(b) $$ \frac{4}{7} imes 2 \frac{5}{8} $$

Question

(b) $$ \frac{4}{7} 	imes 2 \frac{5}{8} $$

UpStudy AI · Accepted Answer

To solve the expression $$ \frac{4}{7} \times 2 \frac{5}{8} $$, follow these steps:

### Step 1: Convert the Mixed Number to an Improper Fraction

A mixed number like $$ 2 \frac{5}{8} $$ can be converted to an improper fraction using the formula:

$$
\text{Mixed Number} = \frac{( \text{Whole Number} \times \text{Denominator} ) + \text{Numerator}}{\text{Denominator}}
$$

Applying this:

$$
2 \frac{5}{8} = \frac{(2 \times 8) + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8}
$$

### Step 2: Multiply the Fractions

Now, multiply $$ \frac{4}{7} $$ by $$ \frac{21}{8} $$:

$$
\frac{4}{7} \times \frac{21}{8} = \frac{4 \times 21}{7 \times 8} = \frac{84}{56}
$$

### Step 3: Simplify the Fraction

Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 28:

$$
\frac{84 \div 28}{56 \div 28} = \frac{3}{2}
$$

### Final Answer

$$
\frac{4}{7} \times 2 \frac{5}{8} = \frac{3}{2} \quad \text{or} \quad 1 \frac{1}{2}
$$
$$ \frac{4}{7} \times 2 \frac{5}{8} = \frac{3}{2} \quad \text{or} \quad 1 \frac{1}{2} $$

(b) \( \frac{4}{7} \times 2 \frac{5}{8} \)

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