What is 3 3/4 x 2/5 in simplest form
The Correct Answer and Explanation is:
To multiply the mixed number (3 \frac{3}{4}) by the fraction (\frac{2}{5}), we need to follow a few steps to ensure that we simplify the expression correctly.
Step 1: Convert the Mixed Number to an Improper Fraction
First, convert the mixed number (3 \frac{3}{4}) into an improper fraction. To do this, multiply the whole number part (3) by the denominator (4) and add the numerator (3):
[
3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}
]
Step 2: Multiply the Improper Fraction by the Fraction
Next, we can multiply (\frac{15}{4}) by (\frac{2}{5}):
[
\frac{15}{4} \times \frac{2}{5} = \frac{15 \times 2}{4 \times 5} = \frac{30}{20}
]
Step 3: Simplify the Resulting Fraction
Now, simplify (\frac{30}{20}). To do this, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 30 and 20 is 10. We divide both the numerator and denominator by their GCD:
[
\frac{30 \div 10}{20 \div 10} = \frac{3}{2}
]
Step 4: Convert Back to a Mixed Number (Optional)
The simplified result, (\frac{3}{2}), can also be expressed as a mixed number if desired. To convert (\frac{3}{2}) to a mixed number, we divide 3 by 2:
[
3 \div 2 = 1 \quad \text{(whole number)}
]
[
3 – (2 \times 1) = 1 \quad \text{(remainder)}
]
Thus, (\frac{3}{2} = 1 \frac{1}{2}).
Conclusion
In simplest form, the product of (3 \frac{3}{4} \times \frac{2}{5}) is (\frac{3}{2}) or (1 \frac{1}{2}) if expressed as a mixed number. Therefore, the final answer is:
[
\frac{3}{2} \text{ or } 1 \frac{1}{2}
]