unit 3 sec 2.2

Unit 3 sec 2.2 Adding and subtracting fraction

06 November 2015

22:43

It is important that you are able to add, subtract, multiply and divide fractions, not only by using your calculator, but also on paper.

  One reason for this is that it is useful to be able to do arithmetic. Simple fractions without having to resort to your calculator. Another reason is that you will need to use these techniques when you learn algebra waiter in the module, stop. Remember that you can add or subtract fractions only if they are the same type.

Fractions are not the same type, then you cannot add or subtract them directly stop you need to change the fractions into cover once fractions of the same type - that is, you need to write them with a common denominator. Remember that to find fraction equivalent to a particular fraction you multiply (or divide) top and bottom of the fraction by the same number.

Example 4 adding and subtracting fractions

carry out the following fraction additions and subtractions.

(A)       +      (B)  +     (C)  -      (D)  +

Solution

(A)       the denominators are the same, so add numerators. Write the answer in its simplest form, by cancelling.

 + =  = .

(B)       Make the denominators the same. Write each fraction with denominator 18.

 +  =  +  =  =

The answer  cannot be simplified by cancelling. You can write it as the mixed number or just leave it as .

(C)        Write each fraction with denominator 21

 -  =  -  =

(D)       And the integer part of the mixed numbers together, and add the fractional parts together, separately.

 +  = 1 + 4 +  +  = 5 +  +  = 5 +  = 5 +  =

Strategy to add or subtract fractions

v make sure that the denominators of the same stop (you may need to write each fraction as an appropriate equivalent fraction.)

v Add or subtract the numerators.

v Write the answer in its simplest form.

The trickiest part of adding and subtracting fractions is making the denominators the same. The number chosen has to be a common multiple of 9 and 6. Any common multiple of 9 and sex will do. The best number to choose is the lowest common multiple of 9 and 6, which is 18. Once you have chosen 18, then sense 18 = 2×9 and 18 = 3 × 6, you have to multiply the numerator and the denominator of the 1^st and 2^nd fractions by 2 and 3, respectively.