Ratios

Understanding Ratios

• A ratio is a way of comparing quantities or amounts.
• It expresses the relationship between two or more quantities.
• Ratios can be written in three different forms: as a fraction (1/2), with a colon (1:2), or using the word “to” (1 to 2).
• A ratio can be simplified just like a fraction. The highest common factor (HCF) should be divided from both sides to make the ratio simplest.

Dividing a Quantity in a Given Ratio

• To divide a quantity in a given ratio, the first step is to calculate the total number of parts in the ratio. For instance, the total parts in the ratio 3:4 are 7 (3+4).
• Next, the total amount or quantity should be divided by the total number of parts to find the value of each part.
• Finally, multiply each side of the ratio by the value of each part to find the amount corresponding to each side.

Increasing and Decreasing Quantities by a Ratio

• To increase a quantity by a ratio, multiply the original quantity by the ratio as a fraction. For example, to increase 50 by a ratio of 3:2, multiply 50 by 1.5 (3/2 as a fraction). The increase is 25, so the new quantity is 75.
• To decrease a quantity by a ratio, divide the original quantity by the ratio as a fraction. For example, to reduce 80 by a ratio of 4:5, divide 80 by 1.25 (5/4 as a fraction). The decrease is 16, so the new quantity is 64.

Using Ratios to Solve Problems

• Direct proportion problems can be solved using ratios. If two quantities are in direct proportion, they increase or decrease together at the same ratio.
• When solving ratio word problems, always ensure to interpret and represent the problem scenario accurately.
• Converting units may be necessary when dealing with ratios involving different measurement units. Follow the BIDMAS rule (Brackets, Indices, Division/Multiplication, Addition/Subtraction) when performing calculations.