Equations with Fractions
Grade 5The quickest fix — eliminate the fractions
Fractions in equations look intimidating, but there is a clean trick: multiply every term on both sides by the lowest common denominator (LCD). The fractions disappear and you are left with a straightforward equation to solve.
Worked example
EXAMPLE
Solve: x/3 + x/4 = 7
LCD of 3 and 4 is 12. Multiply every term by 12: 12 × x/3 + 12 × x/4 = 12 × 7. Simplify: 4x + 3x = 84. Combine: 7x = 84. Divide: x = 12. Check: 12/3 + 12/4 = 4 + 3 = 7 ✓.
When the denominator contains x
EXAMPLE
Solve: 5/(x − 2) = 2
Multiply both sides by (x − 2): 5 = 2(x − 2). Expand: 5 = 2x − 4. Add 4: 9 = 2x. Divide: x = 4.5.
One thing to watch
After solving, check that your answer does not make any denominator equal to zero — that would make the original equation undefined. If it does, there is no valid solution.
Try this one
Aisha thinks of a number. She multiplies it by 4 and then subtracts 9. Her answer is 23.
Form an equation and solve it to find Aisha's number.
[3 marks]
Nova's hint:
Try to Solve it with Nova?
This uses forming and solving a linear equation from a written description.
Ask yourself: 'How do I write the operations described in words as an algebraic equation?'
Call the unknown number \( n \). The phrase 'multiplies by 4 then subtracts 9' becomes \( 4n - 9 \). Set that equal to the result and solve.
