Write and construct formulae - Year 7 PDF Download

Introduction

• Understanding algebraic notation and the order of operations (BIDMAS) will help in using formulae successfully.
• A formula is a rule that links variables and may be expressed in words or in mathematical symbols.
• Formulae connect variables in a mathematical relationship, allowing the calculation of one variable when others are known.
• Numbers can be substituted into a formula to find the value of the subject variable.
• Formulas can be rearranged to change the subject variable, enabling different calculations based on the same relationship.

Using formulae given in words

A formula provided in words contains the necessary instructions to calculate something. Here's how to utilize a written formula:

• Substitute a given value for the variable.
• Follow each step in the formula instructions to calculate the subject of the formula.

Example

Example: The formula for converting a distance in miles to a distance in kilometres is to divide by five and then multiply by eight.
Use the formula to convert 65 miles to kilometres.
Sol:

Substitute the given value for the distance in miles (65) and follow the formula instructions.
Divide 65 by 5, then multiply by eight (65 ÷ 5 × 8).
65 miles is 104 kilometres.

Constructing formulae from words

A formula written in words can be expressed using mathematical symbols.

• Assign a letter or symbol to each variable.
• The formula always starts with the subject variable, followed by the equals symbol.
• The expression after the equals symbol represents each instruction in the written formula using correct algebraic notation. The variables must be defined.

Confidence in writing mathematical formulae from a worded formula relies on a good understanding of algebraic notation.

Example

Example: The time taken to cook a pie depends on its mass. Cook for 25 minutes per 500g plus an extra 15 minutes.
Sol:

• A letter or symbol is assigned to the subject and each variable. T represents the time to cook the pie. M represents the mass of the pie in grams. The formula always starts with the subject variable followed by the equals symbol. The subject of this formula is the time. The formula starts with T =
  
• Each 500 g of pie is cooked for 25 minutes. To find out how many lots of 500g there are, the mass (M) is divided by 500, this is M/500. This amount is multiplied by 25. The extra 15 minutes is then added on. The formula is T = M/500 × 25 + 15. The formula can be simplified.
  
• Dividing the mass by 500 and then multiplying by 25 can be simplified to the mass divided by 20 because 25/500 is equivalent to 1/20. (500 and 25 are both divided by 25). The formula simplifies to T = M/20 + 15

Substitution using Formulae

• A formula is a rule expressed using mathematical symbols. Values are substituted into a formula to calculate a result.
• To use an algebraic formula:
  • Substitute the given value(s) for the variable(s).
  • Follow each step in the formula's instructions to determine the subject.
• When a formula involves multiple steps, it is crucial to follow the correct order of operations to ensure an accurate calculation.
• Formulae are rules written using mathematical symbols:
  

Example

Example: Use the formula to work out the perimeter of the rectangle.
Sol: Substitute the given values of length (20) and width (4) for the variables (𝒍 and 𝒘) in the formula.
Follow each step in the formula instructions. Multiply the length by two, multiply the width by two and add the results together.
2 × 20 + 2 × 4 = 48
The perimeter of the rectangle is 48 cm.

Real-life maths

• Formulae are frequently used in real life, such as for calculating the amount of paint needed to decorate a room, the size of a radiator to heat a room, or the length of ribbon required to wrap a gift.
• For example, a decorator buys the amount of paint needed to complete a job. One litre of emulsion paint will cover approximately 12 square meters (12 m²).
• To work out how many litres of paint are required, the formula is:
  
  • 𝑳 = number of litres of paint needed
  • 𝒉 = height of walls
  • 𝒘 = total width of all walls
  • 𝒄 = number of coats of paint required
• For a room that will need three coats of paint with a wall height of 2۰8 metres and a total wall width of 14 metres, the calculation will be
• The paint required is 9۰8 litres.