in the dividend. From there, you divide as if both numbers were plain whole numbers. So 7.5 divided by 3 just becomes 75 divided by 3, with the decimal floating back into place at 2.5. One trick, every problem.
Key takeaways:
- Set up long division with the decimal as the dividend.
- Place the decimal in the quotient directly above the decimal in the dividend.
- Divide as if both numbers were whole.
- If the dividend doesn't divide evenly, add trailing zeros and continue.
- Example: \(9.6\div 4=2.4\), straight division, decimal stays in place.
Dividing a decimal by a whole number is like dividing by normal. In this step-by-step guide, you will learn how to divide decimal numbers by whole numbers.
The division of a decimal with a whole number is like the normal division. We put the decimal point in the quotient according to the decimal of the dividend.
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A step-by-step guide to dividing decimals by whole numbers
The decimal division process is similar to the normal division process, but we only have to keep in mind the decimal point which should be correctly placed in the quotient.
The following steps will help us understand the decimal division process.
- To divide a decimal number by a whole number, the division is done in the same way as the whole numbers. First, we divide the two numbers regardless of the decimal point.
- Then, the decimal point in the quotient is placed in the same position as in the dividend.
Dividing Decimals by Whole Numbers, Example 1:
Calculate. \(78.92 ÷ 4\)
Solution:
First, ignore the decimal point and divide normally to get \(0\) as the remainder:
\(7892 ÷ 4=1973\)
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Then, put the decimal point in the quotient in the same position as given in the dividend. \(78.92 ÷ 4=19.73\). Thus, we take \(19.73\) as the answer, where the decimal is placed according to the decimal of the dividend.
Exercises for Dividing Decimals by Whole Numbers
Calculate.
- \(\color{blue}{0.16024 ÷ 4}\)
- \(\color{blue}{15.75 ÷ 25}\)
- \(\color{blue}{0.9936 ÷ 23}\)
- \(\color{blue}{1.683\div 9}\)
- \(\color{blue}{0.04006}\)
- \(\color{blue}{0.63}\)
- \(\color{blue}{0.0432}\)
- \(\color{blue}{0.187}\)
Recommended EffortlessMath Books
For a workbook that covers decimal division alongside the other operations, the Grade 5 Math for Beginners walks through decimal division with worked examples and practice. For pre-algebra-level fluency, the Pre-Algebra for Beginners connects decimal operations to fractions, percents, and basic equations.
Frequently Asked Questions
How do you divide decimals by whole numbers step by step?
Set up long division with the decimal inside the bracket and the whole number outside. Next, bring the decimal point straight up into the quotient. Then divide exactly as you would with whole numbers. For 9.6 ÷ 4: 4 goes into 9 two times with 1 left, bring down 6 to make 16, and 4 goes into 16 four times. The answer is 2.4, and 2.4 × 4 = 9.6 checks it.
How do you divide decimals by whole numbers with remainders?
Instead of writing a remainder, add zeros to the end of the dividend and keep dividing. Adding zeros after the last decimal digit does not change the value. For 3.4 ÷ 4, 4 goes into 34 tenths eight times with 2 left over. Write 3.4 as 3.40, bring down the 0 to make 20, and 4 goes into 20 five times. So 3.4 ÷ 4 = 0.85.
How do you divide decimals by whole numbers without a calculator?
Long division works on paper because each step uses only small whole-number facts. Take 12.96 ÷ 8, the price per can when 8 cans cost $12.96. 8 goes into 12 once with 4 left, 49 gives 6 with 1 left, and 16 gives 2. With the decimal placed above, the answer is 1.62, or $1.62 per can. Multiplying 1.62 × 8 = 12.96 confirms it.
How do you divide decimals by whole numbers using models?
Base-ten blocks or a grid model show what the division means. To find 1.2 ÷ 3, trade the 1 whole for 10 tenths, so you have 12 tenths in all. Share the 12 tenths equally into 3 groups, and each group gets 4 tenths. So 1.2 ÷ 3 = 0.4. Models like this help students see why the decimal point stays in the same place.
How do you divide decimals by whole numbers in 5th grade?
In 5th grade, students divide decimals to the hundredths place by whole numbers, often starting with models and moving to long division. A typical problem is 4.56 ÷ 6. Since 6 does not go into 4, write 0 above the 4 and place the decimal point, then divide 45 by 6 to get 7 with 3 left, and 36 by 6 to get 6. The answer is 0.76.
How do you solve word problems that divide decimals by whole numbers?
Look for words like split, shared equally, each or per, which signal division. The total amount is the decimal dividend, and the number of groups is the whole-number divisor. If four friends split a $45.60 bill equally, compute 45.60 ÷ 4 = 11.40, so each person pays $11.40. Finish by checking that the answer makes sense: 4 × $11.40 brings you back to $45.60.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
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