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Dividing Decimals
Here we will learn about dividing decimals including how to divide decimals by a whole number, divide whole numbers by a decimal and divide decimals by decimals.
There are also dividing decimals worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What is dividing decimals?
Dividing decimals is where we divide a number into another where at least one of the numbers is a decimal.
To divide decimals we can use a variety of division methods. We will use short division for our examples but the use of long division or equivalent fractions are also appropriate methods.
Dividing decimals is important when dealing with money problems, the conversion of currency and converting between metric units. You may also encounter division problems involving areas of shapes or ratio.
If we are dividing a decimal by an integer, we can use short division method to obtain the answer.
E.g.
If we are dividing a number by a decimal, we can adjust the division problem to make the decimal an integer.
E.g.
We can treat the division like a fraction and find an equivalent fraction which has an integer denominator.
The easiest way to do this is to multiply both the numerator and denominator by the same power of ten.
This equivalent division will have the same answer as our original problem.
The answer of the division is also referred to as the quotient. The number we are dividing is known as the dividend.
What is dividing decimals?
Recap of multiplying and dividing by 10,100,1000,…
In order to solve problems involving dividing decimals, we need to multiply and divide by powers of ten.
If we divide by a power of ten, each digit decreases in place value.
When we multiply by
E.g.
If we divide by
E.g.
How to divide decimals
In order to divide decimals:
- If the divisor is already an integer, you can go straight to step
3 . Otherwise, write the division as a fraction with the divisor as the denominator of the fraction. - Multiply both the numerator and denominator by the same power of
10 (or other appropriate value) to get an equivalent fraction with an integer denominator. (You can simplify the fraction further if possible to make the division easier to calculate). - Use short division to calculate the answer to the original division problem. If the dividend is a decimal, line up the decimal point for your answer. You may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.
Explain how to divide decimals in 3 steps
Dividing decimals worksheet
Get your free dividing decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREE Dividing decimals worksheet
Get your free dividing decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREERelated lessons on decimals
Dividing decimals is part of our series of lessons to support revision on decimals. You may find it helpful to start with the main decimals lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Dividing decimals examples
Example 1: dividing a decimal by an integer
Work out:
- If the divisor is already an integer, you can go straight to step
3 . Otherwise, write the division as a fraction with the divisor as the denominator of the fraction.
The divisor is an integer so go to step
2Multiply both the numerator and denominator by the same power of
Not required for this question.
3Use short division to calculate the answer to the original division problem. If the number we are dividing is a decimal, line up the decimal point for your answer and you may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.
The answer is
Example 2: dividing an integer by a decimal
Work out:
If the divisor is already an integer, you can go straight to step
Multiply both the numerator and denominator by the same power of
Use short division to calculate the answer to the original division problem. If the number we are dividing is a decimal, line up the decimal point for your answer and you may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.
The answer is
Example 3: dividing a decimal by a decimal
Work out:
If the divisor is already an integer, you can go straight to step
Multiply both the numerator and denominator by the same power of
Use short division to calculate the answer to the original division problem. If the number we are dividing is a decimal, line up the decimal point for your answer and you may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.
The answer is
Example 4: dividing a decimal by a decimal
Work out
If the divisor is already an integer, you can go straight to step
Multiply both the numerator and denominator by the same power of
Once we have found the equivalent fraction by multiplying both numerator and denominator by
Use short division to calculate the answer to the original division problem. If the number we are dividing is a decimal, line up the decimal point for your answer and you may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.
We had to add the decimal point and a trailing zero to complete this division.
The answer is
Common misconceptions
- Reversing the multiplying steps once the division has taken place
A common error is to forget that the answer of the equivalent fraction is the same as the answer of the original division problem. If both of the numbers we are dividing have been multiplied by
E.g.
Practice dividing decimals questions
1. Work out 17.43\div7
Use short division. Make sure the decimal of the quotient lines up with the decimal of the dividend.
2. Work out 0.846\div3
Use short division. Make sure the decimal of the quotient lines up with the decimal of the dividend.
3. Work out 9\div0.6
Multiply both by 10 then use short division.
4. Work out 75\div0.12
Multiply both the numerator and denominator by 100 then use short division.
5. Work out 30.04\div0.16 .
Multiply both the numerator and denominator by 100 , simplify the fraction, then use short division. Add a decimal point and trailing zeros to the dividend. Remember to line up the decimal of the quotient with the decimal of the dividend.
6. Work out 87.22\div1.4 .
Multiply both by 10 then use short division. Remember to line up the decimal of the quotient with the decimal of the dividend.
Dividing decimals GCSE questions
1.
(a) Work out 5.1\div0.17 .
(b) Work out 7.776\div12 .
(4 marks)
(a)
Method to calculate 510\div17 seen.
(1)
Correct answer of 30 .
(1)
(b)
Attempt at short or long division.
(1)
Correct answer of 0.648 .
(1)
2.
(a) The total cost of 8 identical theatre tickets is £101.20 . Find the cost of one ticket.
(b) A bag of compost holds 5kg . A single plant pot can hold 0.12kg of compost.
How many plant pots can be completely filled from one 5kg bag?
(5 marks)
(a)
A method to divide 101.2 by 8 .
(1)
Correct answer of £12.65 .
(1)
(b)
A method to divide 5 by 0.12 , eg 500\div12 .
(1)
41.666 ….. seen.
(1)
Correct answer of 41 .
(1)
3. The area of a triangle is 8.64cm^2 . The base of the triangle is 3.2cm .
Find the height of the triangle.
(2 marks)
Correct start to calculation, 8.64 \times 2 =17.28 or 17.28\div 3.2 or 8.64\div1.6 or equivalent.
(1)
Correct answer of 5.4 cm
(1)
Learning checklist
You have now learned how to:
- Understand and use place value for decimals, measures and integers of any size
- Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
The next lessons are
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