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Place value Decimal places Arithmetic Equivalent fractionsThis topic is relevant for:
Here we will learn about multiplying and dividing with decimals, including calculations involving integers and decimals, or just decimals using formal written methods.
There are also multiplying and 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.
Multiplying and dividing decimals is the skill of carrying out a calculation involving multiplication and division where one or more of the values is a decimal.
For this skill the ability to multiply and divide by powers of ten is essential.
When multiplying with decimals we change any decimals in the calculation into integers (whole numbers) by multiplying by powers of katex is not defined This gives us a scaled calculation which is easier to carry out. Remember when multiplying by katex is not defined the decimal point doesn’t move, rather the digits move up changing their place value.
For example,
katex is not defined
katex is not defined
katex is not defined
We now need to scale this answer down to find the solution to the original calculation. We do this by dividing by the same powers of katex is not defined which we multiplied by in the first step. Remember when dividing by katex is not defined the decimal point doesn’t move, rather the digits move down changing their place value.
katex is not defined
Another method of decimal multiplication, or as a way of checking your answer, is to count the number of decimal places. The combined number of decimal places in the question should be the same as the number of decimal places in the answer.
katex is not defined
For example, katex is not defined
Sometimes trailing zeros may need to be written when the solution has more decimal places than the decimal number being divided.
For example,
katex is not defined
For example, katex is not defined
First we write this division as a fraction katex is not defined
Then we decide what to multiply katex is not defined by in order to make it an integer. Most often we will multiply by a power of ten. We then write the equivalent fraction which has a denominator that is an integer.
Step-by-step guide: Equivalent fractions
This tells us that katex is not defined is equivalent to katex is not defined and therefore the answers to each of these calculations will be the same.
katex is not defined
Therefore katex is not defined
Sometimes a combination of equivalent fractions and short division is needed.
For example,
katex is not defined
Multiplying and dividing decimals is used in many real life contexts.
For example,
In order to multiply with decimals:
Get your free multiplying and dividing decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free multiplying and dividing decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEMultiplying and 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:
Calculate katex is not defined
Multiply katex is not defined by katex is not defined to make the integer katex is not defined
katex is not defined
katex is not defined
katex is not defined (This is the scaled calculation.)
2Calculate the answer to this scaled calculation.
katex is not defined
3Divide the answer to step 2 by the same powers of ten which you multiplied by in step 1.
In step katex is not defined we multiplied by katex is not defined so now we divide by katex is not defined
katex is not defined
4Check your answer by ensuring that the combined number of decimal places in the question is the same as the number of decimal places in the answer.
katex is not defined
Calculate katex is not defined
Change any decimals in the calculation into integers (whole numbers) by multiplying by powers of katex is not defined
Multiply katex is not defined by katex is not defined to make the integer katex is not defined
Multiply katex is not defined by katex is not defined to make the integer katex is not defined
katex is not defined
katex is not defined
katex is not defined (This is the scaled calculation.)
Calculate the answer to this scaled calculation.
katex is not defined
Divide the answer to step 2 by the same powers of ten which you multiplied by in step 1.
In step katex is not defined we multiplied by katex is not defined and by katex is not defined so now we divide by katex is not defined and by katex is not defined
katex is not defined
Check your answer by ensuring that the combined number of decimal places in the question is the same as the number of decimal places in the answer.
katex is not defined
Calculate katex is not defined
Change any decimals in the calculation into integers (whole numbers) by multiplying by powers of katex is not defined
Multiply katex is not defined by katex is not defined to make katex is not defined
katex is not defined
katex is not defined
katex is not defined (This is the scaled calculation.)
Calculate the answer to this scaled calculation.
Use a long multiplication method of your choice such as this column method.
katex is not defined
Divide the answer to step 2 by the same powers of ten which you multiplied by in step 1.
In step katex is not defined we multiplied katex is not defined by katex is not defined so now we divide by katex is not defined
katex is not defined
Check your answer by ensuring that the combined number of decimal places in the question is the same as the number of decimal places in the answer.
katex is not defined
As katex is not defined is the same as katex is not defined the answer can be written in either format, unless the question specifies writing the answer to katex is not defined decimal place.
