As you'll be required to demonstrate the ability to work with percentages, fractions, ratios and averages, we have pulled together a few key formulas to help get your revision started.

### Percentage Increase

Deduct the original number from the new number, divide the difference by the original number, and times by 100.

Example: find the percentage increase of 300 to 550

550 - 300 = 250

250 ÷ 300 = 0.83

0.83 x 100 = 83

Answer: 83%

### Percentage Decrease

Minus the new number from the original number, divide the difference by the original number, and times by 100.

Example: find the percentage decrease of 800 to 320

800 - 320 = 480

480 ÷ 800 = 0.6

0.6 x 100 = 60

Answer: 60%

### Adding Percentages

Add 100 to each given percentage, then transform it into decimals. Times the base figure by the first decimal, then multiply the resulting value by the second decimal.

Example: your phone bill is £50. It increases by 10% after 12 months, and a further 15% increase is applied six months later. What's the price of your phone bill after 18 months?

10 + 100 = 110, expressed as 1.10 as a decimal

15 + 100 = 115, expressed as 1.15 as a decimal

50 x 1.10 = 55

55 x 1.15 = 63.25

Answer: £63.25

### Converting Percentages into Fractions

Write the percentage as a portion of 100, then simplify that number is required.

Example: Convert 25% into a fraction

25/100 simplified to 1/4

Answer: 1/4

### Mean Averages

Add all the numbers together and divide the total by the amount of numbers presented.

Example: find the mean average of 6, 30, 16 and 44

6 + 30 + 16 + 44 = 96

96 ÷ 4 = 24

Answer: 24

### Adding Fractions

Start by making sure the denominators are the same. Add the two numerators together, then place them over the denominator. If necessary, simplify the fraction.

Example: 2/7 + 4/7

As the denominators are the same, 2 + 4 = 6

Answer: 6/7

If your denominators are different, times one fraction by the required amount to have two equal denominators. You have to times the denominator and numerator to keep the correct value of the fraction.

Example: work out 4/6 + 2/12

To get a common denominator, multiply 4/6 by 2

4 x 2 = 8

6 x 2 = 12

Now work out 8/12 + 2/12

8 + 2 = 10

Answer: 10/12

### Subtracting Fractions

Minus one numerator from the other then place the answer over the denominator.

Example: work out 4/8 - 1/8

4 – 1 = 3

Answer: 3/8

If the denominators are different, follow the same steps as above to find the common denominator.

### Multiplying Fractions

Times the numerators, then times the denominators and write down as the new fraction.

Example: 2/6 x 4/7

2 x 4 = 8

6 x 7 = 42

Answer: 8/42

### Dividing Fractions

You can find the reciprocal of the dividing fraction by flipping it upside down and timesing the first fraction by this reciprocal.

Example: 2/5 ÷ 1/4

1/4 becomes 4/1

2 x 4 = 8

5 x 1 = 5

Answer: 8/5

### Expressing Mixed Fractions as Improper Fractions

Take the entire number of the mixed fraction and times by the denominator of the fractional part. Add the result to the numerator and place it above the existing denominator.

Example: convert 4 2/4 into an improper fraction

4 x 4 = 16

16 + 2 = 18

Answer: 18/4, simplified to 9/2

## Effective test-taking strategies

Revision and practice tests will go a long way to helping you succeed in your numerical reasoning test, however, there are a few other strategies that will help you achieve the highest score possible.

Ensure you read the instructions carefully at the beginning of each test, as we've mentioned, every test is different.

Before you head into the timed questions, you'll likely be given a set of practice questions - take your time familiarising yourself with these and settle into the format before starting the timed questions.

Lastly, be aware of distractors placed throughout the test in the form of similar data or multiple-choice answers that are designed to identify if you have read the question properly. Remaining critical and focussed throughout will ensure you identify distractors quickly.