Question

write the fraction \\(\frac{32}{24}\\) in simplest form.

Explanation:

Step1: Find GCD of 32 and 24

The factors of 32 are 1, 2, 4, 8, 16, 32. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest common divisor (GCD) is 8.

Step2: Divide numerator and denominator by GCD

Divide 32 by 8: \( \frac{32}{8} = 4 \). Divide 24 by 8: \( \frac{24}{8} = 3 \). So \( \frac{32}{24} = \frac{4}{3} \) (or as a mixed number \( 1\frac{1}{3} \), but simplifying the improper fraction first, we get \( \frac{4}{3} \) when in simplest improper form, or \( 1\frac{1}{3} \) as a mixed number. However, since we can also check, \( \frac{32\div8}{24\div8}=\frac{4}{3} \), and 4 and 3 have no common divisors other than 1. If we want a mixed number, \( \frac{4}{3}=1\frac{1}{3} \), but let's confirm the simplification. Wait, 32 and 24, GCD is 8. 32÷8=4, 24÷8=3. So \( \frac{4}{3} \) is the simplified improper fraction, or \( 1\frac{1}{3} \) as a mixed number. But the problem says "simplest form", which can be either, but usually, if it's an improper fraction, simplifying to lowest terms (4/3) or as a mixed number. Let's check: 4 and 3 are coprime, so \( \frac{4}{3} \) is simplest, or \( 1\frac{1}{3} \). Wait, maybe I made a mistake earlier. Wait, 32/24, divide numerator and denominator by 8: 32÷8=4, 24÷8=3. So \( \frac{4}{3} \) is correct. Alternatively, if we divide by 4 first: 32÷4=8, 24÷4=6, then divide by 2: 8÷2=4, 6÷2=3. So same result. So the simplest form is \( \frac{4}{3} \) (or \( 1\frac{1}{3} \), but let's see the original fraction is improper, so simplest form can be improper or mixed. But the box has a fraction and a mixed number option. Let's see: 32/24, divide numerator and denominator by 8: 4/3. 4/3 as a mixed number is 1 1/3. So either way, but let's do it step by step.

Step1: Identify GCD of 32 and 24

GCD(32,24) = 8 (since 8×4=32, 8×3=24)

Step2: Divide numerator and denominator by GCD

\( \frac{32\div8}{24\div8} = \frac{4}{3} \)
If we convert to mixed number: \( \frac{4}{3} = 1\frac{1}{3} \) (since 3×1=3, 4-3=1, so 1 + 1/3)

But the problem's input box: if we use the fraction button, we can put 4/3, or the mixed number button for 1 1/3. Let's confirm the simplification. Since 4 and 3 are coprime, \( \frac{4}{3} \) is in simplest form.

Answer:

\( \frac{4}{3} \) (or \( 1\frac{1}{3} \), but typically, for the fraction \( \frac{32}{24} \), simplifying gives \( \frac{4}{3} \) as the improper fraction in simplest form, or \( 1\frac{1}{3} \) as a mixed number. However, since 4 and 3 have no common factors other than 1, \( \frac{4}{3} \) is the simplified fraction.)