Question

Write the ratio in the lowest terms \[\$ 90\] to \[\$ 80\].

Answer 1

Hint: We have to find the ratio in the lowest terms \[\$ 90\] to \[\$ 80\], so we will write it as a fraction i.e., \[\dfrac{{\$ 90}}{{\$ 80}}\]. This question is based on the concept of reducing the fractions into its lowest terms. Reducing into the lowest terms means finding equivalent numbers in which the numerator and denominator become relatively prime numbers.

Complete step by step answer:
In this question, we have to find the ratio in the lowest terms \[\$ 90\] to \[\$ 80\]. As it is a ratio, so we will write it as a fraction i.e., \[\dfrac{{\$ 90}}{{\$ 80}}\].A fraction is said to be in lowest form if its numerator and denominator are relatively prime numbers i.e., numerator and denominator have no common factors other than \[1\].Reduction of fraction in the lowest terms involves the operation of division. The number in the numerator is \[90\] and the number in the denominator is \[80\].

Breaking down the number into its factors, we get
\[ \Rightarrow 90 = 2 \times 3 \times 3 \times 5\] and \[80 = 2 \times 2 \times 2 \times 2 \times 5\]
So, we can write
\[ \Rightarrow \dfrac{{90}}{{80}} = \dfrac{{2 \times 3 \times 3 \times 5}}{{2 \times 2 \times 2 \times 2 \times 5}}\]
On cancelling the common terms from the numerator and the denominator, we get
\[ \Rightarrow \dfrac{{90}}{{80}} = \dfrac{{3 \times 3}}{{2 \times 2 \times 2}}\]
On simplifying, we get
\[ \therefore \dfrac{{\$ 90}}{{\$ 80}} = \dfrac{{\$ 9}}{{\$ 8}}\]

Therefore, the ratio in the lowest terms \[\$ 90\] to \[\$ 80\] is \[\$ 9\] to \[\$ 8\] or \[9:8\].

Note: We can also solve this problem by calculating the Greatest Common Factor of both the numerator and denominator and then dividing the numerator and the denominator individually by this GCF. The GCF of the numerator and the denominator i.e., \[90\] and \[80\] is \[10\]. We get the same ratio in the lowest terms on dividing \[10\] with the numerator and the denominator.