Year 9 Interactive Maths - Second Edition

Equations Containing Fractions

Clear the fractions by multiplying both sides of the equation by the lowest common multiple of the denominators. Then solve the equation for the unknown by performing the same operation on both sides of it.

Example 17

Lowest common multiple of 4 and 1 is 4. So, we multiply both sides by 4 to obtain:

Example 18

Solution:

Lowest common multiple of 10 and 15 is 30.  So, we multiply both sides by 30 to obtain:

Example 19

Solution:

Lowest common multiple of 4 and 3 is 12.  So, we multiply both sides by 12 to obtain:

Problem Solving

Linear equations are used to solve practical problems.  The unknown quantity is represented by a suitable pronumeral (i.e. letter); and then the information given in the problem is translated into an equation which is solved as explained in the previous sections.

Example 20

If one-third of a certain number is added to one-half of the same number, the result is 15.  Find the number.

Solution:

Let x be the number.

We are given that:

The lowest common denominator of 3, 2 and 1 is 6.  So, we multiply both sides by 6 to obtain

So, the number is 18.

Key Terms

pronumeral