Question

Find the product
$1.2\times2\frac{2}{5}\times\frac{3}{4}$

• A. 2.4
• B. 2.5
• C. 2.16
• D. 2.1

Answer 1

Answer:

C. 2.16

The product is $2.16$ (or $\frac{54}{25}$ in fraction form).

Step 1: Convert all numbers into improper fractions

• Convert the decimal: $1.2 = \frac{12}{10} = \frac{6}{5}$

• Convert the mixed fraction: $2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$

• The third fraction is already simplified: $\frac{3}{4}$

Step 2: Multiply the fractions together
$\text{Product} = \frac{6}{5} \times \frac{12}{5} \times \frac{3}{4}$

Step 3: Simplify by canceling common terms

• Divide $12$ in the numerator and $4$ in the denominator by $4$:
  $\text{Product} = \frac{6}{5} \times \frac{3}{5} \times \frac{3}{1}$

Step 4: Multiply the remaining numerators and denominators

• Numerator: $6 \times 3 \times 3 = 54$

• Denominator: $5 \times 5 \times 1 = 25$

$\text{Fraction Form} = \frac{54}{25}$

Step 5: Convert to decimal form
$\frac{54}{25} = 2.16$