Chapter 06

Fractions, decimals and percents

A half, 0.5 and 50% are the same amount written three ways. Which one a question uses is usually a matter of what it is about: shop prices are percents, measurements are decimals, and recipes are fractions.

Moving between the three is the skill this chapter is for, because a question asked in one of them is often easiest answered in another.

Three ways of writing a part

Fractions, decimals and percents are three ways of showing part of a whole. The same amount can be written all three ways.

  • 1/2 is the same as 0.5, which is the same as 50%.
  • 1/4 is the same as 0.25, which is the same as 25%.
  • 3/4 is the same as 0.75, which is the same as 75%.
  • When the bottom numbers match, add the top numbers.

Adding fractions

1/4 + 2/4 = 3/4

The bottom numbers are the same, so add the top numbers.

Percent and money formulas

A few of these are usually memorised. The rest follow from what they describe: profit is what is left after the cost comes off, which is the formula itself stated in words.

Percent and money

Percent of a number

part = percent × whole

Turn the percent into a decimal first. 20% becomes 0.20.

Example

What is 20% of 80?

0.20 × 80 = 16

Profit

profit = selling price − cost price

What is left over when what you paid comes off what you sold it for.

Example

You buy a bike for $80 and sell it for $95.

95 − 80 = 15

The profit is $15.

Loss

loss = cost price − selling price

The same subtraction the other way round, when you sold it for less than you paid.

Discount

discount = marked price − sale price

The money taken off the price. As a percent it is discount ÷ marked price × 100.

Example

A $50 shirt is on sale for $40.

50 − 40 = 10

The discount is $10, which is 20%.

Sale price

sale price = marked price × (100 − discount %) ÷ 100

What you actually pay once the percent has come off.

Example

A $80 jacket is 15% off.

80 × 85 ÷ 100 = 68

You pay $68.

Where this leads

The adding machine
Its percent key converts and reads as a percentage of the running total, which is how a till works out a discount.