Bar Models, Units and Ratio

In short: A bar model draws each amount as a bar made of equal units, which turns a word problem into a picture. Find what 1 unit is worth, then multiply, and to share in a ratio, add the parts to find the total number of units.

Before you start

• Fractions of an amount (see the Fractions unit).
• Equivalent fractions: making two fractions have the same numerator, like $\frac{3}{4}=\frac{6}{8}$ and $\frac{2}{5}=\frac{6}{15}$.
• A ratio like $2:3$ compares two amounts: for every 2 of the first there are 3 of the second.

The unitary method

Sharing in a ratio

A fraction of one equals a fraction of another

This type of question appears on almost every selective test.

Quick summary

• Draw each amount as equal units, find 1 unit, then multiply.
• To share in a ratio, add the parts to find how many parts in total.
• Give the smallest share 1 unit to avoid fractions.
• If a fraction of A equals a fraction of B, make the numerators equal. The denominators then give the units for A and B.
• To make two amounts equal, the richer one gives away half the difference.

Quiz