What comes after 3/4 on the number line

To find the fraction that comes after $\frac{3}{4}$ on the number line, we need to compare the given fractions with $\frac{3}{4}$ and $1$. The fractions available are $\frac{1}{3}, \frac{7}{8}, \frac{1}{4}, \frac{1}{5}, \frac{6}{8}$. Step 1: Convert $\frac{3}{4}$ and $1$ to a common denominator, such as $8$, or to decimals. $$ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} $$ $$ 1 = \frac{8}{8} $$ So we are looking for a fraction $x$ such that $\frac{6}{8} < x < \frac{8}{8}$. Step 2: Evaluate the given fractions: $\frac{1}{3}$: This is approximately $0.333$, which is less than $\frac{3}{4}$ ($0.75$). $\frac{7}{8}$: This is $0.875$. Comparing with $\frac{3}{4} = \frac{6}{8}$: $$ \frac{6}{8} < \frac{7}{8} $$ Comparing with $1 = \frac{8}{8}$: $$ \frac{7}{8} < \frac{8}{8} $$ So, $\frac{7}{8}$ fits the condition $\frac{3}{4} < \frac{7}{8} < 1$. $\frac{1}{4}$: This is $\frac{2}{8}$, which is less than $\frac{3}{4}$. $\frac{1}{5}$: This is $0.2$, which is less than $\frac{3}{4}$. $\frac{6}{8}$: This fraction is equal to $\frac{3}{4}$, not after it. Step 3: Identify the fraction that fits the position. From the comparison, $\frac{7}{8}$ is the only fraction from the list that is greater than $\frac{3}{4}$ and less than $1$. The fraction that comes after $\frac{3}{4}$ on the number line is $\boxed{\frac{7}{8}}$. That's 2 down. 3 left today — send the next one.