In this checkpoint, we’ll go through fractions separately and then percentages and decimals.

Fractions

Fractions are parts of a whole and written as [X/Y] where the top number is the part (numerator) and the bottom number is the number of parts it's divided by (denominator)

There are different types:

Proper – top number is small than the bottom.

Improper – top number is bigger than the bottom.

Mixed number – whole number and then a proper fraction next to it.

We’ll go over the following ‘must-know’ list below at a high level using the 2 fractions below as an example (the video will show you how it's done):

[6/12] and [2/8]

‘Must-know’ List – See how you can learn to do the following:

• Simplifying – look at factors.
• Converting to same denominator – look at multiples.
• Adding – same denominator, keep denominator and add top numbers.
• Subtracting – same denominator, keep denominator and minus the top numbers.
• Multiplying – multiply across both top and bottom.
• Dividing – swap the denominator and numerator around for one of the fractions and then multiply.
• Comparing – same denominator and compare the top numbers.

Percentages and Decimals

Decimals and percentages are the same as fractions but they're expressed in different ways.

Percentages are expressed as fractions out of 100.

Here are some fractions: 1/100, 2/100, 10/100, 20/100, 17/100, 83/100

Here are their corresponding percentages: 1%, 2%, 10%, 20%, 17%, 83%

Let's look at decimals now… if it's a fraction, why do we need this? It's just a different form of expression. What is the most commonly seen decimal? It’s the expression of price e.g. $2.50

Let’s see how you can convert from one to another:

• To convert from fractions to decimal—Divide the top number by the bottom number. E.g. 10/20
• To convert a decimal to a fraction—use the place value of numbers in the decimal. Remember decimals go up by 10ths.

Common Fractions, Decimals and Percentages

Fraction	Decimal	Percent
1/20	0.05	5%
1/10	0.1	10%
1/5	0.2	20%
1/4	0.25	25%
2/5	0.4	40%
1/2	0.5	50%
3/5	0.6	60%
3/4	0.75	75%
4/5	0.8	80%
2/2	1.0 or 1	100%
4/2	2.0 or 2	200%

Decimal Movement

Here are some shortcuts:

The short cuts for multiplication

• If additional zeros added on (a) If nothing else changes, decimal point on answer moves right by the number of zeros that were added. E.g. 10 x 1.1 = 11; 100 x 1.1 = 110 (point moved one unit right due to extra zero, every time it moves right it will add a zero unless there is already a number there e.g. 10 x 0.123 = 1.23; 100 x 0.123 = 12.3)
• If zeros taken off (a) If nothing else changes, decimal point on answer moves left by the number of zeros that were added. E.g. 100 x 1.1 = 110; 10 x 1.1 = 11 (point moved one unit left due to zero taken away).

The short cuts for division

• Move decimal to the left if the 'number being divided' is reduced and/or if the 'number dividing by' increases and Move decimal to the right if the 'number being divided' is increased and/or if the 'number dividing by' decreases

Tips and Tricks

• A seemingly whole number is really a number with a decimal point at the end with zeros. E.g. 145 = 145.000000 = 145.000 = 145.0
• This is a reason why if moving a decimal point to the right/left and there is no existing number, we add a zero to it because there are already existing 'zero' numbers

Example Question/s

Watch video for explanation of the following question/s:

If 20 ÷ 2.50 = 8.0, then 20 ÷ 250 = ?

A 800 B 8 C 0.8 D 0.08

Paloma made 2000ml of lemonade by mixing 750ml of lemon juice with 250ml of syrup with the remainder being water. What fraction of the lemonade was just water?

A 3/4 B 4/4 C 3/8 D 4/8

Solve for x

[(x-7)/6] + [1/2] = [8/6]

A X = 12 B X = 1/3 C X = 1 1/3 D X = 5/6 E 8

The next 3 questions refer to the following information:

This multiplication table shows that, for example 50 x 0.5 = 25

Multiplied by	50	5	0.5	0.05
50	2500	250	25	2.5
5	250	25	2.5
0.5	25	2.5		0.025
0.05	2.5	0.25	0.025

Using the number pattern shown in the table

0.5 x 0.5= ?

A 2.5 B 25 C 0.25 D 250

From the information given in the table.

0.025 ÷ 0.5 = ?

A 0.5 B 2.5 C 250 D 0.05

From the information given in the table

500 x 0.5 = ?

A 250 B 25 C 25 D 500

If 0.4 x 0.6 = 0.24, what is 40 x 0.06 = ?

A 0.0024 B 0.024 C 2.4 D 24

Key Rules to remember

• Fractions, Decimals and Percentages are the same thing expressed differently.
• Know how to add, subtract, multiply, divide and convert.
• Follow the short cuts with decimal points.

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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