Ratios Flashcards

All 18 cards in this deck

What does it mean to write a ratio in its simplest form?

Divide every part by their highest common factor, so the parts are whole numbers with no common factor.
e.g. $12:18 = 2:3$

How do you write a ratio in the form $1:n$?
e.g. write $4:10$ in the form $1:n$

Divide both parts by the left-hand part.
$4:10 = 1:2.5$ (here $n$ need not be a whole number)

What are the steps to write a ratio from a worded context and simplify it?
e.g. a bag has 12 red and 18 blue counters; write red : blue

1. Write the amounts in the order named: $12:18$
2. Divide both parts by their HCF ($6$)
3. Answer: $2:3$

How do you express one quantity as a fraction of another?
e.g. express $15$ as a fraction of $12$

Put the first quantity over the second, then simplify.
$\frac{15}{12} = \frac{5}{4}$ (a fraction greater than 1 is fine)

True or false? The ratio $3:5$ means the same as the ratio $5:3$.

False. The order of a ratio matters — it must match the order of the things named.

True or false? Two quantities must be converted to the same unit before writing them as a ratio.

True. Ratios compare like with like.
e.g. $50$ cm $: 2$ m $= 50:200 = 1:4$

What are the steps to share an amount in a given part : part ratio?
e.g. share $84$ in the ratio $2:5$

1. Add the parts: $2+5=7$
2. Divide to find one part: $84 \div 7 = 12$
3. Multiply each part: $24$ and $60$

How do you find a share when the ratio is given as part : whole?
e.g. red counters : all counters $= 3:8$ in a bag of $40$ counters

Multiply the total by that part over the whole.
$\frac{3}{8} \times 40 = 15$ red counters

How do you find the total when one share is known?
e.g. an amount is shared $3:4$ and the larger share is $20$

Divide the known share by its number of parts, then multiply by the total number of parts.
$20 \div 4 = 5$, $5 \times 7 = 35$

What are the steps to find the shares when the difference between them is known?
e.g. money shared $2:5$, one person gets £24 more

1. Difference in parts: $5-2=3$
2. One part: $£24 \div 3 = £8$
3. Shares: $£16$ and $£40$

True or false? If counters are in the ratio red : blue $= 1:2$, then half of the counters are red.

False. There are $1+2=3$ parts, so $\frac{1}{3}$ are red and $\frac{2}{3}$ are blue.

True or false? To divide $120$ in the ratio $3:5$ you work out $120 \div 3$ and $120 \div 5$.

False. You divide by the total number of parts ($3+5=8$), then multiply by $3$ and by $5$.

What are the steps to scale a recipe using the unitary method?
e.g. a recipe for 4 people, needed for 6 people

1. Divide each amount by the number given: $\div 4$ gives the amount for 1 person
2. Multiply by the number wanted: $\times 6$
3. Equivalent to multiplying every amount by $1.5$

What does a map scale of $1:25\,000$ mean?

1 unit on the map represents $25\,000$ of the same unit in real life.
e.g. 1 cm on the map is $25\,000$ cm $= 250$ m

True or false? To find a real distance from a distance measured on a map you divide by the scale factor.

False. You multiply the map distance by the scale factor; you divide when going from real distance to map distance.

How do you find the scale of a scale drawing?
e.g. a $2$ cm line on the drawing represents $10$ m in real life

Convert both to the same unit, then divide the real length by the drawing length.
$1000 \div 2 = 500$, so the scale is $1:500$

How do you find the amount of one ingredient in a mixture from the amount of the other?
e.g. red : yellow paint $= 2:3$ and $10$ litres of red is used

Find the value of one part, then multiply by the other number of parts.
$10 \div 2 = 5$ litres per part, so yellow $= 3 \times 5 = 15$ litres

How do you find a ratio from an equation linking two letters?
e.g. $5c + d = c + 4d$, find $c:d$

Rearrange so one letter is a multiple of the other, then read off the ratio.
$4c = 3d$, so $c:d = 3:4$