USING DIVISION TO SOLVE EQUATIONS

About "Using division to solve equations"

Using division to solve equations :

Multiplication and division equations are the equations which contain multiplication or division. 

For example, 

4x  =  16

y/2  =  6

We use division to solve equations which contain multiplication. 

That is, when an equation contains multiplication, solve by dividing both sides of the equation by the same nonzero number.

Using division to solve equations - Examples

Example 1 :

Solve the equation 9a  =  54 and graph the solution on a number line.

Solution :

9a  =  54

Since we are trying to solve for "a", we have to get rid of "9" which is multiplied by a in the above equation. 

To get rid of 9, we have to divide by 9 on both sides. 

9a / 9  =  54 / 9

a  =  6

Graphing the solution on a number line 

Example 2 :

Solve the equation 18  =  6d and graph the solution on a number line.

Solution :

18  =  6d

Since we are trying to solve for "d", we have to get rid of "18" which is multiplied by d in the above equation. 

To get rid of 6, we have to divide by 6 on both sides. 

18 / 6  =  6d / 6

3  =  d

Graphing the solution on a number line 

Example 3 :

The product of two numbers is 20. If one number is 8, find the other number. 

Solution : 

Let "x' be the other number. 

According to the question, we have

8x   =  20

Here, 8 is multiplied by x. To get rid of 8, we have to divide by 8 on both sides and solve the equation as explained below. . 

8x / 8  =  20/8 

x  =  2.5

Hence, the other number is 2.5.

Example 4 :

John had some candies. He shared the candies equally to his 3 kids. If each kid had received 7 candies, how many candies did John have ?

Solution : 

Let "m' be the no. of candies that John initially . 

According to the question, we have

m/3   =  7

Here 3 divides m. To get rid of 3, we have to multiply by 3 on both sides and solve the equation as explained below.  

(m/3) x 3  =  7 x 3

m  =  21

Hence, John initially had 21 candies.

Example 5 :

Deanna has a recipe for potato cakes that requires 12 eggs to make 3 batches of potato cakes. Represent the given situation as an equation.

Model the equation and find how many eggs are needed per batch.

Solution : 

Write a word equation based on the situation.

Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

Let x represent the number of eggs needed per batch.

Then, we have

Therefore, the equation " 3x  =  12 " represents the given situation. 

Let us model the equation " 3x  =  12 " using algebra tiles. 

To find how many eggs are needed per batch, we have to solve for "x'.

To solve for "x" in the above model, we have to isolate "x". 

There are three x tiles, so draw circles to separate the tiles into 3 equal groups. 

One group has been circled here.

In the circled group above, we find one "x' on the left side and four "1" tiles on the right side. 

So, the value of "x" is 4.

Hence, 4 eggs are needed per batch.

After having gone through the stuff given above, we hope that the students would have understood "Using division to solve equations".

Apart from the stuff given above, if you want to know more about "Using division to solve equations", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6