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.
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