Equations with brackets, decimals and fractions · Usually met around P6
Equations with decimals, fractions and percentages
Divide both sides by the number in front of x.
How to do it
Method
Divide both sides by the number in front of x
0.4x = 6 → x = 6 ÷ 0.4 = 15
Another way
Find one part first
(34)x = 12: 12 ÷ 3 = 4, 4 × 4 = 16
In full
The number in front of x (its coefficient) may be a decimal, a fraction or a percentage; the method is the same: divide both sides by it. 0.4x = 6: x = 6 ÷ 0.4 = 60 ÷ 4 = 15; or multiply both sides by 10 first to get 4x = 60, then divide by 4. (34)x = 12: x = 12 ÷ 34 = 12 × 43 = 16; or find one part first: 3 parts of x are 12, one part is 12 ÷ 3 = 4, and 4 parts are 4 × 4 = 16. 25% × x = 9: 25% = 14, so x = 9 × 4 = 36. If something is added or taken away, move it first, then divide. Last, check: 0.4 × 15 = 6.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Solve 0.2x + 5.6 = 6.2. x = □
Show the answer and working
Answer: 3
Take 5.6 from both sides: 0.2x = 0.6; divide by 0.2: x = 3.
Example 2
Solve 0.6x = 4.8. What is x?
- A. 0.8
- B. 2.88
- C. 4.2
- D. 8
Choose the right answer
Show the answer and working
Answer: D. 8
x = 4.8 ÷ 0.6: move both points right together, giving 8.
Example 3
Solve 2.5x + 0.8x = 9.9. x = □
Show the answer and working
Answer: 3
Join: 3.3x = 9.9, x = 9.9 ÷ 3.3 = 3.
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