Note that the last digit in the number katex is not defined is a zero and so when we divided by katex is not defined we still wrote this digit in its place value because this then matches the number of decimal places in the question.
In order to divide with decimals:
Calculate katex is not defined
Check if the divisor is an integer or a decimal.
(a) Integer – go to step 3.
(b) Decimal – write the calculation as a fraction.
The divisor (the number we are dividing by) is an integer katex is not defined so we can go to step katex is not defined
Use short division to calculate the answer.
Answer is katex is not defined
Calculate katex is not defined
Check if the divisor is an integer or a decimal.
(a) Integer – go to step 3.
(b) Decimal – write the calculation as a fraction.
The divisor (the number we are dividing by) is an integer katex is not defined so we can go to step katex is not defined
Use short division to calculate the answer.
Answer is katex is not defined
Calculate katex is not defined
Check if the divisor is an integer or a decimal.
(a) Integer – go to step 3.
(b) Decimal – write the calculation as a fraction.
The divisor (the number we are dividing by) is a decimal katex is not defined so we write the calculation as a fraction.
katex is not defined
Write an equivalent fraction which has a denominator that is an integer.
Note: The best option is often to multiply the numerator and denominator by a power of ten. Then check if the fraction simplifies before moving onto step 3.
We could simplify the fraction here but you might also spot that katex is not defined.
Use short division to calculate the answer.
As the numbers in this question are part of the times tables we can calculate the answer mentally without the need for short division.
katex is not defined
Answer is katex is not defined
Calculate katex is not defined
Check if the divisor is an integer or a decimal.
(a) Integer – go to step 3.
(b) Decimal – write the calculation as a fraction.
The divisor (the number we are dividing by) is a decimal katex is not defined so we write the calculation as a fraction.
katex is not defined
Write an equivalent fraction which has a denominator that is an integer.
Note: The best option is often to multiply the numerator and denominator by a power of ten. Then check if the fraction simplifies before moving onto step 3.
Note that we only need the denominator to be an integer.
We could now simplify the fraction by dividing by katex is not defined
Use short division to calculate the answer.
Calculate katex is not defined
Answer is katex is not defined
1) Calculate katex is not defined
katex is not defined
katex is not defined
katex is not defined
katex is not defined
2) Multiply together katex is not defined and katex is not defined
Multiply katex is not defined by katex is not defined to get katex is not defined
Multiply katex is not defined by katex is not defined to get katex is not defined
katex is not defined
katex is not defined
Dividing katex is not defined by katex is not defined we have
katex is not defined
This means that katex is not defined
3) Calculate katex is not defined
katex is not defined
katex is not defined
katex is not defined
katex is not defined
4) Divide katex is not defined by katex is not defined
5) Calculate the value of katex is not defined
Write the division as a fraction katex is not defined
Write an equivalent fraction which has a denominator that is an integer.
Now using short division,
Answer is katex is not defined
6) Calculate the value of katex is not defined
Write the division as a fraction katex is not defined
Write an equivalent fraction which has a denominator that is an integer.
We could now simplify the fraction.
Lastly using short division,
Answer is katex is not defined
1. Calculate
(a) katex is not defined
(b) katex is not defined
(3 marks)
(a) katex is not defined
(1)
(b) katex is not defined
(1)
katex is not defined
(1)
2. The piece of ribbon is katex is not defined metres long. The ribbon is going to be cut into katex is not defined pieces of equal length. How long will each piece of ribbon be?
(2 marks)
katex is not defined
(1)
katex is not defined
(1)
3. A sandpit is katex is not defined metres long and katex is not defined metres wide. Calculate the area of the sandpit giving your answer in metres squared.
(2 marks)
katex is not defined
(1)
katex is not defined
(1)
4. Two positive numbers less than katex is not defined are multiplied together to give katex is not defined Give one possible pair of values.
(1 mark)
Either of the following pairs of numbers (in any order),
katex is not defined
(1)
katex is not defined
(1)
You have now learned how to:
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