Algebra

Ontario 09 Applied (MFM1P)

Equivalent expressions

Lesson

We've already learnt about the components of an expression, how to identify like terms and how to identify missing terms that make number sentences equivalent or equal. Now we are going to build on this knowledge and learn how to generate our own equivalent expressions with number sentences and word problems.

It's really important to remember the rules of algebra because there are many ways of writing equivalent algebraic expressions. For example, $2a+7$2`a`+7 could be written as $7+2a$7+2`a`, $a\times2+7$`a`×2+7 or $7+a\times2$7+`a`×2 just to name a few.

It's good to be flexible so that no matter how an algebraic expression is written, you'll know what it means. Let's look through some examples and remember, there is more than one way to write a equivalent algebraic expression.

Fill in the blanks to make an expression that is equivalent to $h+f-8+h+4$`h`+`f`−8+`h`+4.

$2\editable{}+\editable{}-\editable{}$2+−

Select all expressions that are equivalent to $5x-13t+10r$5`x`−13`t`+10`r`.

$2x+5r+3x-13t+5r$2

`x`+5`r`+3`x`−13`t`+5`r`A$2x+3x-13t+10r$2

`x`+3`x`−13`t`+10`r`B$5x+10r-13t+10r$5

`x`+10`r`−13`t`+10`r`C$2x+3x+13t-10r$2

`x`+3`x`+13`t`−10`r`D$2x+5r+3x-13t+5r$2

`x`+5`r`+3`x`−13`t`+5`r`A$2x+3x-13t+10r$2

`x`+3`x`−13`t`+10`r`B$5x+10r-13t+10r$5

`x`+10`r`−13`t`+10`r`C$2x+3x+13t-10r$2

`x`+3`x`+13`t`−10`r`D

Fill in the blanks below to make an expression equivalent to $12p+15$12`p`+15.

$3\left(4\editable{}+\editable{}\right)$3(4+)

Relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations