Directed Numbers

NZ Level 5

Evaluate expressions with integers using order of operations

Lesson

Now you know the correct order of operations (see Maths in Order for a refresher), you can use it to solve problems with positive and negative numbers that have more than one operation.

**Evaluate:** $\left(48\div12+5\right)\times3$(48÷12+5)×3

**Think:** We need to simplify the problem by using our order of operation rules. Firstly, we perform any operations inside the brackets; division first followed by addition. Then we perform any other multiplication or division that is remaining, working from left to right.

**Do: **

$\left(48\div12+5\right)\times3$(48÷12+5)×3 | $=$= | $\left(4+5\right)\times3$(4+5)×3 |

$=$= | $9\times3$9×3 | |

$=$= | $27$27 |

Here's another example.

**Evaluate:** $48-6\times\left(8-4\right)$48−6×(8−4)

**Think: **Using our order of operations we want to first perform the subtraction in the brackets. We then want to evaluate the multiplication. Finally, we can subtract the product from $48$48.

**Do:**

$48-6\times\left(8-4\right)$48−6×(8−4) | $=$= | $48-6\times4$48−6×4 |

$=$= | $48-24$48−24 | |

$=$= | $24$24 |

Evaluate $70-8\times\left(-7\right)$70−8×(−7)

Evaluate $\left(-14\right)\div2-18\div\left(-2\right)$(−14)÷2−18÷(−2)

Understand operations on fractions, decimals, percentages, and integers