Solving an Equation by Multiplication/ Division: Solving an equation with fractions

Exercises on Both Sides (of the Equation)Combining like termsBinomialNumber of termsDecimal numbersRearranging EquationsUsing additional geometric shapesUsing fractionsSolving an equation using all techniquesOne sided equationsEquations with variables on both sidesAddition, subtraction, multiplication and division
Question 1

\( \frac{-y}{5}=-25 \)

Question 2

Solve for X:

\( \frac{x+4}{3}=\frac{7}{8} \)

Question 3

Solve for x:

\( \frac{8x-4}{5}=\frac{2x+2}{4} \)

Question 4

\( 4=3y \)

Question 5

\( 6x=-12.6 \)

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

Exercise #1

−y5=−25 \frac{-y}{5}=-25

Video Solution

Step-by-Step Solution

We begin by multiplying the simple fraction by y:

−15×y=−25 \frac{-1}{5}\times y=-25

We then reduce both terms by −15 -\frac{1}{5}

y=−25−15 y=\frac{-25}{-\frac{1}{5}}

Finally we multiply the fraction by negative 5:

y=−25×(−5)=125 y=-25\times(-5)=125

Answer

y=125 y=125

Exercise #2

Solve for X:

x+43=78 \frac{x+4}{3}=\frac{7}{8}

Video Solution

Step-by-Step Solution

First, we cross multiply:

8×(x+4)=3×7 8\times(x+4)=3\times7

We multiply the right section and expand the parenthesis, multiplying each of the terms by 8:

8x+32=21 8x+32=21

We rearrange the equation remembering change the plus and minus signs accordingly:

8x=21−32 8x=21-32
Solve the subtraction exercise on the right side and divide by 8:

8x=−11 8x=-11

8x8=−118 \frac{8x}{8}=-\frac{11}{8}

Convert the simple fraction into a mixed fraction:

x=−138 x=-1\frac{3}{8}

Answer

−138 -1\frac{3}{8}

Exercise #3

Solve for x:

8x−45=2x+24 \frac{8x-4}{5}=\frac{2x+2}{4}

Video Solution

Step-by-Step Solution

To get rid of the fraction mechanics, we will cross multiply between the sides:

4(8x−4)=5(2x+2) 4(8x-4)=5(2x+2)

We expand the parentheses by multiplying the outer element by each of the elements inside the parentheses:

32x−16=10x+10 32x-16=10x+10

We arrange the sides accordingly so that the elements with the X are on the left side and those without the X are on the right side:

32x−10x=10+16 32x-10x=10+16

We calculate the elements:

22x=26 22x=26

We divide the two sections by 22:

22x22=2622 \frac{22x}{22}=\frac{26}{22}

x=2622 x=\frac{26}{22}

Answer

2622 \frac{26}{22}

Exercise #4

4=3y 4=3y

Video Solution

Answer

y=113 y=1\frac{1}{3}

Exercise #5

6x=−12.6 6x=-12.6

Video Solution

Answer

x=−2.1 x=-2.1

Question 1

\( 3b=\frac{7}{6} \)

Question 2

\( \frac{3x}{4}=16 \)

Question 3

Solve for X:

\( \frac{x+2}{3}=\frac{4}{5} \)

Question 4

Solve for X:

\( \frac{x-4}{18}=\frac{7}{9} \)

Question 5

Solve for X:

\( \frac{x-5}{7}=\frac{2}{11} \)

Exercise #6

3b=76 3b=\frac{7}{6}

Video Solution

Answer

b=718 b=\frac{7}{18}

Exercise #7

3x4=16 \frac{3x}{4}=16

Video Solution

Answer

x=2113 x=21\frac{1}{3}

Exercise #8

Solve for X:

x+23=45 \frac{x+2}{3}=\frac{4}{5}

Video Solution

Answer

25 \frac{2}{5}

Exercise #9

Solve for X:

x−418=79 \frac{x-4}{18}=\frac{7}{9}

Video Solution

Answer

18 18

Exercise #10

Solve for X:

x−57=211 \frac{x-5}{7}=\frac{2}{11}

Video Solution

Answer

6911 \frac{69}{11}

Question 1

\( 4x-6.9=2.2x+5 \)

Question 2

\( 70=4\frac{1}{2}b \)

Question 3

\( \frac{a}{6}=\frac{6}{7} \)

Question 4

Solve for X:

\( \frac{5}{8-x}=\frac{3}{2x} \)

Question 5

Solve for X:

\( \frac{5}{x-8}=\frac{3}{4x} \)

Exercise #11

4x−6.9=2.2x+5 4x-6.9=2.2x+5

Video Solution

Answer

x=61118 x=6\frac{11}{18}

Exercise #12

70=412b 70=4\frac{1}{2}b

Video Solution

Answer

b=1559 b=15\frac{5}{9}

Exercise #13

a6=67 \frac{a}{6}=\frac{6}{7}

Video Solution

Answer

a=517 a=5\frac{1}{7}

Exercise #14

Solve for X:

58−x=32x \frac{5}{8-x}=\frac{3}{2x}

Video Solution

Answer

2413 \frac{24}{13}

Exercise #15

Solve for X:

5x−8=34x \frac{5}{x-8}=\frac{3}{4x}

Video Solution

Answer

−2417 \frac{-24}{17}

Question 1

Lionel buys \( x \) packs of paper.

The price of each pack is $4.5 and he pays a total of $45.

Calculate \( x \).

Question 2

Solve for X:

\( \frac{5-x}{8}=\frac{3+x}{2} \)

Question 3

Solve for X:

\( \frac{-8+x}{3}=\frac{x+4}{9} \)

Question 4

1 kg of tomatoes costs $2.8.

Maggie buys 2 kg of tomatoes and 0.6 kg of cucumbers, costing a total of $7.1.

Express the value per kg of cucumbers in terms of \( x \) (in dollars).

Exercise #16

Lionel buys x x packs of paper.

The price of each pack is 4.5andhepaysatotalof4.5 and he pays a total of 45.

Calculate x x .

Video Solution

Answer

x=10 x=10

Exercise #17

Solve for X:

5−x8=3+x2 \frac{5-x}{8}=\frac{3+x}{2}

Video Solution

Answer

−1410 \frac{-14}{10}

Exercise #18

Solve for X:

−8+x3=x+49 \frac{-8+x}{3}=\frac{x+4}{9}

Video Solution

Answer

14 14

Exercise #19

1 kg of tomatoes costs 2.8.<br><br>Maggiebuys2kgoftomatoesand0.6kgofcucumbers,costingatotalof2.8.<br><br>Maggie buys 2 kg of tomatoes and 0.6 kg of cucumbers, costing a total of 7.1.

Express the value per kg of cucumbers in terms of x x (in dollars).

Video Solution

Answer

x=2.5 x=2.5