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
Solve the equation \( 0.6x - 1.2 = 3 \).
Nova's hint:
Try to Solve it with Nova?
This is a linear equation involving decimals.
Ask yourself: 'how do I move the number that is subtracted, then remove the decimal multiplier?' For example, in \( 0.2y - 1 = 3 \) you would add \( 1 \) first, then divide.
