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Sharing in a Ratio
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Foundational Skills
Find the total number of parts in a ratio
\[ 3:5 \rightarrow 8 \text{ parts} \]
Add the parts of a ratio to find the total.
Find the total parts in a three-part ratio
\[ 2:3:5 \rightarrow 10 \text{ parts} \]
Add all three parts of a ratio.
Find the value of one part given the total
\[ £40 \div 8 = £5 \text{ per part} \]
Divide total by total parts.
Using Bar Models to Solve
Draw a bar model for a sharing problem
\[ 3:4 \text{ with total} \]
Draw bars showing ratio structure.
Draw a bar model when one share is given
\[ 2:5 \text{, smaller } = 18 \]
Label known share on bar model.
Draw a bar model when difference is given
\[ 3:7 \text{, diff } = 20 \]
Show difference on bar model.
Use a bar model to find one share
\[ \text{Total } 72 \rightarrow \text{larger?} \]
Read bar model to calculate share.
Use a bar model when one share is given
\[ \text{Smaller } 14 \rightarrow \text{total?} \]
Find total from labelled share.
Use a bar model to find both shares from diff
\[ \text{Diff } 21 \rightarrow \text{both?} \]
Calculate both shares from difference.
Sharing Given Total (2-part)
Share in a 2-part ratio (find smaller)
\[ £48 \text{ in } 3:5 \]
Find the smaller share.
Share in a 2-part ratio (find larger)
\[ 72 \text{ in } 4:5 \]
Find the larger share.
Share in a 2-part ratio (find both)
\[ £56 \text{ in } 3:4 \]
Find both shares.
Share between named people
\[ \text{Ali and Ben in } 2:3 \]
Find a specific person’s share.
Share money (with pence)
\[ £4.80 \text{ in } 5:7 \]
Divide amounts with decimals.
Sharing Given Total (3-part)
Share in a 3-part ratio (find one)
\[ 120 \text{ in } 2:3:5 \]
Find largest/smallest share.
Share in a 3-part ratio (find all)
\[ £180 \text{ in } 2:3:4 \]
Find all three shares.
Share between three people
\[ \text{Amy, Ben, Cara} \]
Find one person’s share.
Share money in 3-part (with pence)
\[ £6.30 \text{ in } 2:3:4 \]
3-part sharing with decimals.
Given One Part
Find another share when one is given (2-part)
\[ \text{Jo gets £18} \rightarrow \text{Kim?} \]
Use one share to find another.
Find the total when one share is given
\[ \text{Smaller } = £14 \rightarrow \text{total?} \]
Find total from one share.
Find another share when one is given (3-part)
\[ \text{Largest } = £40 \rightarrow \text{smallest?} \]
3-part: one share to another.
Find all shares when one is given
\[ \text{Middle } = 24 \rightarrow \text{total?} \]
Find total from middle share.
Find how many more one gets than another
\[ \text{Tia gets £56} \rightarrow \text{difference?} \]
Find difference between shares.
Given Difference
Find shares when difference is given (2-part)
\[ 3:7 \text{, diff } = 20 \]
Use difference to find both shares.
Find total when difference is given
\[ 2:5 \text{, £24 more} \rightarrow \text{total?} \]
Use difference to find total.
Find larger share when difference is given
\[ 5:8 \text{, diff } = 18 \]
Use difference to find larger.
Find shares in 3-part ratio from difference
\[ 1:2:5 \text{, diff } = 36 \]
3-part: use difference for all.
Problem Contexts
Share angles in a ratio
\[ \text{Straight line } 2:3 \]
Angles summing to 180°.
Share angles in a 3-part ratio
\[ \text{Triangle } 1:2:3 \]
Triangle angles in ratio.
Sharing with subsequent calculation
\[ \text{Share then find cost} \]
Two-step ratio problem.
Share then find fraction remaining
\[ 3:5 \rightarrow \text{fraction?} \]
Connect ratio to fractions.
Interpret ratio sharing results
\[ \text{More or less than £100?} \]
Reason without full calculation.
Work backwards to find the ratio
\[ £24 : £36 \rightarrow \text{ratio?} \]
Find ratio from given amounts.
Special Cases
Share in the ratio 1:n
\[ £24 \text{ in } 1:5 \]
When one part of ratio is 1.
Share in a ratio with repeated values
\[ 2:2:3 \text{ or } 1:1:2 \]
Equal parts in ratio.
Form a ratio from a worded description
\[ \text{“twice as much”} \]
Convert description to ratio.
Share and reason about changed situation
\[ \text{Remove one colour} \]
New ratio after change.
Algebraic ratio sharing setup
\[ x \rightarrow \text{larger share?} \]
Express shares algebraically.
Sharing with mixed units
\[ 1.5\text{m in } 2:3 \rightarrow \text{cm?} \]
Answer in different unit.
Timer (Optional)
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Question