Fractions, Decimals and Percentages

Fractions represent parts of a whole. For example, 3/4 represents three parts of a total which is divided into four equal parts.
There are two types of fractions: Proper fractions (e.g. 3/4), where the numerator is less than the denominator, and improper fractions (e.g. 7/4), where the numerator is greater than the denominator.
Fractions can be simplified by dividing both the numerator and the denominator by their highest common factor (HCF). For example, 6/8 can be simplified to 3/4.
Mixed numbers include a whole number and a fraction, e.g. 1 3/4. These can be converted into improper fractions.
When adding or subtracting fractions, it’s necessary to have a common denominator.
Multiplication of fractions is straightforward; just multiply the numerators to get the new numerator and the denominators to get the new denominator.
For division, flip the second fraction upside down (this is now called the reciprocal) and then perform multiplication.
Decimals offer another way of representing fractions and percentages. These are based on powers of 10, where each decimal place represents a tenth, a hundredth, a thousandth, etc. of the whole.
To convert fractions to decimals, divide the numerator by the denominator. Some fractions will give recurring decimal numbers.
Conversely, to convert decimals to fractions, identify what place value the last decimal figure is at. The decimal becomes the numerator while the denominator is 10 raised to the number of decimal places.
To convert percentages to decimals, divide the value by 100, and to convert decimals to percentages, multiply the value by 100.
To convert fractions to percentages, first convert the fraction to a decimal and then convert the decimal to a percentage.
Percentages are used to express a portion of 100. For example, 45% means 45 out of 100. They’re commonly used in real-life applications such as discounts, interest rates, and growth rates.
When finding percentages of amounts, think of the percentage as a fraction or decimal. For example, to find 15% of 200, either calculate 15/100 x 200 or 0.15 x 200.
The ‘percentage change’ is a widely used concept and it is calculated by the formula: ((final value - initial value) / initial value) x 100%
Remember, practice makes perfect. Regular practice with a range of problems involving fractions, decimals and percentages will strengthen understanding and fluency with these concepts.