List the factors of that number from smallest to largest, not forgetting to include 1 or that number. For example, this is how you would list the factors of the numerator and denominator of the fraction, 24/32: 24: 1, 2, 3, 4, 6, 8, 12, 24. 32: 1, 2, 4, 8, 16, 32.
24: 1, 2, 3, 4, 6, 8, 12, 24. 32: 1, 2, 4, 8, 16, 32. The GCF of 24 and 32 is 8, because 8 is the largest number that evenly divides into both 24 and 32.
24/8 = 3 32/8 = 4 The simplified fraction is 3/4.
3 * 8 = 24 4 * 8 = 32 You have returned to the original fraction, 24/32. You can also examine the fraction to make sure that it cannot be reduced any more. Since 3 is a prime number, it can only be divisible by 1 and itself, and four is not divisible by 3, so the fraction cannot be reduced further.
For the fraction 24/32, the number 2 works well. Since both numbers are even, they will be divisible by 2.
24/2 = 12 32/2 = 16 Your new fraction is 12/16.
12/2 = 6 16/2 = 8 Your new fraction is 6/8.
6/2 = 3 8/2 = 4 Your new fraction is 3/4.
For example, if you have the fraction 10/40, and are dividing the numerator and denominator by 5, you will be left with 2/8. You cannot keep dividing the numerator and denominator by 5, but you can divide both by 2 to get the final answer of 1/4.
3/4 * 2/2 = 6/8 6/8 * 2/2 = 12/16 12/16 * 2/2 = 24/32. Note that you’ve divided 24/32 by 2 * 2 * 2, which is the same as dividing it by 8, the greatest common factor (GCF) of 24 and 32.
For example, if your fraction is 24/60, start off with 24. You’d write: 24 – 1, 2, 3, 4, 6, 8, 12, 24 Then, move onto 60. You’d write: 60 – 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
For our example, the biggest number that is a factor of both numbers is 12. Therefore, we divide 24 by 12 and 60 by 12, leaving us with 2/5 – our reduced fraction!
Start with the numerator. From 24, branch off into 2 and 12. Since 2 is a prime number already, you’re done with that branch! Then take 12 into two more numbers: 2 and 6. 2 is a prime number – great! Now divide 6 into two numbers: 2 and 3. You now have 2, 2, 2, and 3 as your prime numbers. Move onto the denominator. From 60, branch off your tree to 2 and 30. 30 will then split into 2 and 15. Then split 15 into 3 and 5,both prime. You now have 2, 2, 3 and 5 as your prime numbers.
So, for 24, you have 2 x 2 x 2 x 3 = 24. For 60, you have 2 x 2 x 3 x 5 = 60
What we are left with is 2 and 5 – or 2/5! The same answer we got with the above method. if both numerator and denominator are even numbers, just think of splitting the number in half. keep on doing it to both until they are to small to split any more.
