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Check the units and the scale

What this lesson is about

Most confident wrong answers break at the units or the order of size. Check those two before anything else.

At the block office a clerk adds 40 litres of diesel to 600 kilometres and writes 640 in the register. What now?

Why this matters

Most confident wrong answers break at the unit or at the order of size, not at the arithmetic. Those two are also the cheapest things to check.

You can find the first place two units were mixed inside somebody else's working.

Most confident wrong answers break at the unit or at the order of size, not at the arithmetic. Those two are also the cheapest things to check.

Check the unit before the arithmetic: people and households are not the same.
Two numbers add or compare only with the same unit and the same period.
A scale error survives every later step, so look for it first.

Task

A working adds forty litres of petrol to six hundred kilometres and reports six hundred and forty.

Weak approach Adding forty and six hundred again, getting six hundred and forty, and passing the working. The arithmetic was checked twice and neither check looked at what was being added.

Stronger approach Marking line four: forty litres and six hundred kilometres cannot be added together. That line had to divide instead, to give the distance for each litre.

Why the stronger approach works The arithmetic was right and the step was wrong. The unit is the thing that showed it.

Try a changed situation A shop's stock book shows sixty bags brought in and forty-five kilograms sold, and the owner writes fifteen left. What went wrong?

Make something yourself Take a worked answer with at least four numbers in it. Write the unit of every number, then mark the first place where two units are mixed.

Lesson 6 of 9 on Reasoning and maths for AI worknextBreak a word problem into stepsPart 2 ends in a work sample you can send The rules this work sample is read against

Read the primary or official source: NCERT · Class 8 Maths, Direct and Inverse Proportions