Introduction to Ratios Flashcards

All 18 cards in this deck

What does the ratio notation $a : b$ mean?

e.g. red : blue $= 3 : 4$

For every $a$ of the first there are $b$ of the second.

e.g. for every 3 red counters there are 4 blue counters.

In the question "write the ratio of the number of cows to the number of sheep", which number is written first?

The number of cows.

The parts go in the order named in the question.

True or false? The ratio $2 : 3$ means the same as the ratio $3 : 2$.

False.

The order of a ratio matters — $2:3$ and $3:2$ describe different situations.

True or false? If red : blue $= 1 : 4$, then $\frac{1}{4}$ of the counters are red.

False.

There are $1+4=5$ parts altogether, so $\frac{1}{5}$ of the counters are red.

How do you find the fraction of the total that one part of a ratio represents?

e.g. red : blue $= 3 : 4$, what fraction are red?

Write that part over the total number of parts.

$\frac{3}{3+4} = \frac{3}{7}$ are red.

What is an equivalent ratio?

A ratio made by multiplying or dividing both parts by the same number.

e.g. $2:3$, $4:6$ and $20:30$ are all equivalent.

What are the steps to write a ratio in its simplest form?

e.g. simplify $24 : 36$

1. Find the HCF of the parts: HCF of 24 and 36 is 12
2. Divide both parts by it: $24\div12 : 36\div12$
3. Answer: $2 : 3$

How do you simplify a ratio of two quantities given in different units?

e.g. $2$ m $: 50$ cm

Convert to the same unit first, then simplify and drop the units.

$200$ cm $: 50$ cm $= 4 : 1$

How do you simplify a ratio containing decimals or fractions into whole numbers?

e.g. $0.4 : 1.2$

Multiply both parts by the same number to clear them, then simplify.

$\times 10$ gives $4 : 12 = 1 : 3$

How do you write a ratio in the form $1 : n$?

e.g. write $12 : 30$ in the form $1 : n$

Divide both parts by the first part.

$12\div12 : 30\div12 = 1 : 2.5$

True or false? When a ratio is written in the form $n : 1$, the value of $n$ must be a whole number.

False.

$n$ is often a decimal or fraction, e.g. $5:4$ becomes $1.25 : 1$.

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 the amount by the total parts: $84\div7=12$
3. Multiply: shares are $2\times12=24$ and $5\times12=60$

True or false? To share £60 in the ratio $1 : 3$ you divide £60 by 3.

False.

You divide by the total number of parts, $1+3=4$.

How do you find each part when you are given a part : whole ratio?

e.g. blue : total $= 3 : 5$ for 40 counters

Use the part over the whole as a fraction of the amount.

Blue $=\frac{3}{5}\times40=24$, so the rest is $40-24=16$.

How do you find the total when you know one share and the ratio?

e.g. ratio $3 : 5$ and the smaller share is 12

Divide the share by its number of parts, then multiply by the total parts.

$12\div3=4$ per part, total $=4\times8=32$.

How do you find the other share when you know one share and the ratio?

e.g. $A : B = 2 : 7$ and $A = 6$

Find the value of one part, then multiply by the other number of parts.

$6\div2=3$ per part, so $B=7\times3=21$.

How do you express the division of a quantity into two parts as a ratio?

e.g. 20 sweets split into 15 and 5

Write the two parts in the order asked, then simplify.

$15 : 5 = 3 : 1$

True or false? Simplifying a ratio does not change what the ratio means, so $24 : 36$ and $2 : 3$ describe the same relationship.

True. Both parts were divided by $12$, giving an equivalent ratio.