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Combining Ratios
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Foundational Skills
Identify the shared term in two ratios
\[ A:B \text{ and } B:C \rightarrow B \]
Recognise which term is common to two ratios.
Recognise when ratios can be combined
\[ A:B \text{ and } B:C \rightarrow \text{Yes} \]
Determine if two ratios share a common term.
Find the scale factor needed
\[ B=3, B=6 \rightarrow \times 2 \]
Calculate the multiplier for equal shared terms.
Scale a ratio by a given factor
\[ 2:5 \times 3 = 6:15 \]
Multiply all parts of a ratio by the same number.
Combining Two Ratios (Shared Middle)
Combine with matching shared term
\[ 2:3, 3:5 \rightarrow 2:3:5 \]
Combine when shared term already matches.
Combine requiring scaling of one ratio
\[ 2:3, 6:5 \rightarrow 4:6:5 \]
Scale one ratio to make shared term equal.
Combine requiring scaling of both ratios
\[ 2:5, 3:4 \rightarrow 6:15:20 \]
Scale both ratios using LCM.
Finding a Missing Ratio
Find the third ratio given two
\[ A:B:C \rightarrow B:C \]
Extract one 2-part ratio from a 3-part ratio.
Find and simplify component ratio
\[ 6:10:15 \rightarrow 3:5 \]
Find and simplify from combined ratio.
Find combined from three linked ratios
\[ A:B, B:C, C:D \rightarrow A:B:C:D \]
Chain three ratios into a 4-part ratio.
Find a missing term in combined ratio
\[ 4:\square:10, A:B=2:3 \]
Use a known ratio to find missing value.
Working with Quantities
Find quantities from combined ratio
\[ 2:3:4, \text{total}=45 \]
Share a total into three parts.
Find quantity given another
\[ 3:4:5, B=24, A=? \]
Use one quantity to find others.
Find difference between quantities
\[ 2:5:8, \text{diff}=? \]
Calculate difference between parts.
Combine then find quantities
\[ A:B, B:C, \text{total}=100 \]
Combine ratios then share quantity.
Problem Contexts
Recipe scaling with combined ratios
\[ 4:2:1, 280\text{g flour} \]
Scale recipe quantities using ratios.
Compare two quantities in ratio
\[ 3:5:7, C \div A = ? \]
Find multiplicative relationship.
Find fraction one part is of another
\[ 2:5:8, X/Z = ? \]
Express part as fraction of another.
Combined ratio with percentage
\[ 2:3:5, \text{blue} = ?\% \]
Convert part of ratio to percentage.
Special Cases
Combine then simplify
\[ 2:4, 4:6 \rightarrow 1:2:3 \]
Combine ratios that need simplifying.
Combine with 1:1 component
\[ 1:1, 3:5 \rightarrow 3:3:5 \]
Handle ratios with equal parts.
Shared term is double
\[ 2:3, 6:7 \rightarrow 4:6:7 \]
Scale when one is multiple of other.
Ratio with multiplicative statement
\[ A:B=4:5, C=2B \]
Combine ratio with word statement.
Ratio chain with reversal
\[ A:B, C:B \rightarrow A:B:C \]
Shared term in same position.
Combine larger numbers
\[ 10:15, 15:25 \rightarrow 2:3:5 \]
Combine and simplify larger ratios.
Invalid ratio combination
\[ A:B, C:D \rightarrow \text{No} \]
Recognise when ratios can’t combine.
Timer (Optional)
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