Find 2/5(-3.75). Write your answer as a mixed number in simplest form.
The Correct Answer and Explanation is:
To find the result of ( \frac{2}{5} \times (-3.75) ) and express the answer as a mixed number in its simplest form, let’s follow these steps:
Step 1: Convert -3.75 to a Fraction
First, we need to express the decimal -3.75 as a fraction.
- The decimal -3.75 can be rewritten as:
[
-3.75 = -\frac{375}{100}
] - Now simplify ( \frac{375}{100} ) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 25:
[
\frac{375 \div 25}{100 \div 25} = \frac{15}{4}
]
Thus, ( -3.75 = -\frac{15}{4} ).
Step 2: Multiply Fractions
Now that we have ( \frac{2}{5} ) and ( -\frac{15}{4} ), we can multiply these two fractions:
[
\frac{2}{5} \times \left(-\frac{15}{4}\right) = \frac{2 \times -15}{5 \times 4} = \frac{-30}{20}
]
Step 3: Simplify the Fraction
Next, we simplify ( \frac{-30}{20} ). To do this, we divide both the numerator and denominator by their GCD, which is 10:
[
\frac{-30 \div 10}{20 \div 10} = \frac{-3}{2}
]
Step 4: Convert the Fraction to a Mixed Number
The fraction ( \frac{-3}{2} ) is an improper fraction. To convert it to a mixed number, divide 3 by 2:
[
3 \div 2 = 1 \text{ with a remainder of } 1
]
Thus, ( \frac{3}{2} = 1 \frac{1}{2} ). Since the original fraction was negative, the mixed number is:
[
-1 \frac{1}{2}
]
Final Answer:
The result of ( \frac{2}{5} \times (-3.75) ) is ( \boxed{-1 \frac{1}{2}} ).
Explanation:
In this problem, we first converted the decimal -3.75 into a fraction, then multiplied it by ( \frac{2}{5} ), followed by simplifying the product to ( \frac{-3}{2} ). Finally, we converted the improper fraction into a mixed number and expressed the final result as ( -1 \frac{1}{2} ), which is the simplest form of the answer.