Here we are looking at solving equations with fractions. This may look tricky, but we can follow the exact same steps that we did when solving equations with whole numbers.
Once again we will follow the reversed order of operations and make the variable the subject of the equation.
It may be helpful to write any fractions as improper fractions rather than mixed numbers.
Let's look through the process using an example: $2a+\frac{1}{3}=9$2a+13=9.
| $2a+\frac{1}{3}$2a+13 | $=$= | $9$9 | (Subtract $\frac{1}{3}$13 from both sides) |
| $2a$2a | $=$= | $8$8$\frac{2}{3}$23 | (Convert the mixed fraction into an improper fraction) |
| $2a$2a | $=$= | $\frac{26}{3}$263 | (Divide both sides by $2$2) |
| $a$a | $=$= | $\frac{26}{6}$266 | (Simplify the answer) |
| $a$a | $=$= | $\frac{13}{3}$133 |
You can check your solution by substituting it back into the original equation.
Let' s do that now and substitute $a=\frac{13}{3}$a=133 into our equation:
| $LHS$LHS | $=$= | $2a+\frac{1}{3}$2a+13 |
| $=$= | $2\times\frac{13}{3}+\frac{1}{3}$2×133+13 | |
| $=$= | $\frac{26}{3}+\frac{1}{3}$263+13 | |
| $=$= | $\frac{27}{3}$273 | |
| $=$= | $9$9 | |
| $=$= | $RHS$RHS |
Worked Examples
Question 1
Solve the following equation: $-x-\frac{7}{8}=3$−x−78=3
Question 2
Solve the equation $\frac{x}{-9}+6=6$x−9+6=6
Question 3
Solve the equation $\frac{x-4}{-8}=-4$x−4−8=−4