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Ratio with Fractions and Percentages
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Foundational Skills
Identify the whole in a ratio context
\[ 3:5 \rightarrow \text{whole} = 8 \]
Find the total parts in a ratio.
Fraction for one part
\[ 3:5 \rightarrow \frac{1}{8} \]
One part as a fraction of the whole.
Part-to-part vs part-to-whole
\[ 2:5 \rightarrow \frac{2}{7} \text{ of total} \]
Distinguish relationship types.
Ratio as fraction of another part
\[ 2:5 \rightarrow \frac{2}{5} \]
One part as fraction of another.
Bar Models with Fractions and Percentages
Shade bar model fraction
\[ 3:5 \rightarrow \frac{3}{8} \text{ shaded} \]
Read fraction from shaded bar.
Read fraction from bar model
\[ \text{4 of 10 shaded} = \frac{2}{5} \]
Express shaded portion as fraction.
Bar model to ratio and fraction
\[ 3:5 \text{ and } \frac{3}{8} \]
Write both ratio and fraction.
Label bar model with %
\[ 1:4 \rightarrow 20\%, 80\% \]
Calculate percentage per section.
Match bar model to percentage
\[ 1:3 \rightarrow 25\% \]
Find percentage from bar model.
Ratio to Fraction (2-part)
Fraction for smaller part
\[ 3:7 \rightarrow \frac{3}{10} \]
Smaller part as fraction of whole.
Fraction for larger part
\[ 2:5 \rightarrow \frac{5}{7} \]
Larger part as fraction of whole.
Both fractions from ratio
\[ 3:5 \rightarrow \frac{3}{8}, \frac{5}{8} \]
Convert both parts to fractions.
Named quantity fraction
\[ 4:5 \rightarrow \frac{4}{9} \text{ boys} \]
Fraction for named part in context.
Ratio to Fraction (3-part)
One part of 3-part ratio
\[ 1:2:5 \rightarrow \frac{1}{4} \text{ blue} \]
One part as fraction of whole.
All fractions from 3-part ratio
\[ 2:3:5 \rightarrow \frac{1}{5}, \frac{3}{10}, \frac{1}{2} \]
All parts as fractions.
Combined fraction (two parts)
\[ 2:3:5 \rightarrow \frac{1}{2} \text{ (red or blue)} \]
Sum two parts as fraction.
Fraction to Ratio
Same denominator to ratio
\[ \frac{3}{8}, \frac{5}{8} \rightarrow 3:5 \]
Fractions to ratio (same denom).
Different denominators to ratio
\[ \frac{1}{3}, \frac{2}{3} \rightarrow 1:2 \]
Fractions to ratio (diff denom).
Fraction and complement to ratio
\[ \frac{3}{5} \text{ red} \rightarrow 3:2 \]
Use complement to find ratio.
Ratio to Percentage (2-part)
One part to % (exact)
\[ 2:3 \rightarrow 40\% \text{ boys} \]
Convert one part to exact %.
Both parts to percentages
\[ 3:2 \rightarrow 60\%, 40\% \]
Convert both parts to %.
Ratio to % (with rounding)
\[ 5:7 \rightarrow 41.7\% \]
Convert with rounding to 1 d.p.
Ratio to Percentage (3-part)
3-part ratio to percentages
\[ 1:2:2 \rightarrow 20\%, 40\%, 40\% \]
All 3 parts as percentages.
Percentage to Ratio
Two percentages to ratio
\[ 40\%:60\% \rightarrow 2:3 \]
Convert two % to simplified ratio.
% and complement to ratio
\[ 30\% \text{ red} \rightarrow 3:7 \]
Use % complement for ratio.
Three % to 3-part ratio
\[ 50\%, 30\%, 20\% \rightarrow 5:3:2 \]
Convert 3 percentages to ratio.
Problem Solving
Ratio → fraction → calculate
\[ 3:5, 40 \text{ total} \rightarrow 25 \]
Use fraction from ratio to solve.
Ratio → % → calculate
\[ 7:3 \rightarrow 70\% \rightarrow 42 \]
Use % from ratio to solve.
Compare ratio and fraction
\[ 2:5, \frac{2}{5} \text{ correct?} \]
Check if claim is correct.
Fraction → ratio
\[ \frac{3}{8} \text{ children} \rightarrow 3:5 \]
Work backwards from fraction.
Percentage → ratio
\[ 35\% \text{ tea} \rightarrow 7:13 \]
Work backwards from %.
Special Cases
Part as fraction of other part
\[ 3:5 \rightarrow \frac{3}{5} \text{ of larger} \]
Part-to-part fraction.
50% means 1:1
\[ 50\% \text{ of total} \rightarrow 1:1 \]
Equal parts from 50%.
33.3% / 66.7% ratios
\[ 1:2 \rightarrow 66.7\% \]
Recurring decimal percentages.
25% / 75% ratios
\[ 25\%:75\% = 1:3 \]
Quarter and three-quarters.
Mixed fraction and % problem
\[ \frac{2}{5} \text{ boys} \rightarrow 60\% \text{ girls} \]
Convert via complement.
Verify fraction matches ratio
\[ 2:3, \frac{3}{5} \text{ blue?} \]
Check if fraction is correct.
% change to ratio
\[ 25\% \text{ increase} \rightarrow 4:5 \]
Original to new value ratio.
Timer (Optional)
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