GED Mathematical Reasoning: Equations III – Multiplying and Dividing

Example 1

Solve the equation and check your answer: 3x = 24.6

 

We’ll focus on the left side since it’s the side containing the variable. The operation between the variable and the number 3 is multiplication, so to solve for “x,” we’ll divide both sides by 3. Notice that I use a fraction bar to denote the division of 3 on both sides.

On the left side, 3 divided by 3 equals one. So the multiplication and division undo each other, leaving just “x” on the left side.

On the right side, we need to divide 24.6 by 3. The result is 8.2

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To check our solution, we’ll substitute back into the original equation to make sure the statement is true. Is 3 times 8.2 equal to 24.6 ? The answer is yes. So our solution checks out.

3x = 24.6
3(8.2) = 24.6
24.6 = 24.6

 

Example 2

Solve the equation and check your answer: \frac{n}{5} = \$7

 

The variable “n” is showing on the left side and the operation between the variable and the number 5 is division. So to solve for “n,” we will multiply both sides by 5.

On the left side, the 5’s cross-cancel when we divide by a common factor of five. One times “n” equals simply “n,” leaving just “n.”

On the right side, we need to multiply $7 by 5, which is $35.

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For a check of this solution, let’s substitute $35 back into the original equation for “n” and verify that the statement is true. Is $35 divided by 5 equal to $7? The answer is yes! So our solution checks out.

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