2. At the V6 Math Site
Tutorial on Solving Equations with Fractions
3. Steps for Solving Equations:
1. Clear any fractions
2.Distribute if possible.
3. Simplify each side of equation
4. Move Constants & Variables to
opposite sides of equation
5. Simplify, divide by coefficient,
solve for variable
4. How to Solve Fractional Equations
Solving one fraction equations: The goal is always to clear
the fractions the easiest way possible.
C.
𝟏
𝟑
x -
𝟏
𝟑
= 9 How many terms are there?
2. Instead, let's clear the fractions by multiplying each term
by the number which cancels the denominator
(⅓x) (⅓) = 9 ; x - 1 = 27
1. Combine like terms if easier. Are there like terms?
Yes, there are, but let's not combine them now.
3. Isolate the variable on the left, then divide by its
coefficient. x = 28
𝟑
𝟏
𝟑
𝟏
𝟑
𝟏
𝟑
𝟏
5. How to Solve Fractional Equations
Solving Equations with More than one Fraction:
𝟏
𝟐
x - 3 =
𝟏
𝟓
x + 3
1. Since combining like terms is easy this time, do that first.
1/2x = 1/5x + 6
2. Here we have 2 different denominators, so we find the
Least Common Denominator (LCD); The LCD of 2 and 5
is ? Now we have: 5/10x = 2/10x + 6.
What is our next step?
Multiply all 3 terms by 10/1; Our equation now looks like:
5x = 2x + 60; Completing the steps we get: 5x - 2x; 3x = 60;
x = 20
6. How to Solve Fractional Equations
Clearing Decimals from Equations
1. .3x + .4 = .6x + .7 -.5x
2. 0.32x + 0.4 = 0.6x + 0.7 -0.55x
𝟏
𝟐
x - 3 =
𝟏
𝟓
(x + 3)
What if…The equation looks like this:
How many terms are there?
This is one term
(10)
𝟏
𝟐
x – (10)3 = (10)
𝟏
𝟓
(x + 3)
5x – 30 = 2(x + 3); 5x – 30 = 2x + 6; 3x = 36; x = 12
7. Warm-Up/Test Prep:
1. $270.00 is divided among A, B, and C. B gets twice as
much money as A. C gets $20 more than B. How much does
each receive?
2. Andy is 2 times younger than his sister and his father is
25 years older than him. If the total of their ages is 53
years, what is Andy’s age and his father’s age?
Other Equations:
And Finally..
8. Class Work
Work independently or in pairs
All Problems
You Must Show Each Step for Every
Problem including checking your answer.
Example: x + 5 = - 7
x = -7 - 5
x = - 12
-12 + 5 = - 7
