**Question**

**Introduction**

This
is a primary school ratio problem that is quite a favourite among question
setters, but poses headaches for pupils and parents. The trouble is that the ratios use different
base units and this makes it difficult to compare the ratios. Can we avoid using algebra or trial and error?

**Strategy**

Note [H04, H09] that the difference in the areas
between the rectangle and the square (including the shaded overlapping part) is
exactly the same as the difference between them without the overlapping part. With this crucial observation, we can proceed
to try to equalise the

*ratio units*[H10] of the aforementioned differences. This can be done by multiplying to get to the Lowest Common Multiple, which, in this example is 6. Henceforth we can be sure of using the same ratio units, because the same number of units are used to refer to the same quantity.**Solution**

**Summary**

Ratio
problems are solved by making sure that we use the same type of units.

H02. Use a
diagram / model [ table ]

H04. Look for
pattern(s)

H05. Work
backwards

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

**Suitable Levels**

*****Primary School Mathematics

* other syllabuses that involve areas and
ratios

* anyone who wants to learn
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