Expanding and simplifying fractions: More examples

There's a lot to say about expanding and simplifying fractions. If you saw the first video, there are a few tricks in that. When you have multiplication in the denominator and in the numerator, you can look for common factors. Here for example, you can divide both the denominator and the numerator by five. And five divided by five is one, and one has no use in multiplication.

Three times one is three. And 12 times one is 12. So, we can cross the ones out. Did you noticed what just happened? When you have the same factors in the denominator and the numerator, you can remove them right away.

The same factors in denominators and numerators cancel each other out. But be careful, this only applies to factors or terms of multiplication. Look at this expression. Can you cross both fives here as well? No.

There is addition in the numerator. So, we cannot cross the fives out. To expand or simplify, you have to multiply or divide the entire denominator and the entire numerator by the same number. Otherwise, the ratio between the numerator and the denominator hence the value changes. What you can do here is split the fraction apart into a sum of two fractions with the same denominator, and now you can simplify.

Both fractions can be divided by five. Then you only have to calculate the sum. A fraction can be split up into several fractions with the same denominator one fraction for each term in the numerator. ​Take a look at this fraction. Can you simplify it? Yes.

Since both the denominator and numerator are divisible by 25, you can simplify by 25 and get two-fifths. The fact that 25 divides both 50 and 125 might be obvious. What about this fraction? 66 divided by 42. Can you simplify it?

If you don't see it right away, start by checking if both the denominator and the numerator are even numbers. In that case, you can simplify by two. You can then test if they are divisible by prime numbers, three, five or seven. Here, both are divisible by three, 11 and 7th and this is the end. You could have simplified by six directly.

Both 66 and 42 are in the times six table. But if you don't see straight away how you can simplify, you can do as we did here and simplify step by step, one prime number at a time. Feel free to watch the lesson on divisibility to learn a few tricks about how to find out which numbers are evenly divisible.