Answer :
Let's work through the problem step-by-step to perform the operation and simplify the result.
1. Multiply the Fractions:
To multiply two fractions, multiply their numerators together and their denominators together.
[tex]\[
\left(-\frac{5}{7}\right) \times \left(-\frac{14}{15}\right)
= \frac{(-5) \times (-14)}{7 \times 15}
\][/tex]
2. Calculate the Numerator and Denominator:
- Numerator: [tex]\((-5) \times (-14) = 70\)[/tex]
- Denominator: [tex]\(7 \times 15 = 105\)[/tex]
So, the fraction becomes:
[tex]\[
\frac{70}{105}
\][/tex]
3. Simplify the Fraction:
To simplify [tex]\(\frac{70}{105}\)[/tex], find the greatest common divisor (GCD) of 70 and 105. The GCD of 70 and 105 is 35.
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{70 \div 35}{105 \div 35} = \frac{2}{3}
\][/tex]
So, the simplified form of the product [tex]\(\left(-\frac{5}{7}\right) \times \left(-\frac{14}{15}\right)\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
1. Multiply the Fractions:
To multiply two fractions, multiply their numerators together and their denominators together.
[tex]\[
\left(-\frac{5}{7}\right) \times \left(-\frac{14}{15}\right)
= \frac{(-5) \times (-14)}{7 \times 15}
\][/tex]
2. Calculate the Numerator and Denominator:
- Numerator: [tex]\((-5) \times (-14) = 70\)[/tex]
- Denominator: [tex]\(7 \times 15 = 105\)[/tex]
So, the fraction becomes:
[tex]\[
\frac{70}{105}
\][/tex]
3. Simplify the Fraction:
To simplify [tex]\(\frac{70}{105}\)[/tex], find the greatest common divisor (GCD) of 70 and 105. The GCD of 70 and 105 is 35.
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{70 \div 35}{105 \div 35} = \frac{2}{3}
\][/tex]
So, the simplified form of the product [tex]\(\left(-\frac{5}{7}\right) \times \left(-\frac{14}{15}\right)\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
