1/2, 3/4, 4/10 are fractions. The numbers on top are called numerators. These are the numbers 1, 3 and 4. The numbers below are called denominators. These are the numbers 2, 4 and 10.
The denominator gives how many equal parts are there. The numerator represents how many of these are taken.
The denominator cannot be 0. For example 1/0 is not allowed. This is so as division by 0 is not defined.
However, 0/1 is allowed and is equal to 0.
If numerator and denominator are the same the fraction becomes equal to 1. For example:
2/2=1 and 9/9=1
We can also have fractions like 10/2=5 and 18/6=3.
Mixed Numbers
These numbers are made up of a whole number and a
fraction. For example:
5 1/2 is a mixed number and is equal to 5 + 1/2.
A mixed number may be changed into fraction through the following steps:
Step 1
Multiply the whole number and the denominator of the
fraction part.
For example in 5 1/2 we multiply 5 and 2 to get 10.
Step 2
To the result of Step 1 add the numerator of the
fraction part.
In our example the numerator of the fraction part 1/2 is 1. So 10 + 1 = 11.
Step 3
Write the result of Step 2 as the numerator and the
denominator of the fraction part as the denominator.
In our exampls we get 11/2.
So 11/2 = 5 1/2 which shows that we can change a fraction where the numerator is greater than the denominator into a mixed number. For doing this follow these steps:
Step 1
Divide the numerator by the denominator and obtain
the remainder.
In our example 11/2, 2 goes 5 times into 11 leaving a remainder of 1.
as 2 x 5 = 10
and 11 – 10 = 1
Step 2
The remainder over the denominator gives us the
fractional part. So we get.
11/2 = 5 1/2
Whole Numbers and Mixed Numbers
12/3 = 4 0/3 = 4
Here 0/3 is obviously = 0 hence 4 0/3 = 4.
However representing 4 as 12/3 is useful at times. We need to do this when we do calculations between whole numbers and fractions.
Multiplication of Fractions
Say we want to multiply 3/4 with 5/6.
We do this by multiplying 3 x 5 which gives us the result 15, which is the numerator of the result. Similarly 4 x 6 gives the result 24 which is the new denominator. We can write this multiplication as under:
3/4 x 5/6 = (3×5) / (4×6) =15/24.
Dividing Fractions
Say we want to divide 7/8 by 3/4.
For this we have the following steps:
Step 1
Invert 3/4, or in other words write it up side down
with 4 as the numerator and 3 as the denominator.
Step 2
Now multiply this with the first fraction. That is:
7/8 x 4/3 = (7×4) / (8×3) = 28/24
Reducing a Fraction to Lowest Terms
Look at the two fractions given below:
5/6 and 4/8
In the first fraction 5 is a prime number. So its factors are 1 and 5. That is 5 = 1 x 5. However, 6 = 1 x 2 x 3. There are no common factors (neglecting 1). We say that 5/6 is already expressed in its lowest terms.
In the fraction 4/8, 4 = 2 x 2 and 8 = 2 x 2 x 2. Here 2 x 2 is common to both 4 and 8. Hence 4/8 can be written as;
4/8 = (2×2) / (2x2x2) = 1/2
2×2 being common to both numerator and denominator can be cancelled. This leaves us with 1/2 as the result.
By changing 4/8 to 1/2 we say that 4/8 has been reduced to its lowest terms.
The value of 4/8 and 1/2 is the same as cancelling common factors does not change the value of the fraction.
Adding Fractions
5/16 + 7/16 = (5+7)/16 = 12/16 = 3/4
Notice the denominator of 5/16 and 7/16 is the same. This has been done to aid explaining addition of fractions. For adding fractions follow the following steps:
Step 1
Write the common denominator.
Step 2
Add the numerators, which gives us 12/16 which in its
lowes terms is 3/4.
If the denominators of the fractions are not the same we have to make them so before adding the fractions. For example:
5/6 + 1/4
Here 6 x 2 = 12 and 4 x 3 = 12
So we can re-write the fractions as:
(5×2) / (6×2) = 10/12 and (1×3) / (4×3) = 3/12
Then add 10/12 + 3/12 = (10+3)/12 = 13/12 = 1 1/12
Here 5/6 and 10/12 are equivalent fractions as they have the same value. 1/4 and 3/12 are also equivalent fractions for the same reason.
Subtracting Fractions
3/4 -1/4 = (3-1)/4 = 2/4 =1/2
It is similar to the steps used in adding fractions as explained above.