Algebra

NZ Level 5

Multiply algebraic terms with negatives

Lesson

Remember that when we write algebraic terms such as $2y$2`y`, this means $2$2 groups of $y$`y` and there is an unwritten multiplication sign between the $2$2 and the $y$`y` (otherwise we would write it as $2\times y$2×`y`). So when we are multiplying with numbers and algebraic terms, we can multiply our numbers as normal and then multiply the algebraic terms.

**Question**: Simplify the expression $4\times r\times s$4×`r`×`s`

**Think**: that we don't normally write the multiplication sign between letters and numbers

**Do:** $4rs$4`r``s` (you could also write this as $4sr$4`s``r`)

**Question**: What term should be written in the space to make this statement true? $8t$8`t`$\times$×$\text{something }$something $=$=$56t$56`t`

**Think:** $8$8$\times$×**7**$=$=$56$56. The $t$`t` does not have to change.

**Do:** $7$7 should be written in the space.

Simplify the expression $8m\times2m$8`m`×2`m`.

Simplify the expression $\left(-2pq\right)\times6q\times\left(-2n\right)$(−2`p``q`)×6`q`×(−2`n`).

Simplify the expression $\frac{1}{9}\times45uvw\times8w$19×45`u``v``w`×8`w`.

Generalise the properties of operations with fractional numbers and integers.