Linlithgow Academy · Mathematics · S3 Revision

Gradient

Gradient = vertical height ÷ horizontal distance. Convert units first, then simplify.

The formula

horizontal distance vertical height

From the formula sheet:

gradient =  vertical height horizontal distance

⚠ Both measurements must be in the same units before you divide.

Gradient

Gradient with mixed units

A ramp rises 3·6 m vertically over a horizontal distance of 480 cm. Calculate the gradient of the ramp. Give your answer as a fraction in its simplest form.(2 marks)
480 cm 3·6 m
Convert so both measurements are in the same unit.3·6 m = 360 cm✓1
In plain EnglishThe height is in metres and the distance is in centimetres — you can't divide them yet. Multiply 3·6 by 100 to convert metres into centimetres.
3·6 × 100 = 360 cm.
Write the gradient as a fraction.gradient = 360480
In plain EnglishUse the formula: gradient = vertical height ÷ horizontal distance.
gradient = 360/480
Simplify to its simplest form. 360 480 ÷ 120 ÷ 120 = 34 3 4 ✓2
In plain EnglishFind the highest number that divides into both 360 and 480. That's 120.
360 ÷ 120 = 3  |  480 ÷ 120 = 4
3 and 4 share no common factors, so 3/4 is the final answer. ✓
⚠ Common errors
  • Writing 3·6/480 without converting — units must match before you divide.
  • Inverting the fraction to give 4/3 — gradient is always vertical ÷ horizontal.
  • Stopping at 360/480 without fully simplifying — M2 is not awarded.
Marking points
M1 Consistent units — 360 cm and 480 cm (or 3·6 m and 4·8 m)
M2 Gradient as a fraction in its simplest form: 3/4

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