Question

find the product. use the greatest common factor to simplify your answer. gcf = 2 \\(\frac{7}{8} \times \frac{2}{3} = \frac{14}{24}\\) \\(\boxed{?}\\)

Explanation:

Step1: Simplify fractions using GCF

We know GCF = 2. For \(\frac{14}{24}\), divide numerator and denominator by 2: \(\frac{14\div2}{24\div2}=\frac{7}{12}\)? Wait, no, wait. Wait the problem is \(\frac{7}{8} \times \frac{2}{3}\) (since \(\frac{14}{24}\) simplifies to \(\frac{7}{12}\)? Wait no, let's re - examine. Wait the original problem is to find \(\frac{7}{8}\times\frac{2}{3}\) (because \(\frac{14}{24}\) can be simplified using GCF = 2: 14÷2 = 7, 24÷2 = 12? Wait no, maybe I misread. Wait the problem shows \(\frac{7}{8}\times\frac{2}{3}\) (since 14/24 simplifies to 7/12? No, wait 14 and 24: GCF is 2, so 14÷2 = 7, 24÷2 = 12? Wait no, 24÷2 is 12? Wait no, 24÷2 is 12? Wait no, 24÷2 is 12? Wait, no, 14/24 = (14÷2)/(24÷2)=7/12. But the problem has \(\frac{7}{8}\times\frac{2}{3}\) (maybe a typo? Wait no, let's do the multiplication of fractions. When multiplying fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\). But we can also use cross - simplification. The numerator 2 and denominator 8: GCF of 2 and 8 is 2. So 2÷2 = 1, 8÷2 = 4. Now the fractions become \(\frac{7}{4}\times\frac{1}{3}\).

Step2: Multiply the simplified fractions

Now multiply the numerators: \(7\times1 = 7\), multiply the denominators: \(4\times3=12\)? Wait no, wait original fractions: \(\frac{7}{8}\times\frac{2}{3}\). Cross - simplify 2 and 8: GCF(2,8)=2. So 2/2 = 1, 8/2 = 4. So now we have \(\frac{7}{4}\times\frac{1}{3}=\frac{7\times1}{4\times3}=\frac{7}{12}\)? Wait no, wait the other way: maybe the original problem is \(\frac{7}{8}\times\frac{2}{3}\). Let's calculate directly: 7×2 = 14, 8×3 = 24, then simplify 14/24 with GCF = 2: 14÷2 = 7, 24÷2 = 12. Wait, so \(\frac{7}{8}\times\frac{2}{3}=\frac{14}{24}=\frac{7}{12}\)? Wait no, 7×2 = 14, 8×3 = 24. Then GCF of 14 and 24 is 2, so 14÷2 = 7, 24÷2 = 12. So the product is \(\frac{7}{12}\)? Wait, no, let's do it step by step.

Wait, the problem shows \(\frac{7}{8}\times\frac{2}{3}\). Let's use cross - cancellation. The 2 in the numerator of the second fraction and the 8 in the denominator of the first fraction: GCF(2,8)=2. So divide 2 by 2: 1, divide 8 by 2: 4. Now the fractions are \(\frac{7}{4}\times\frac{1}{3}\). Now multiply numerators: 7×1 = 7, multiply denominators: 4×3 = 12. So the product is \(\frac{7}{12}\).

Wait, but let's check the original fractions. If we consider \(\frac{14}{24}\) as the product before simplification, then \(\frac{7}{8}\times\frac{2}{3}=\frac{14}{24}\), and simplifying \(\frac{14}{24}\) with GCF = 2 gives \(\frac{7}{12}\).

Answer:

\(\frac{7}{12}\)