NZ Level 3
Mixed questions on 4 operations with number
Lesson

## The order of the day

When we solve number problems, the rules we need to follow tell us how to work with brackets, as well as other operators, including addition, subtraction, multiplication and division. In fact, we've seen what happens if we don't solve things according to the order of operations!

The brackets are very important, but what happens if we have brackets inside brackets! Let's find out.

#### Worked Example

##### Question 1

Evaluate $\left(\left(36-\left(10+10\right)\right)\div2\right)+14\times6$((36(10+10))÷​2)+14×6

### When words are not enough

Words are great, but to solve a problem, we need to have a number problem. We can start by looking for key words, such as more, as well as, groups of, shared between, less than, which we can see when we think of the language of maths.

Sometimes, the problem is written a little differently, so we just need to be careful how we write our number problem out. Come and look how we solve a written problem, and find out that we can't just work from left to right. In fact, if we weren't concentrating, we could solve our problem incorrectly! Let's see how.

#### Worked Example

##### Question 2

Write the number sentence described as:

The product of $9$9 and $2$2 is added to $4$4, and then everything is divided by $5$5.

### True or false

When we have two expressions, with an equals sign, both sides must equal the same amount. To check if it's true, we can work out the answer to each side, or we can sometimes estimate the answer.

For these equations, can you see anything that helps you check whether it's true, or do you need to work them out?

 Hint $10+4$10+4 $=$= $20-6$20−6 Can you solve each side easily? $6\times3$6×3 $=$= $5\times3+3$5×3+3 How many groups of $3$3 are on the right hand side?

#### Worked Example

##### Question 3

True or False?

$6875\div55=6875\div275\times5$6875÷​55=6875÷​275×5.

1. True

A

False

B

True

A

False

B
2. Hence fill in the missing blank.

$2000\div25$2000÷​25 = $2000$2000 ÷ $\editable{}$ × $5$5

### Outcomes

#### NA3-1

Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.