Section 5.7 & 5.8 Solving Equations with Fractions Algebra Concepts Section 5.7 & 5.8 Solving Equations with Fractions

Warm-up Solve the following equations for x. #1 𝑥−6=−2 #2 3𝑥=20 #1 𝑥−6=−2 #2 3𝑥=20 #3 𝑥− −4 =7 #4 𝑥 4 =12

Now –it’s time to solve equations with fractions.

Try solving these. #1 𝑥− 1 3 = 1 5 #2 5=𝑛+ 1 2 #3 1 3 +𝑡= 5 6 *Recall dividing by a fraction is multiplying by the reciprocal #4 𝑞− − 2 3 =8

Reciprocals

Do NOT mix up reciprocals and opposites! Reciprocals-flip 2 3 3 2 Opposites-change the sign 2 3 − 2 3

Try these. #1 1 3 𝑟= 3 4 *Recall dividing by a fraction is multiplying by the reciprocal #2 4 5 𝑥= 6 5 #3 1 4 𝑚= 9 11

Mixed numbers are not welcome in equations! Improper fractions are welcome and encouraged!

Getting mixed numbers changed to improper fractions!

Mixed MAD Improper

Try these! #1 4 5 7 #2 −1 1 3 #3 3 2 5 #4 −1 1 8

In equations, check for mixed numbers. Change all mixed numbers!!!!!

Recall! You do NOT need a common denominator to multiply fractions. Just multiply across! Whole numbers can be written as a fraction. The denominator is 1.

Try these. #1 𝑥+3 1 5 =4 1 2 #2 9 1 3 =𝑥− 4 5 #3 5 1 2 𝑥=16 1 3 #4 2 1 2 𝑥=12

Homework #35 pg. 260 #11-21 odd, 37-39 pg. 264 #6-33 multiples of 3, 58-60