Answer :
To find the product of [tex]\(3 \frac{3}{4} \times -\left(\frac{12}{25}\right)\)[/tex], we can follow these steps:
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\(3 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
- First, multiply the whole number 3 by the denominator 4:
[tex]\[
3 \times 4 = 12
\][/tex]
- Then add the numerator 3:
[tex]\[
12 + 3 = 15
\][/tex]
- So [tex]\(3 \frac{3}{4}\)[/tex] is equivalent to [tex]\(\frac{15}{4}\)[/tex].
2. Multiply the two fractions:
Now, multiply the improper fraction [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
- Multiply the numerators:
[tex]\[
15 \times (-12) = -180
\][/tex]
- Multiply the denominators:
[tex]\[
4 \times 25 = 100
\][/tex]
- This gives the product as:
[tex]\[
\frac{-180}{100}
\][/tex]
3. Simplify the fraction:
The fraction [tex]\(\frac{-180}{100}\)[/tex] can be simplified.
- Find the greatest common divisor (GCD) of 180 and 100, which is 20.
- Divide both the numerator and the denominator by 20:
[tex]\[
\frac{-180 \div 20}{100 \div 20} = \frac{-9}{5}
\][/tex]
So, the product of [tex]\(3 \frac{3}{4} \times -\left(\frac{12}{25}\right)\)[/tex] is [tex]\(-\frac{9}{5}\)[/tex].
Therefore, the correct answer is option (b) [tex]\(-\frac{9}{5}\)[/tex].
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\(3 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
- First, multiply the whole number 3 by the denominator 4:
[tex]\[
3 \times 4 = 12
\][/tex]
- Then add the numerator 3:
[tex]\[
12 + 3 = 15
\][/tex]
- So [tex]\(3 \frac{3}{4}\)[/tex] is equivalent to [tex]\(\frac{15}{4}\)[/tex].
2. Multiply the two fractions:
Now, multiply the improper fraction [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
- Multiply the numerators:
[tex]\[
15 \times (-12) = -180
\][/tex]
- Multiply the denominators:
[tex]\[
4 \times 25 = 100
\][/tex]
- This gives the product as:
[tex]\[
\frac{-180}{100}
\][/tex]
3. Simplify the fraction:
The fraction [tex]\(\frac{-180}{100}\)[/tex] can be simplified.
- Find the greatest common divisor (GCD) of 180 and 100, which is 20.
- Divide both the numerator and the denominator by 20:
[tex]\[
\frac{-180 \div 20}{100 \div 20} = \frac{-9}{5}
\][/tex]
So, the product of [tex]\(3 \frac{3}{4} \times -\left(\frac{12}{25}\right)\)[/tex] is [tex]\(-\frac{9}{5}\)[/tex].
Therefore, the correct answer is option (b) [tex]\(-\frac{9}{5}\)[/tex].