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NSW Y12 Maths Standard 1 NSW Y12 Maths Standard 2 NSW Y12 Maths Advanced NSW Y12 Maths Extension 1 NSW Y12 Maths Extension 2

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Rates and Ratios Networks Investments and Loans Non-Right Angled Trigonometry Simultaneous Equations Bivariant Data Analysis Annuities Non-Linear Relationships Normal Distribution Critical Path Analysis

NSW Y12 Maths - Standard 2 Rates and Ratios Ratio Calculations

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Ratio Calculations Theory

A ratio is used to compare amounts of the same units in a definite order.\\ \begin{multicols}{2} \textbf{Example 1}\\ Three sides of a triangle are in the ratio \(5: 12: 13\). If the shortest side is \(3.5 \mathrm{~cm}\) then what is the length of the longest side? \\ \textbf{Example 1 solution}\\ $\begin{aligned} 5 \text { units } & =3.5 \mathrm{~cm} \\ 1 \text { unit } & =3.5 \div 5 \\ & =0.7 \mathrm{~cm} \\ 13 \text { units } & =13 \times 0.7 \\ & =9.1 \mathrm{~cm} \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ There are a total of 70 balls. The ratio of the number of white balls to red balls is \(2: 3\). The ratio of the number of red balls to blue balls is \(4: 5\). How many red balls are there? \\ \textbf{Example 2 solution}\\ Let \(W=\) white, \(R=\) red and \(B=\) blue \\ $\begin{aligned} & \therefore \quad W: R=2: 3 \quad R: B=4: 5 \\ & W: R=2 \times 4: 3 \times 4 \quad R: B=4 \times 3: 5 \times 3 \\ & W: R=8: 12 \quad R: B=12: 15 \\ & \therefore W: R: B=8: 12: 15 \\ & \text { Total parts }=8+12+15=35 \\ & 35 \text { parts }=70 \rightarrow 1 \text { part }=2 \\ & \therefore \text { Red balls }=2 \times 12 \\ & \qquad\qquad\qquad =24 \end{aligned}$\\ \end{multicols}

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Videos

Videos relating to Ratio Calculations.

  • Ratio Calculations - Video - Ratio Calculations

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  • Ratio Calculations - Video - Ratios 1

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  • Ratio Calculations - Video - Ratios 2

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  • Ratio Calculations - Video - Dividing a Quantity in a Given Ratio 1

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  • Ratio Calculations - Video - Dividing a Quantity in a Given Ratio 2

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