Equivalent & Simplified Ratios Flashcards

All 7 cards in this deck

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 $1.25 : 1$.

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.