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Algebra Help Solving Multiplication and Division Equations

By Stuart Ackerman MSc.Ed.,B.A.

Solving Multiplication Equations

When solving an algebraic multiplication equation you should use the inverse operation of division. That is, you must divide both sides by the same non-zero number.

For example, street A is about 34,000 yards long. It is twice as long as street B. How long is street B?

We can write a multiplication equation to find the answer to problems like this. Our unknown number is the width of street B. Let x represent this width. We know that 2x is the length of street A. We can write our equation like this:

2x = 34,000 yards

To solve this equation, we can use the inverse of multiplying by 2, which is dividing by 2.

If we divide the left side of the equation by 2, we will get x by itself on the left.

Remember, any operation done to one side must also be done to the other side, so we must also divide the right side by 2 as well.

2x = 34,000 yards

2 2

x = 17,000 yards

We divide, and find that x is equal to 17,000 yards.

Solving Division Equations

When solving an algebraic division equation you must use the inverse operation of multiplication. That is, multiply both sides by the same number.

For example, country A has a border of about 14,800 miles. This is about ½ the length of the border of country B. About how many miles more is the border of country A than that of country B?

x = 14,800

2

We can write a division equation to find the answer to problems like this. Our unknown number is the length of the border of country B. Let x represent this number. We know that x divided by 2 is the approximate length of the border of country A. We can write the equation like this:

To solve this equation, we can use the inverse of dividing by 2, or multiplying by 2. If we multiply the left side of the equation by 2, we will get x by itself on the left.

x = 14,800

2

x x 2 = 14,800 x 2

2

x = 29,600
Remember, any operation done to one side must also be done to the other side, so we must also multiply the right side by 2.