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Answer :
To solve the problem of dividing the fractions [tex]\(\frac{7}{8}\)[/tex] by [tex]\(\frac{14}{15}\)[/tex], we can follow these steps:
1. Understand the division of fractions: Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a fraction is created by swapping its numerator and denominator.
2. Find the reciprocal: For the fraction [tex]\(\frac{14}{15}\)[/tex], its reciprocal is [tex]\(\frac{15}{14}\)[/tex].
3. Multiply the fractions: Now, multiply [tex]\(\frac{7}{8}\)[/tex] by [tex]\(\frac{15}{14}\)[/tex].
[tex]\[
\frac{7}{8} \times \frac{15}{14}
\][/tex]
4. Multiply the numerators and the denominators: When you multiply two fractions, you multiply the numerators with each other and the denominators with each other.
- Numerator: [tex]\(7 \times 15 = 105\)[/tex]
- Denominator: [tex]\(8 \times 14 = 112\)[/tex]
This gives us the fraction:
[tex]\[
\frac{105}{112}
\][/tex]
5. Simplify the fraction if possible: Check if the fraction [tex]\(\frac{105}{112}\)[/tex] can be simplified further by finding any common factors. In this case, [tex]\(105\)[/tex] and [tex]\(112\)[/tex] do not have any common factors other than 1, so the fraction is already in its simplest form.
So, the result of dividing [tex]\(\frac{7}{8}\)[/tex] by [tex]\(\frac{14}{15}\)[/tex] is [tex]\(\frac{105}{112}\)[/tex], which is approximately equal to [tex]\(0.9375\)[/tex] when expressed as a decimal.
1. Understand the division of fractions: Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a fraction is created by swapping its numerator and denominator.
2. Find the reciprocal: For the fraction [tex]\(\frac{14}{15}\)[/tex], its reciprocal is [tex]\(\frac{15}{14}\)[/tex].
3. Multiply the fractions: Now, multiply [tex]\(\frac{7}{8}\)[/tex] by [tex]\(\frac{15}{14}\)[/tex].
[tex]\[
\frac{7}{8} \times \frac{15}{14}
\][/tex]
4. Multiply the numerators and the denominators: When you multiply two fractions, you multiply the numerators with each other and the denominators with each other.
- Numerator: [tex]\(7 \times 15 = 105\)[/tex]
- Denominator: [tex]\(8 \times 14 = 112\)[/tex]
This gives us the fraction:
[tex]\[
\frac{105}{112}
\][/tex]
5. Simplify the fraction if possible: Check if the fraction [tex]\(\frac{105}{112}\)[/tex] can be simplified further by finding any common factors. In this case, [tex]\(105\)[/tex] and [tex]\(112\)[/tex] do not have any common factors other than 1, so the fraction is already in its simplest form.
So, the result of dividing [tex]\(\frac{7}{8}\)[/tex] by [tex]\(\frac{14}{15}\)[/tex] is [tex]\(\frac{105}{112}\)[/tex], which is approximately equal to [tex]\(0.9375\)[/tex] when expressed as a decimal.
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