Simplifying answers
In each of these examples, the answer we got was the final answer.
Let’s try another example to see one more step we need to take to complete the calculation.
We have the correct answer, but can the answer be simplified?
If both the numerator and denominator are even, we can divide them by 2 to get a simpler answer. For
example, 4/8 could be simplified to ½ because both 4 and 8 are divisible by 4.
We see with the above answer of 15/27 that 15 and 27 can’t be divided by 2, but they are both evenly
divisible by 3 (15 ÷ 3 = 5 and 27 ÷ 3 = 9).
The answer of 15/27 can be simplified to 5/9.
Each time you calculate fractions, you should give the answer in its simplest form. Check to see if the
numerator and denominator are both divisible by 2, 3 or 5, or any other number. If so, divide them to
give the answer in its simplest form. For instance, 21/28 would become ¾ (21 ÷ 7 = 3 and 28 ÷ 7 = 4).
Let’s try another example, 2/3 + ¾.
In this example the top number (numerator) is larger than the bottom number (denominator). When
this is the case, we have to divide the top number by the bottom, and express the remainder as a
fraction. So, 12 divides one time into 17 with 5 remainder. Our answer is written like this:
15/12
Test yourself
Try these for yourself:
a) ¼ + 1/3 =
b) 2/5 + ¼ =
c) ¾ 1/5 =
d) ¼ + 3/5 =
How did you go? The answers are:
a) 7/12
b) 13/20
c) 19/20
d)17/20
If your maths teacher says you must use the lowest common denominator to add fractions, is there an
easy way to find it? Yes, you simply multiply the denominators and then see if the answer can be
simplified. If you multiply the denominators you certainly have a common denominator, even if it isn’t
the lowest. (You should understand the standard method of adding and subtracting fractions as well as
the methods taught in this book.)
A shortcut
Here is a shortcut. If the numerators are both 1, we add the denominators to find the numerator of the
answer (top number), and we multiply the denominators to find the denominator of the answer. These
can easily be done in your head.
Here is an example:
For you just to look at a problem like this and call out the answer will make everyone think you are a
genius!