**Question**

**Introduction**

This looks
like a difficult problem because there are different fractions and different
numbers. There seems to be so much
information. How do we deal with that?

**Solution**

One good
way to organise information is to use a two-way table. I have a row for the “speckies” (bespectacled
people) and a row for the “non-speckies”.
I put one column for the ladies and one column for the men. Put in column- and row- totals and the grand
total. Instead of spelling out the
words, I use icons to represent the different groups. Who says you cannot be creative in maths?

I use
“circle” units for the women and “square” units for the men. This is my Distinguished Ratio Units
method. It is easy to work out the total
for the speckies. Just subtract 282
from 456. After filling up the table, we get a diagram
like this:-

Notice the
1 “circle” unit? It is easy to multiply this by 5 so
as to match the 5 “circle” units. So I multiply everything from the speckies’
row by 5. I am imagining what would happen if there
were five times as many bespectacled men and women. For then the numbers of bespectacled women
would be the same as the number of the clear-sighted women. The result is shown in green below.

With the “circle” units equalised to 5
units each, we can now compare the
25 “square” units with the 4 “square” units. The difference of 21 “square” units must be due to the
difference between 870 and 282, which is
588. That allows us to work out
the value of 1 “square” unit and then 5
“square” units (representing the number of male speckies). Knowing two of the numbers in the speckies’
row, we can finally work out the remaining number, which is the number of
female speckies.

**Ans:**34 women wear spectacles.

**Summary**

In this
article, I have demonstrated the use of Distinguished Ratio Units and the use
of tables for organising information. I
have also demonstrated the technique of equalising one type of units (in this
case the “circle” units), so that we can compare the other type of units (here the “square” units). I hope you have found this article useful.

H02. Use a
diagram / model

H04. Look for
pattern(s)

H05. Work
backwards

H08. Make
suppositions

H11. Solve part
of the problem

**Suitable Levels**

*****Primary School Mathematics

* other syllabuses that involve whole
numbers and ratios

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