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Divide [tex]\(\frac{7}{24}\)[/tex] by [tex]\(\frac{35}{48}\)[/tex] and reduce the quotient to the lowest fraction.

A. [tex]\(\frac{245}{1152}\)[/tex]

B. [tex]\(\frac{4}{10}\)[/tex]

C. [tex]\(\frac{42}{48}\)[/tex]

D. [tex]\(\frac{2}{5}\)[/tex]


Sagot :

To solve the problem of dividing [tex]\(\frac{7}{24}\)[/tex] by [tex]\(\frac{35}{48}\)[/tex] and reducing the quotient to its lowest terms, follow these steps:

1. Recall how to divide fractions: To divide by a fraction, multiply by its reciprocal. This means that [tex]\(\frac{7}{24} \div \frac{35}{48}\)[/tex] is equivalent to [tex]\(\frac{7}{24} \times \frac{48}{35}\)[/tex].

2. Multiply the fractions:
[tex]\[ \frac{7}{24} \times \frac{48}{35} \][/tex]

3. Simplify the multiplication:
- Multiply the numerators: [tex]\(7 \times 48 = 336\)[/tex]
- Multiply the denominators: [tex]\(24 \times 35 = 840\)[/tex]

So, [tex]\(\frac{7}{24} \times \frac{48}{35} = \frac{336}{840}\)[/tex].

4. Reduce the fraction: To reduce [tex]\(\frac{336}{840}\)[/tex] to its lowest terms, find the greatest common divisor (GCD) of 336 and 840. The GCD of 336 and 840 is 168.

- Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{336 \div 168}{840 \div 168} = \frac{2}{5} \][/tex]

So, the reduced fraction is [tex]\(\frac{2}{5}\)[/tex].

Therefore, the best answer is:

D. [tex]\(\frac{2}{5}\)[/tex]