Answer :
To find [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex], we use the division rule for fractions, which states that dividing by a fraction is the same as multiplying by its reciprocal. Here's a step-by-step explanation of how to do this:
1. Identify the Division: We have the expression [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex].
2. Reciprocal of the Divisor: The reciprocal of [tex]\(\frac{7}{5}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex].
3. Change Division to Multiplication: Replace the division operation with multiplication by the reciprocal:
[tex]\[
\frac{14}{15} \times \frac{5}{7}
\][/tex]
4. Carry Out the Multiplication: Multiply the numerators and the denominators:
[tex]\[
\frac{14 \times 5}{15 \times 7} = \frac{70}{105}
\][/tex]
5. Simplify the Fraction: To simplify [tex]\(\frac{70}{105}\)[/tex], find the greatest common divisor (GCD) of 70 and 105, which is 35. Divide both the numerator and the denominator by 35:
[tex]\[
\frac{70 \div 35}{105 \div 35} = \frac{2}{3}
\][/tex]
Considering the options given:
- Option A: Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex] is correct because it reflects multiplying [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{5}{7}\)[/tex] (which is the reciprocal).
- Option C: Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7 and then by [tex]\(\frac{1}{5}\)[/tex] also leads to the same process, since ultimately, swapping factors in multiplication doesn't change the product.
Thus, the correct statements are A and C because they show the right method of finding the result: multiplying by the reciprocal of the divisor. The simplified answer to the division is [tex]\(\frac{2}{3}\)[/tex].
1. Identify the Division: We have the expression [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex].
2. Reciprocal of the Divisor: The reciprocal of [tex]\(\frac{7}{5}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex].
3. Change Division to Multiplication: Replace the division operation with multiplication by the reciprocal:
[tex]\[
\frac{14}{15} \times \frac{5}{7}
\][/tex]
4. Carry Out the Multiplication: Multiply the numerators and the denominators:
[tex]\[
\frac{14 \times 5}{15 \times 7} = \frac{70}{105}
\][/tex]
5. Simplify the Fraction: To simplify [tex]\(\frac{70}{105}\)[/tex], find the greatest common divisor (GCD) of 70 and 105, which is 35. Divide both the numerator and the denominator by 35:
[tex]\[
\frac{70 \div 35}{105 \div 35} = \frac{2}{3}
\][/tex]
Considering the options given:
- Option A: Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex] is correct because it reflects multiplying [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{5}{7}\)[/tex] (which is the reciprocal).
- Option C: Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7 and then by [tex]\(\frac{1}{5}\)[/tex] also leads to the same process, since ultimately, swapping factors in multiplication doesn't change the product.
Thus, the correct statements are A and C because they show the right method of finding the result: multiplying by the reciprocal of the divisor. The simplified answer to the division is [tex]\(\frac{2}{3}\)[/tex].
