For equations containing fractions or decimals, the basic approach is to first convert them into integers and then solve them.
Equations Containing Fractions
Multiply both sides by the least common multiple of the denominators to clear the denominators.
Example 1
Solve x/3＋x/4＝7.
Solution:
Both sides ×12: 4x＋3x＝84
7x＝84
x＝12
Solve x/3＋x/4＝7.
Solution:
Both sides ×12: 4x＋3x＝84
7x＝84
x＝12
Example 2
Solve (2x－1)/3 ＝ (x＋2)/2.
Solution:
Both sides ×6: 2(2x－1)＝3(x＋2)
4x－2＝3x＋6
x＝8
Solve (2x－1)/3 ＝ (x＋2)/2.
Solution:
Both sides ×6: 2(2x－1)＝3(x＋2)
4x－2＝3x＋6
x＝8
Equations Containing Decimals
Multiply both sides by 10, 100, or another power of 10 to convert the decimals into integers.
Example 3
Solve 0.3x＋0.7＝1.9.
Solution:
Both sides ×10: 3x＋7＝19
3x＝12
x＝4
Solve 0.3x＋0.7＝1.9.
Solution:
Both sides ×10: 3x＋7＝19
3x＝12
x＝4
Key Points
- Fractions → Multiply both sides by the least common multiple
- Decimals → Multiply both sides by a power of 10
- After multiplying, solve it as an equation with integers
Practice Problems
- Solve x/2－x/5＝3.
- Solve 0.2x＋1.4＝2.0.
Answers and Explanations
- Answer:x＝10
Explanation: The least common multiple of the denominators is 10. Both sides ×10: 5x－2x＝30. 3x＝30. x＝10. Check: 10/2－10/5＝5－2＝3 ✓ - Answer:x＝3
Explanation: Both sides ×10: 2x＋14＝20. 2x＝6. x＝3. Check: 0.2×3＋1.4＝0.6＋1.4＝2.0 ✓