Solving an Equation by Multiplication/ Division: Using fractions

Exercises on Both Sides (of the Equation)Combining like terms Binomial Number of terms Decimal numbers Rearranging Equations Using additional geometric shapes Solving an equation using all techniques One sided equations Solving an equation with fractions Equations with variables on both sides Addition, subtraction, multiplication and division

Question 1

Find the value of the parameter X

$\frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}$

Question 2

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

Question 3

Find the value of the parameter X

$3x-\frac{1}{9}=\frac{8}{9}$

Question 4

Find the value of the parameter X

$\frac{2}{3}x+\frac{1}{4}=\frac{3}{4}$

Question 5

Find the value of the parameter X

$\frac{8}{3}-\frac{4}{5}x=-\frac{2}{10}x$

Examples with solutions for Solving an Equation by Multiplication/ Division: Using fractions

Exercise #1

Find the value of the parameter X

$\frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}$

Video Solution

Step-by-Step Solution

First, we will arrange the equation so that we have variables on one side and numbers on the other side.

Therefore, we will move $\frac{5}{6}$ to the other side, and we will get

$\frac{1}{3}x=-\frac{1}{6}-\frac{5}{6}$

Note that the two fractions on the right side share the same denominator, so you can subtract them:

$\frac{1}{3}x=-\frac{6}{6}$

Observe the minus sign on the right side!

$\frac{1}{3}x=-1$

Now, we will try to get rid of the denominator, we will do this by multiplying the entire exercise by the denominator (that is, all terms on both sides of the equation):

$1x=-3$

$x=-3$

Answer

-3

Exercise #2

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

Video Solution

Answer

$\frac{1}{3}$

Exercise #3

Find the value of the parameter X

$3x-\frac{1}{9}=\frac{8}{9}$

Video Solution

Answer

$\frac{1}{3}$

Exercise #4

Find the value of the parameter X

$\frac{2}{3}x+\frac{1}{4}=\frac{3}{4}$

Video Solution

Answer

$\frac{3}{4}$

Exercise #5

Find the value of the parameter X

$\frac{8}{3}-\frac{4}{5}x=-\frac{2}{10}x$

Video Solution

Answer

$\frac{40}{9}$

Question 1

Solve for X:
$\frac{2}{3}x-\frac{4}{6}=\frac{1}{3}$

Question 2

Solve for X:
$\frac{4}{5}x+\frac{3}{7}=\frac{2}{14}$

Question 3

Solve for X:
$\frac{4}{9}+\frac{3}{5}x=\frac{4}{3}$

Question 4

Solve for X:

$\frac{1}{6}x-\frac{1}{3}=\frac{1}{3}$

Question 5

Solve for X:

$\frac{9}{11}-\frac{8}{15}x=\frac{8}{22}$

Exercise #6

Solve for X:
$\frac{2}{3}x-\frac{4}{6}=\frac{1}{3}$

Video Solution

Answer

$\frac{3}{2}$

Exercise #7

Solve for X:
$\frac{4}{5}x+\frac{3}{7}=\frac{2}{14}$

Video Solution

Answer

$-\frac{5}{14}$

Exercise #8

Solve for X:
$\frac{4}{9}+\frac{3}{5}x=\frac{4}{3}$

Video Solution

Answer

$\frac{40}{27}$

Exercise #9

Solve for X:

$\frac{1}{6}x-\frac{1}{3}=\frac{1}{3}$

Video Solution

Answer

$4$

Exercise #10

Solve for X:

$\frac{9}{11}-\frac{8}{15}x=\frac{8}{22}$

Video Solution

Answer

$\frac{75}{88}$

Question 1

$$ 12y+4y+5-3=2y $$

$y=\text{?}$

Question 2

$\frac{-5+7x}{2}=22$

How much is Xworth?

Exercise #11

$12y+4y+5-3=2y$

$y=\text{?}$

Video Solution

Answer

$-\frac{1}{7}$

Exercise #12

$\frac{-5+7x}{2}=22$

How much is Xworth?

Video Solution

Answer

$7$