In this checkpoint we’ll look at units and how to convert them and look at how to start visualising inequalities and equivalence to make it easier to solve problems. We’ll also look at approximations and how to address such questions.

Common units

Here are common units you need to know for your exam.

Distance units

Units that measure distance i.e. how long something is (the length) such as the length of a table, from smallest unit size to largest unit size are: millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

Here are their conversions:

• 1cm (cent = 100) = 1/100 of a m = 10mm = 1/100,000 of a km.
• 1 m = 100 cm = 1/1000 km = 1000 mm
• 1 km (kilo = 1000) = 1000 m = 100,000 cm = 1,000,000 mm

Or expressed differently, it’s:

• 10 mm = 1 cm
• 100 cm = 1 m
• 1000 m = 1km

To convert larger units to smaller units, multiply. For 1km to be expressed in metres, do 1 x 1000 = 1000 m.

To convert small units to larger sized units, divide. For example, 1 metre to 1km, divide 1 by 1000, therefore, 1 m = 0.001 km (or 1 / 1000 km).

This rule also applies to mass, time units and volume units.

Mass units

Mass units show weight – e.g. heavy or light. The common units are grams and kilograms and they equate each other in the following way: 1 kg = 1000 g

Time units

Time units show…time. The common units are seconds, minutes and hours. They equate each other in the following way:

• 60 seconds = 1 minutes
• 60 minutes = an hour

Volume units

Volume units show the fill of something, usually in a container. The common units are millilitres and litres and they equate each other in the following way: 1 L = 1000 mL

Equivalence and Inequalities

An inequality compares 2 values so that one number is different from the other in the following way:

• greater than (>)
• less than (<)

When there are two values and they are the same as each other, they are equivalent.

For example:

2 + 6 = 3 + 4 + 1

If values can be equal to each other OR greater than or less than, they are expressed like this:

• greater than or equal to ≥
• less than or equal to ≤

In an exam, a good way to depict inequalities and equivalence is to do it visually.

For example, if a question asks you:

Container A holds 5 ml of water. Container B holds 25 ml of water. How much water needs to be poured into one jug so that they both have the same amount of water?

To answer this question, equivalence and inequality comes into play and visualising this allows you to clearly see what to do.

You can see from the image that to find out what to do, you need to add the amounts together (5 + 25) and then divide by 2 to get the ‘equal’ water amounts and then, to get the amount poured (the yellow block) you need to take away 5 from 15 (30 / 2) which is 10. So, you’d need to pour 10 ml into the other jug.

Visualising allows you to see what’s happening to make it easier for you to do problem solving.

Approximation questions

Approximation questions may ask you for:

• latest time
• earliest time
• nearest dollar
• nearest cent

It’s important that you just don’t round up or down based on the nearest number (for example, if it’s 9.4, it’s not always correct to say 9). Instead, you need to focus on the content of the question as that will determine whether the nearest approximate number should be higher or lower.

For example, there may be a question like this:

I am building a house and require bricks. If I have calculated the number of bricks that I require to be 743892.3, what is the approximate number of bricks that I have to buy in order to complete the house? I want to buy the lowest quantity possible to complete the house.

A 743800 B 743892 C 743900 D 743950

The answer is C. Even though 743892 is the closest number rounded down, you’ll need more than that (0.3 of a brick) to complete the house so you’ll need to get 743,900.

Example Question/s

Watch video for explanation of the following question/s:

A wooden box filled with apples weighs 10kg. When it is half full, the wooden box and apples together weigh 6kg.

How much does the wooden box weigh?

A 12 kg B 2 kg C 8 kg D None of these

This box weighs 4.2 tonnes. This cylinder weighs 50kg.
How many cylinders are needed to balance the box?

A 21000 cylinders B 300 cylinders C 84 cylinders D 85 cylinders

Minnie has 8 kg of cashew nuts and peanuts in her basket. A quarter of the nuts in her basket are peanuts. How many kilograms of cashew nuts does the basket contain?

A 2 kg B 4 kg C 5 kg D 6 kg E None of these

To fence one side of a plot, 28 posts placed 4 m apart are required. How many posts are required if the posts are placed 3 m apart?

A 39 B 36 C 37 D 40

Key Rules to remember

• To get from larger units to smaller units, multiply.
• To get from smaller units to larger units, divide.
• Use visualisation to problem solve with equivalence and inequalities.
• Approximations should be based on the details and requirements of the question, not just rounding up or down based on closest number.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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