Dividing Quantity into Given Ratio

Dividing a quantity in a given ratio means sharing it so that each share matches its number of parts. To share \(\$72\) in the ratio \(4:5\), there are \(9\) parts, so one part is \(\$8\) and the shares are \(\$32\) and \(\$40\). In NSW Year 8 maths this unitary method handles every case (NESA outcome MA4‑RAT‑C‑01).

You will share amounts in ratios with two, three or four terms, including decimal and fraction ratios, mixed units and money to the cent. You will work backwards from one share, or from the difference between two shares, to find the total. Harder problems hand out a fixed amount first, move marbles from one person to another, or split the angles of a quadrilateral. Garage-sale earnings and concrete mixes are typical. It is part of Year 8 Rates and Ratios.