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Fractions in Context Part 2
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Foundational skills
Identify the operation – addition
\[ \text{Total} \rightarrow \text{Add} \]
Identify that combining requires addition.
Identify the operation – subtraction
\[ \text{Left} \rightarrow \text{Subtract} \]
Identify that finding remainder requires subtraction.
Identify a reverse fraction problem
\[ \frac{1}{5} = 12 \rightarrow \times 5 \]
Recognise when to multiply to find the whole.
Adding fractions in context
Add fractions – same denominator
\[ \frac{2}{7} + \frac{3}{7} = \frac{5}{7} \]
Add fractions with same denominator in context.
Add fractions – related denominators
\[ \frac{1}{2} + \frac{1}{4} = \frac{3}{4} \]
Add fractions where one denominator divides the other.
Add fractions – different denominators
\[ \frac{2}{3} + \frac{3}{4} = 1\frac{5}{12} \]
Add fractions with unrelated denominators.
Add mixed numbers
\[ 2\frac{1}{4} + 1\frac{3}{4} = 4 \]
Add mixed numbers in context.
Add fraction to whole number
\[ 3 + \frac{3}{4} = 3\frac{3}{4} \]
Add a proper fraction to a whole number.
Subtracting fractions in context
Subtract fractions – same denominator
\[ \frac{5}{6} – \frac{2}{6} = \frac{1}{2} \]
Subtract fractions with same denominator.
Subtract fractions – related denominators
\[ \frac{3}{4} – \frac{1}{2} = \frac{1}{4} \]
Subtract where one denominator divides the other.
Subtract fractions – different denominators
\[ \frac{5}{6} – \frac{2}{3} = \frac{1}{6} \]
Subtract fractions with unrelated denominators.
Subtract fraction from whole number
\[ 3 – \frac{2}{5} = 2\frac{3}{5} \]
Subtract a fraction from a whole number.
Subtract mixed numbers
\[ 4\frac{1}{2} – 1\frac{3}{4} = 2\frac{3}{4} \]
Subtract mixed numbers in context.
Multiplying fractions in context
Multiply fraction by whole number
\[ \frac{3}{4} \times 5 = 3\frac{3}{4} \]
Multiply a fraction by a whole number.
Multiply fraction by fraction
\[ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \]
Find a fraction of a fraction.
Scale a recipe using fractions
\[ 300g \times \frac{3}{2} = 450g \]
Scale recipe ingredients by a fraction.
Find area involving fractions
\[ \frac{3}{4} \times \frac{2}{3} = \frac{1}{2} \text{ m}^2 \]
Calculate area with fractional dimensions.
Dividing by fractions in context
Divide by unit fraction – how many fit?
\[ 6 \div \frac{1}{4} = 24 \]
Divide whole number by unit fraction.
Divide by non-unit fraction
\[ 4 \div \frac{2}{3} = 6 \]
Divide by a non-unit fraction.
Divide fraction by whole number
\[ \frac{3}{4} \div 3 = \frac{1}{4} \]
Share a fraction equally.
How many times does one fit?
\[ 2 \div \frac{1}{3} = 6 \]
How many small amounts fit in larger?
Fractional increase and decrease
Increase by a unit fraction
\[ 40 + \frac{1}{4} \text{ of } 40 = 50 \]
Increase an amount by a unit fraction.
Increase by a non-unit fraction
\[ £80 + \frac{2}{5} = £112 \]
Increase an amount by a non-unit fraction.
Decrease by a unit fraction
\[ £45 – \frac{1}{5} = £36 \]
Decrease an amount by a unit fraction.
Decrease by a non-unit fraction
\[ 120 – \frac{2}{3} = 40 \]
Decrease an amount by a non-unit fraction.
Multiplier method
\[ £60 \times \frac{2}{3} = £40 \]
Apply fractional change using multiplier.
Reverse fraction problems
Find whole from unit fraction
\[ \frac{1}{5} = 12 \rightarrow 60 \]
Find the whole given a unit fraction of it.
Find whole from non-unit fraction
\[ \frac{3}{4} = 18 \rightarrow 24 \]
Find the whole given a non-unit fraction.
Find original after increase
\[ \text{After } +\frac{1}{4}: £60 \rightarrow £48 \]
Work backwards from fractional increase.
Find original after decrease
\[ \text{After } -\frac{1}{5}: £64 \rightarrow £80 \]
Work backwards from fractional decrease.
Find original when remainder given
\[ \text{After } \frac{1}{3}: 24 \text{ left} \rightarrow 36 \]
Work backwards when remainder is given.
Multi-step problems
Two sequential fraction operations
\[ 120 \rightarrow \frac{1}{4} \rightarrow \frac{1}{3} \]
Multiple fraction operations on remainders.
Combine fractions and percentages
\[ £80 – \frac{1}{4} – 10\% \]
Fractional and percentage changes together.
Sequential sharing with fractions
\[ 1 – \frac{1}{4} – \frac{1}{3} \text{ of rest} \]
Multiple people take fractional shares.
Rate problems with fractions
\[ \frac{1}{5} \text{ per hour} \rightarrow 5 \text{ hrs} \]
Work/rate problems with fractions.
Successive fractional changes
\[ 1000 +\frac{1}{10} -\frac{1}{10} = 990 \]
Successive changes don’t cancel.
Special cases
Fractional remainder in context
\[ 50 \div 6 = 8 \text{ R } \frac{1}{3} \]
Express remainder as fraction.
Problems with fractional rates
\[ 8 \times \frac{3}{4} = £6 \]
Rate involves a fraction.
Unit conversion with fractions
\[ \frac{3}{4} \text{ l} = 750 \text{ ml} \]
Convert between units with fractions.
Ratio and fraction connection
\[ 2:3 \rightarrow \frac{2}{5} \]
Convert ratio to fraction.
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