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Answer :
To solve the problem of dividing the fractions [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{7}{5}\)[/tex], we need to follow the rule for dividing fractions. The rule is to multiply the first fraction by the reciprocal of the second fraction.
Here's a step-by-step guide:
1. Find the Reciprocal:
The reciprocal of a fraction is obtained by swapping its numerator and denominator. So, the reciprocal of [tex]\(\frac{7}{5}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex].
2. Perform the Multiplication:
Multiply [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[
\frac{14}{15} \times \frac{5}{7} = \frac{14 \times 5}{15 \times 7} = \frac{70}{105}
\][/tex]
3. Simplify the Fraction:
Simplify [tex]\(\frac{70}{105}\)[/tex] by finding the greatest common divisor (GCD) of 70 and 105, which is 35. Then divide both the numerator and the denominator by 35:
[tex]\[
\frac{70}{105} = \frac{70 \div 35}{105 \div 35} = \frac{2}{3}
\][/tex]
Let's examine the statements:
- A. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex].
- B. Dividing [tex]\(\frac{14}{15}\)[/tex] by 5, and then multiplying by [tex]\(\frac{1}{7}\)[/tex].
- C. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7, and then multiplying by [tex]\(\frac{1}{5}\)[/tex].
- D. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7.
- E. Multiplying [tex]\(\frac{15}{14}\)[/tex] by 7 and then dividing by 5.
Upon careful consideration and calculation, it turns out that option D, which involves multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7, correctly represents the steps needed to find [tex]\(\frac{14}{15} \times \frac{5}{7}\)[/tex], which gives us the answer [tex]\(\frac{2}{3}\)[/tex]. Therefore, the correct option is D.
Here's a step-by-step guide:
1. Find the Reciprocal:
The reciprocal of a fraction is obtained by swapping its numerator and denominator. So, the reciprocal of [tex]\(\frac{7}{5}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex].
2. Perform the Multiplication:
Multiply [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[
\frac{14}{15} \times \frac{5}{7} = \frac{14 \times 5}{15 \times 7} = \frac{70}{105}
\][/tex]
3. Simplify the Fraction:
Simplify [tex]\(\frac{70}{105}\)[/tex] by finding the greatest common divisor (GCD) of 70 and 105, which is 35. Then divide both the numerator and the denominator by 35:
[tex]\[
\frac{70}{105} = \frac{70 \div 35}{105 \div 35} = \frac{2}{3}
\][/tex]
Let's examine the statements:
- A. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex].
- B. Dividing [tex]\(\frac{14}{15}\)[/tex] by 5, and then multiplying by [tex]\(\frac{1}{7}\)[/tex].
- C. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7, and then multiplying by [tex]\(\frac{1}{5}\)[/tex].
- D. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7.
- E. Multiplying [tex]\(\frac{15}{14}\)[/tex] by 7 and then dividing by 5.
Upon careful consideration and calculation, it turns out that option D, which involves multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7, correctly represents the steps needed to find [tex]\(\frac{14}{15} \times \frac{5}{7}\)[/tex], which gives us the answer [tex]\(\frac{2}{3}\)[/tex]. Therefore, the correct option is D.
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