41
Simple linear equations with fractional coefficients
Textbook, pp. 192–194
GoalSolve simple linear equations with fractional coefficients.
New words
fractional coefficient · kasr koeffitsiyentcommon denominator · umumiy maxrajmultiplying both sides · ikkala tomonni ko‘paytirishchecking · tekshirish
Explanation
Equations with fractional coefficients can be solved in two ways. First: collect the unknown terms on one side and divide by the coefficient: in (2/3)x = 8 we get x = 8 : 2/3 = 8 · 3/2 = 12. Second: multiply both sides by the least common multiple of the denominators to get rid of fractions. For example multiply x/2 + x/3 = 10 by 6: 3x + 2x = 60, 5x = 60, x = 12. Check: 12/2 + 12/3 = 6 + 4 = 10.
Worked examples
(3/4)x = 9: x = 9 : 3/4 = 9 · 4/3 = 12.
x/4 + 3 = 7: x/4 = 4, x = 4 · 4 = 16. Check: 16/4 + 3 = 7.
Class activity
“Get rid of denominators”: groups receive a card with a fractional equation. They find the number that removes all denominators, rewrite the equation and solve it.
Practice
1
Solve (2/3)x = 8.
12
2
Solve x/4 + 3 = 7.
16
3
Solve x/2 + x/3 = 10.
12
4
Why do we multiply both sides of the equation by a common multiple of the denominators?
Then the denominators disappear and the equation has integer coefficients; multiplying both sides by the same number does not change the solution.