Answer :
- Convert the mixed fraction to an improper fraction: $3 \frac{3}{4} = \frac{15}{4}$.
- Multiply the fractions: $\frac{15}{4} \times -\frac{12}{25} = \frac{-180}{100}$.
- Simplify the resulting fraction: $\frac{-180}{100} = -\frac{9}{5}$.
- The product is $\boxed{-\frac{9}{5}}$.
### Explanation
1. Problem Analysis and Conversion to Improper Fraction
We are asked to find the product of $3
\frac{3}{4}$ and $-\frac{12}{25}$. First, we need to convert the mixed fraction $3 \frac{3}{4}$ to an improper fraction.
2. Converting Mixed Fraction to Improper Fraction
To convert $3 \frac{3}{4}$ to an improper fraction, we multiply the whole number (3) by the denominator (4) and add the numerator (3). This gives us $3 \times 4 + 3 = 12 + 3 = 15$. So, the improper fraction is $\frac{15}{4}$.
3. Multiplying the Fractions
Now we need to multiply the two fractions: $\frac{15}{4} \times -\frac{12}{25}$.
4. Performing Multiplication
To multiply the fractions, we multiply the numerators and the denominators:$$\frac{15}{4} \times -\frac{12}{25} = \frac{15 \times -12}{4 \times 25} = \frac{-180}{100}$$
5. Simplifying the Fraction
Now we simplify the fraction $\frac{-180}{100}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 20:$$\frac{-180}{100} = \frac{-180 \div 20}{100 \div 20} = \frac{-9}{5}$$
6. Final Answer and Comparison
So, the product of $3 \frac{3}{4}$ and $-\frac{12}{25}$ is $-\frac{9}{5}$. Comparing this with the given options, we see that option (b) is the correct answer.
### Examples
Understanding fraction multiplication is crucial in many real-life scenarios, such as calculating discounts, scaling recipes, or determining proportions in construction projects. For instance, if a store offers a 20% discount on an item priced at $45
\frac{1}{2}$, you would multiply the price by $\frac{1}{5}$ (since 20% is $\frac{1}{5}$) to find the discount amount. This skill helps in making informed decisions and managing resources effectively.
- Multiply the fractions: $\frac{15}{4} \times -\frac{12}{25} = \frac{-180}{100}$.
- Simplify the resulting fraction: $\frac{-180}{100} = -\frac{9}{5}$.
- The product is $\boxed{-\frac{9}{5}}$.
### Explanation
1. Problem Analysis and Conversion to Improper Fraction
We are asked to find the product of $3
\frac{3}{4}$ and $-\frac{12}{25}$. First, we need to convert the mixed fraction $3 \frac{3}{4}$ to an improper fraction.
2. Converting Mixed Fraction to Improper Fraction
To convert $3 \frac{3}{4}$ to an improper fraction, we multiply the whole number (3) by the denominator (4) and add the numerator (3). This gives us $3 \times 4 + 3 = 12 + 3 = 15$. So, the improper fraction is $\frac{15}{4}$.
3. Multiplying the Fractions
Now we need to multiply the two fractions: $\frac{15}{4} \times -\frac{12}{25}$.
4. Performing Multiplication
To multiply the fractions, we multiply the numerators and the denominators:$$\frac{15}{4} \times -\frac{12}{25} = \frac{15 \times -12}{4 \times 25} = \frac{-180}{100}$$
5. Simplifying the Fraction
Now we simplify the fraction $\frac{-180}{100}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 20:$$\frac{-180}{100} = \frac{-180 \div 20}{100 \div 20} = \frac{-9}{5}$$
6. Final Answer and Comparison
So, the product of $3 \frac{3}{4}$ and $-\frac{12}{25}$ is $-\frac{9}{5}$. Comparing this with the given options, we see that option (b) is the correct answer.
### Examples
Understanding fraction multiplication is crucial in many real-life scenarios, such as calculating discounts, scaling recipes, or determining proportions in construction projects. For instance, if a store offers a 20% discount on an item priced at $45
\frac{1}{2}$, you would multiply the price by $\frac{1}{5}$ (since 20% is $\frac{1}{5}$) to find the discount amount. This skill helps in making informed decisions and managing resources effectively.