Multiply Mixed Numbers: 1 4/12 × 1 4/14 Step-by-Step

Let's solve the problem by following these steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Multiply the improper fractions.
• Step 3: Simplify the resulting fraction and convert back to a mixed number if needed.

Step 1:
Convert $1\frac{4}{12}$ to an improper fraction.

Calculate the improper fraction: $1\frac{4}{12} = \frac{1 \times 12 + 4}{12} = \frac{16}{12}$

Convert $1\frac{4}{14}$ to an improper fraction.

Calculate the improper fraction: $1\frac{4}{14} = \frac{1 \times 14 + 4}{14} = \frac{18}{14}$

Step 2:
Multiply the two improper fractions:

$\frac{16}{12} \times \frac{18}{14} = \frac{16 \times 18}{12 \times 14}$

Simplify the multiplication:

• Numerator: $16 \times 18 = 288$
• Denominator: $12 \times 14 = 168$

The resulting fraction is $\frac{288}{168}$.

Step 3:
Simplify $\frac{288}{168}$.

Find the greatest common divisor (GCD) of 288 and 168, which is 24.

• Divide numerator by GCD: $288 \div 24 = 12$
• Divide denominator by GCD: $168 \div 24 = 7$

The simplified fraction is $\frac{12}{7}$.

Convert $\frac{12}{7}$ back to a mixed number:

12 divided by 7 is 1 with a remainder of 5, so the mixed number is $1\frac{5}{7}$.

Thus, the solution to the problem is $\boxed{1\frac{5}{7}}$.