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Simplifying and Equivalent Ratios
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Simplifying ratios (integers)
Simplify a ratio with a common factor of 2
\[ 6:10 \rightarrow 3:5 \]
Simplify a ratio by dividing both parts by 2.
Simplify a ratio with a common factor of 5 or 10
\[ 15:25 \rightarrow 3:5 \]
Simplify a ratio by dividing both parts by 5 or 10.
Simplify a ratio with any common factor
\[ 12:18 \rightarrow 2:3 \]
Simplify a ratio by finding the HCF.
Simplify a three-part ratio
\[ 6:9:12 \rightarrow 2:3:4 \]
Simplify a three-part ratio by dividing all parts by their HCF.
Simplifying ratios (fractions)
Simplify a ratio of a fraction and an integer
\[ \frac{3}{4}:2 \rightarrow 3:8 \]
Simplify a ratio where one part is a fraction.
Simplifying ratios (units)
Simplify a ratio with different length units
\[ 40\text{ cm} : 2\text{ m} \]
Convert to the same unit, then simplify.
Simplify a ratio with different mass units
\[ 500\text{ g} : 2\text{ kg} \]
Convert to the same unit, then simplify.
Simplify a ratio with different time units
\[ 45\text{ min} : 2\text{ hr} \]
Convert to the same unit, then simplify.
Simplify a ratio with different capacity units
\[ 250\text{ ml} : 1.5\text{ l} \]
Convert to the same unit, then simplify.
Equivalent ratios
Find an equivalent ratio by scaling up
\[ 3:5 \rightarrow 12:20 \]
Multiply both parts by the same number.
Find an equivalent ratio by scaling down
\[ 20:35 \rightarrow 4:7 \]
Divide both parts by the same number.
Find a missing value in equivalent ratios
\[ 4:7 = 20:\square \]
Find the missing value in a pair of equivalent ratios.
Determine if two ratios are equivalent
\[ 6:10 \text{ and } 9:15 \]
Decide if two ratios are equivalent.
The form 1:n
Write a ratio in the form 1:n (integer result)
\[ 3:12 \rightarrow 1:4 \]
Convert a ratio to the form 1:n.
Write a ratio in the form 1:n (terminating decimal)
\[ 4:10 \rightarrow 1:2.5 \]
Convert a ratio to the form 1:n with a decimal.
Write a ratio in the form 1:n (rounding required)
\[ 3:7 \rightarrow 1:2.33 \]
Convert a ratio to the form 1:n with rounding.
The form n:1
Write a ratio in the form n:1 (integer result)
\[ 15:3 \rightarrow 5:1 \]
Convert a ratio to the form n:1.
Write a ratio in the form n:1 (terminating decimal)
\[ 7:4 \rightarrow 1.75:1 \]
Convert a ratio to the form n:1 with a decimal.
Write a ratio in the form n:1 (rounding required)
\[ 7:3 \rightarrow 2.33:1 \]
Convert a ratio to the form n:1 with rounding.
Special cases
Simplify a ratio where both parts are equal
\[ 8:8 \rightarrow 1:1 \]
Simplify a ratio where both parts are the same.
Write a ratio from a frequency table
\[ \text{Cats: 6, Dogs: 9} \]
Extract values from a table and simplify.
Simplify an algebraic ratio
\[ 4x:6x \rightarrow 2:3 \]
Simplify a ratio with algebraic terms.
Convert ratio notation formats
\[ \text{‘5 to 3’} \rightarrow 5:3 \]
Convert between word and colon notation.
Timer (Optional)
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