Year 6 Exam > Year 6 Notes > Year 6 Mathematics > Substitute into simple expressions and formulae
Substitute into simple expressions and formulae | Year 6 Mathematics PDF Download
What is formulae?
- Formulae in mathematics are essentially facts or rules expressed in a mathematical form to help calculate a quantity using related values.
- Letters are often used in formulae to represent numbers, allowing for easy substitution and manipulation based on the given rule.
Finding the Volume of a Cuboid
- When determining the volume of a cuboid, you typically multiply the length by the width by the height.
- As a formula, the volume of a cuboid is calculated as Volume = length x width x height, or simply Volume = lwh.
- The letters are placed adjacent to each other to indicate multiplication.
- Algebraic notation avoids using 'x' for multiplication to prevent confusion with variables.
- Substitution is crucial when dimensions vary, ensuring that the volume calculation remains consistent.
Example
Example: Look at this cuboid.
This time the length = 4cm, width = 2cm, and the height = 3cm.
To find the volume, you’d use the formula:
Volume = lwd
So:
4cm x 2cm x 3cm = 24cm3.
What if the length changed to 3cm, the width to 2cm, and the height to 2cm?
You would still use the same formula to find the volume, but swap in the different measurements.
3cm x 2cm x 2cm = 12cm3
Using words in a formula
- When working with formulas that involve words instead of just letters, it's important to understand how to substitute values effectively.
Example
Example: Libby works in a pet shop. She earns £30 a day plus £10 for every pet she sells.
The formula to show this would be:
Amount earned = £30 + (10 x number of pets sold).
How much would Libby earn if she sold 5 pets on Monday?
To solve this, you would have to substitute the number 5 into the “number of pets sold.”
Amount earned = £30 + (10 x 5)
So Libby would earn £80 on Monday.
How much would Libby earn if she sold 9 pets on Tuesday?
This time, you would substitute the number 9 into the “number of pets sold.”
Amount earned = £30 + (10 x 9).
Libby would earn £120 this time.
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