Equations with Fractions

YUCK!

What to do? What to do? Let’s get rid of the dang fractions! Remember the miracle of multiplying fractions: CANCELLATION!

If you multiply by 2, you get Cancellation If you multiply by 2, you get

If you multiply by 6, you get Cancellation If you multiply by 6, you get

Getting rid of 2 denominators We have to get rid of both a 2 and a 6. What number can we multiply by that will cancel both of them? The Least Common Denominator!

LCD Unless someone flat out asks you what the least common denominator is, you can really use any common denominator in most fraction problems. They just like to use the smallest one to keep the numbers in the problem small.

LCD and Least Common Multiple If thinking of the LCD makes your eyes cross, go for the least common multiple instead! Multiples of 2: 2, 4, 6, 8, 10, 12 Multiples of 6: 6, 12, 18, 24, 30

Smallest number on both lists: Multiples of 2: 2, 4, 6, 8, 10, 12 Least Common Multiple Smallest number on both lists: Multiples of 2: 2, 4, 6, 8, 10, 12 Multiples of 6: 6, 12, 18, 24, 30

Notice that there are other numbers on both lists: Common Multiples Notice that there are other numbers on both lists: Multiples of 2: 2, 4, 6, 8, 10, 12,…,18 Multiples of 6: 6, 12, 18, 24, 30 You could use any of these to get rid of the fractions in your equation.

Let’s Multiply by 6!

Let’s Multiply by 6!

Wrap-up 3x + x + 2 = 42 4x + 2 = 42 4x = 42 – 2 4x = 40 X = 10

Check

Minus Signs Between Fractions Cancel the fractions! Distribute the -1

Dreaded Fractions Any time you have an equal sign and fractions: Determine a common denominator Multiply each term by it. If all your fractions don’t cancel, you picked the wrong number!.