Theory
Simplifying a fraction means writing the same value with smaller numbers.
First find the greatest common divisor of the numerator and denominator.
Then divide the numerator and denominator by that same divisor. Because you do the same thing to the top and the bottom, the value of the fraction stays the same.
- Calculate the GCD of two numbersFind the divisors of both numbers, compare them, and choose the greatest common divisor.
The GCD is the greatest common divisor of two numbers.
For both numbers, make a list of divisors and find which divisors appear in both lists.
The greatest divisor that appears in both lists is the GCD.
- Find the divisors of the first numberTest which numbers fit exactly into the given number and write down all positive divisors.
A divisor is a number that you can divide by exactly, without a remainder.
For 12, for example, 3 is a divisor, because 12 ÷ 3 is exactly 4.
To avoid missing any divisors, test the possible divisors starting from 1 and write down only the numbers where the division comes out exactly.
- Find the divisors of the second numberTest which numbers fit exactly into the given number and write down all positive divisors.
A divisor is a number that you can divide by exactly, without a remainder.
For 12, for example, 3 is a divisor, because 12 ÷ 3 is exactly 4.
To avoid missing any divisors, test the possible divisors starting from 1 and write down only the numbers where the division comes out exactly.
- Find the common divisorsCompare the two rows and write down the numbers that appear in both rows.
In common means: it appears in both rows.
Go through one row carefully and check for each number whether you also see it in the other row.
Write down each number in common once, even if it appears more than once in a row.
- Choose the greatest common divisorCompare all the values and keep the highest number.
The largest number is the number with the highest value.
Compare the numbers one by one and always keep the largest number you have seen so far.
With negative numbers, the number closest to 0 is greater than a number further below 0.
- Find the divisors of the first number
- Divide the numerator and denominator by the GCDDivide both the numerator and the denominator by the GCD.
You can write a fraction in a simpler form by dividing the numerator and denominator by the same number.
You may only do this if the numerator and denominator are both exactly divisible by that divisor.
The value of the fraction does not change, because you remove the same factor from the top and the bottom.
- Divide the numeratorDivide the numerator by the given divisor.
Dividing means sharing an amount fairly or seeing how many equal groups fit into it.
The first number is the total amount. The second number tells you what you divide by.
Always check whether the division works out exactly. If it does not, you get a decimal number or fraction as the answer.
- Divide the denominatorDivide the denominator by the same divisor.
Dividing means sharing an amount fairly or seeing how many equal groups fit into it.
The first number is the total amount. The second number tells you what you divide by.
Always check whether the division works out exactly. If it does not, you get a decimal number or fraction as the answer.
- Write the new fractionWrite the divided numerator above the divided denominator.
- Divide the numerator
- Find the GCDThe GCD of 8 and 20 is 4.
- Find the divisors of the first numberThe positive divisors of 8 are 1, 2, 4, 8.
- Find the divisors of the second numberThe positive divisors of 20 are 1, 2, 4, 5, 10, 20.
- Find the common divisorsIn both rows there are 1, 2, 4.
- Choose the greatest common divisorThe largest number in 1, 2 and 4 is 4.
- Find the divisors of the first number
- Divide the numerator and denominator by the GCD820 ÷ 4 = 25.
- Divide the numeratorNumerator: 8 ÷ 4 = 2.
- Divide the denominatorDenominator: 20 ÷ 4 = 5.
- Write the new fraction820 becomes 25.
- Divide the numerator