Simplify 7 1/2×(7/8-5/24)

Answer 1

To simplify the expression $7\frac{1}{2}\times (\frac{7}{8}-\frac{5}{24})$, we can follow these steps:

1. Convert the mixed number to an improper fraction: $$7\frac{1}{2}=\frac{15}{2}$$

2. Find a common denominator for the fractions: The common denominator for $\frac{7}{8}$ and $\frac{5}{24}$ is $24$.

   • Convert $\frac{7}{8}$ to 24ths: $$\frac{7}{8}=\frac{7\times 3}{8\times 3}=\frac{21}{24}$$

   • $\frac{5}{24}$ is already in terms of $24$: $$\frac{5}{24}=\frac{5}{24}$$

3. Subtract the fractions: $$\frac{21}{24}-\frac{5}{24}=\frac{21-5}{24}=\frac{16}{24}$$

4. Simplify $\frac{16}{24}$: $$\frac{16}{24}=\frac{2}{3}\text{(by dividing numerator and denominator by 8)}$$

5. Multiply $\frac{15}{2}$ by $\frac{2}{3}$: $$\frac{15}{2}\times \frac{2}{3}=\frac{15\times 2}{2\times 3}=\frac{30}{6}$$

6. Simplify $\frac{30}{6}$: $$\frac{30}{6}=5$$

Thus, the simplified result of $7\frac{1}{2}\times (\frac{7}{8}-\frac{5}{24})$ is

$$\boxed{{\displaystyle 5}}$$