Simplify 1 7/8×2 4/5

Answer 1

To simplify \( 1 \frac{7}{8} \times 2 \frac{4}{5} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 1 \frac{7}{8} \): \[ 1 \frac{7}{8} = 1 \times 8 + 7 = 8 + 7 = \frac{15}{8} \]

2. Convert \( 2 \frac{4}{5} \): \[ 2 \frac{4}{5} = 2 \times 5 + 4 = 10 + 4 = \frac{14}{5} \]

Now we multiply the two improper fractions: \[ \frac{15}{8} \times \frac{14}{5} = \frac{15 \times 14}{8 \times 5} \]

Calculating the numerators and denominators:

• Numerator: \( 15 \times 14 = 210 \)
• Denominator: \( 8 \times 5 = 40 \)

So we have: \[ \frac{210}{40} \]

Next, we simplify \( \frac{210}{40} \). We need to find the greatest common divisor (GCD) of 210 and 40. The GCD is 10.

Now we divide the numerator and denominator by their GCD: \[ \frac{210 \div 10}{40 \div 10} = \frac{21}{4} \]

Now we can convert \( \frac{21}{4} \) back to a mixed number: \[ 21 \div 4 = 5 \quad \text{with a remainder of } 1 \] Thus, \( \frac{21}{4} = 5 \frac{1}{4} \).

The final simplified result is: \[ \boxed{5 \frac{1}{4}} \]