Unit 2: Solving Equations - Lesson #11: Solving Equations with Fractions

Vocabulary and key solving strategies from Math 7 Unit 2 Lesson #11 on solving linear equations with fractions.

Option #1 for Solving Equations with Fractions

Multiply every term in the equation by a common multiple (number) to get rid of all the fractions.

Option #2 for Solving Equations with Fractions

Find a common denominator for all terms, rewrite each term with that denominator, and then multiply every term by the denominator.

Reduce before you multiply

A technique used when multiplying equations by a common multiple to simplify or cancel the factor with the denominator before carrying out the multiplication.

Clearing the fractions in $\frac{3x}{2} - \frac{1}{3} = 2$

Multiplying each term by $6$ to obtain the simplified linear equation $9x - 2 = 12$.

Solution to $\frac{3x}{2} - \frac{1}{3} = 2$

$$x = \frac{14}{9}$$

Solution to $\frac{x}{6} = 1 - \frac{x}{4}$

$x = \frac{12}{5}$, found by multiplying every term by $12$ to yield $2x = 12 - 3x$, adding $3x$ to both sides to get $5x = 12$, and dividing by $5$.

Solution to $\frac{x}{5} + \frac{3x}{4} = 19$

$x = 20$, found by multiplying every term by $20$ to yield $4x + 15x = 380$, combining like terms to get $19x = 380$, and dividing by $19$.