Fractions Everywhere

When we have to solve equations with fractions, we use their lowest common denominator to eliminate them. Since we know that a fraction means division, and we can multiply an equation through by any number other than zero and still have equality, that's what we do.

Here's an example:

Solve

We could divide both sides by to get ,

but there's a better way. We can eliminate the fractions completely if we multiply the equation through by 15, the lowest common multiple of the denominators 3 and 5.

Since , and , our equation becomes:

To check, we substitute the answer in the original equation. We see that 1.2 ÷ 3 = 0.4 or 2/5.

Here's another example with 3 fractions:

Solve

The lowest common multiple of 3, 2, and 6 is 6, so we multiply through by 6. We get:

Now we have a simple equation to solve, with no fractions:

2x + 4 + 3x = 1 becomes 5x = – 3
once we collect like terms, so

Again, as always, we check:

this is the same as

Our solution is correct.

Note: here we had to use the fraction form of the answer to check because 1/6 is a repeating decimal. Our solution wouldn't be exact if we did it using decimals.

Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.

Practice Exercises

1) Solve these equations with one step -- division. Check your answers

a)

b)

c)

d)

2) Solve these using multiplication by the lcm of the denominators. Check your answers

a)	b)	c)
d)	e)	f)

Solutions

1) Solve these equations with one step -- division. Check your answers

a) divide by 2/7

b) divide by 3/5

c) divide by ¼ or multiply by 4

d) divide by 8/9

2) Solve these using multiplication by the lcm of the fractions. Check your answers

a) multiply by 6 x + 3 = 9 so x = 6	b) multiply by 12 x + 6 = 15 so x = 9	c) multiply by 4 3x = 2 (x + 6) so x = 12
d) multiply by 12 4(x + 1) = 3 (13 – x) 4x + 4 = 39 – 3x 7x = 35, so x = 5.	e) multiply by 6 2(2x – 4) + (x – 5) = 2 5x – 13 = 2, so x = 3.	f) multiply by 12 3(x – 2) – 2 (x – 4) = 8 x + 2 = 8, so x = 6.

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