Question

Express each ratio as a fraction in simplest form. 18:24

Answer 1

A ratio such as 18:24 can be written in fraction form:

\[\frac{18}{24}\]

A fraction can be reduced to simplest form if the number in the numerator and denominator have common factors. The goal is to:

1. Find the greatest common factor between both numbers.
2. Re-write the fraction to include the factors of each number
3. Cancel the GCF
4. The remaining fraction should be relatively prime

Since
\(6 \times 3 = 18\)
\(6 \times 4 = 24\)

We can re-write \(\dfrac{18}{24}\) as \(\dfrac{6 \times 3}{6 \times 4}\)

Notice that 6 is the GCF

Now re-write the fraction as a multiplication of two fractions as follows:
\[\frac{6}{6} \times \frac{3}{4}\]

Notice that \(\dfrac{6}{6} = 1\)

Notice that \(\dfrac{3}{4}\) is relatively prime

And \(1 \times \dfrac{3}{4} = \dfrac{3}{4}\)

Answer 2

ohhhhh ok thank you so much

Answer 3

By the way if you want to know what relatively prime is:

http://www.mathwords.com/r/relatively_prime.htm

Answer 4

The fraction \(\dfrac{3}{4}\) is in simplest form because the numbers 3 and 4 are relatively prime. In other words, the GCF between both numbers is 1. Which means the fraction cannot be simplified any further.

Answer 5

I hope that helps.

Answer 6

yes it does thank you