When we are dividing algebraic terms, we need to consider how we can simplify the numbers as well as the algebraic terms (or the letters). To do this, it's often easier to write the division problem as an algebraic fraction.

For example, we could write $6x^7\div2x^3$6x7÷2x3 as $\frac{6x^7}{2x^3}$6x72x3 and vice versa.

We can divide the numbers and algebraic terms separately and then multiply the quotients together to get the final answer.

Examples

example 1

Simplify:$8x\div2$8x÷2

Think: We could also write this as $\frac{8x}{2}$8x2 and $8\div2=4$8÷2=4. The $x$x does not change.

Do:$8x\div2=4x$8x÷2=4x

Now let's look at an example where we need to divide both the numbers and the algebraic terms.

example 2

Simplify:$\left(-25y\right)\div5y$(−25y)÷5y

Think:$\left(-25\right)\div5=-5$(−25)÷5=−5 and $y\div y=1$y÷y=1

Do:$\left(-25y\right)\div5y=-5$(−25y)÷5y=−5

Worked Examples

Question 1

Simplify the expression $\frac{10v}{9v}$10v9v.

Question 2

Convert the expression $36w^5\div9w^5$36w5÷9w5 to a fraction and simplify.

Question 3

Simplify the expression $\frac{3u\times9vw}{6v\times4u}$3u×9vw6v×4u.

Outcomes

NA5-8

Generalise the properties of operations with fractional numbers and integers.