Algebra

Ontario 09 Academic (MPM1D)

Rewriting expressions

Lesson

We've started to learn how to write word problems as algebraic expressions. Let's build on that knowledge now. We'll start by refreshing ourselves with some different names for the four operations. They are displayed in the mind map below. Can you think of any more?

Converting worded problems into mathematical expressions takes practice and it helps to be familiar with the language of math. Let's look at some examples below.

Which of the following expressions are equal to the perimeter of a square with sides of $16$16 cm?

Select all correct options.

$16^2$162

A$4\times16$4×16

B$16+16+16+16$16+16+16+16

C$2\times16+2\times16$2×16+2×16

D$16+16+16+16+16$16+16+16+16+16

E$16\times16$16×16

F$16^2$162

A$4\times16$4×16

B$16+16+16+16$16+16+16+16

C$2\times16+2\times16$2×16+2×16

D$16+16+16+16+16$16+16+16+16+16

E$16\times16$16×16

F

In a particular year, Re-source Waste Recovery produces sewerage treatment plants at a cost of $\$u$$`u` per plant. Re-source Waste Recovery also pays a fee of $\$b$$`b` per year for its use of the production facilities.

Using

*only addition*, write an expression that represents the total production cost from $1$1 year if there are $3$3 sewerage treatment plants produced in that year.Which of the following expressions is also equivalent to the production cost in that year?

$3u+b$3

`u`+`b`A$3\left(u+b\right)$3(

`u`+`b`)B$b+b+b+u$

`b`+`b`+`b`+`u`C$bu$

`b``u`D$3u+b$3

`u`+`b`A$3\left(u+b\right)$3(

`u`+`b`)B$b+b+b+u$

`b`+`b`+`b`+`u`C$bu$

`b``u`D

To simplify an expression, Christa writes down her working out below.

$9xy+x+7+x+y+xy+3$9xy+x+7+x+y+xy+3 |
$=$= | $9xy+x+x+y+xy+10$9xy+x+x+y+xy+10 |
(1) | ||||

$=$= | $9xy+2x+y+xy+10$9xy+2x+y+xy+10 |
(2) | |||||

$=$= | $9xy+2xy+xy+10$9xy+2xy+xy+10 |
(3) | |||||

$=$= | $12xy+10$12xy+10 |
(4) |

At which step does Christa make a mistake?

Step (1)

AStep (3)

BStep (4)

CStep (2)

DStep (1)

AStep (3)

BStep (4)

CStep (2)

DChrista asks for your help to simplify this expression. What should the answer actually be?

Simplify numerical expressions involving integers and rational numbers, with and without the use of technology