Share a total
Ratio terms count equal parts of one total
- Add Find the total number of parts
- Divide Find the amount represented by one part
- Multiply and check Allocate the required parts. Check the total and their order
Worked example
Share the grant between the groups in the order shown
\[\begin{gathered}T=\$228\\A:B:C=2:5:5\end{gathered}\]
- \(\displaystyle 2+5+5=12\)Count all equal parts
- \(\displaystyle \$228\div12=\$19\)Find the value of one part
- \(\displaystyle A=2\times\$19=\$38\)Group A receives two parts
- \(\displaystyle B=5\times\$19=\$95\)Group B receives five parts
- \(\displaystyle C=5\times\$19=\$95\)Group C receives five parts
- \(\displaystyle \$38+\$95+\$95=\$228\)The shares account for the whole grant and match the ratio order
Common mistakes
Dividing by one term
✕\(\displaystyle p=228\div2\)✓\(\displaystyle p=228\div(2+5+5)\)
One part comes from dividing by every part in the wholeDifficulty levels
introFind both shares
standardFind all shares or a selected share in a three-term ratio
challengeUse four shares, an unreduced ratio or a difference between shares
Questions about this topic
Must the ratio be simplified first?+
No. The original ratio gives the same shares when every term is used consistently
Can I check only the total?+
No. The amounts must also match the ratio in the named order
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 1: Percentages and ratios
In this chapter
Convert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1A Percentages: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changeAdd GST to a priceFind the GST and the pre-GST price from an inclusive priceExpress a ratio in simplest formComplete an equivalent ratioDivide a quantity in a given ratio1E Dividing in a ratio: Use one known part of a ratio to find the others1F Unitary method: Find the original amount from a percentage1F Unitary method: Use one known part of a ratio to find the othersScale a proportional quantity with the unitary methodDecide which option is the better value