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Reduce these rational numbers to their standard form.

A. [tex]\frac{-27}{15}[/tex]

B. [tex]\frac{100}{18}[/tex]

C. [tex]\frac{-36}{124}[/tex]

D. [tex]\frac{35}{15}[/tex]

E. [tex]\frac{-14}{-49}[/tex]

Answer :

Let's reduce these rational numbers to their standard form. The standard form of a rational number is when the numerator and denominator have no common factors other than 1.

To achieve this, we will find the greatest common divisor (GCD) for the numerator and the denominator and then divide both by this GCD.

A. [tex]\(\frac{-27}{15}\)[/tex]

1. Find the GCD of 27 and 15. The GCD is 3.
2. Divide both the numerator and the denominator by 3:
[tex]\[
\frac{-27 \div 3}{15 \div 3} = \frac{-9}{5}
\][/tex]

B. [tex]\(\frac{100}{18}\)[/tex]

1. Find the GCD of 100 and 18. The GCD is 2.
2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{100 \div 2}{18 \div 2} = \frac{50}{9}
\][/tex]

C. [tex]\(\frac{-36}{124}\)[/tex]

1. Find the GCD of 36 and 124. The GCD is 4.
2. Divide both the numerator and the denominator by 4:
[tex]\[
\frac{-36 \div 4}{124 \div 4} = \frac{-9}{31}
\][/tex]

D. [tex]\(\frac{35}{15}\)[/tex]

1. Find the GCD of 35 and 15. The GCD is 5.
2. Divide both the numerator and the denominator by 5:
[tex]\[
\frac{35 \div 5}{15 \div 5} = \frac{7}{3}
\][/tex]

E. [tex]\(\frac{-14}{-49}\)[/tex]

1. Find the GCD of 14 and 49. The GCD is 7.
2. Divide both the numerator and the denominator by 7. Since both signs are negative, the result is positive:
[tex]\[
\frac{-14 \div 7}{-49 \div 7} = \frac{2}{7}
\][/tex]

Here are the rational numbers reduced to their standard forms:
- [tex]\(\frac{-27}{15} = \frac{-9}{5}\)[/tex]
- [tex]\(\frac{100}{18} = \frac{50}{9}\)[/tex]
- [tex]\(\frac{-36}{124} = \frac{-9}{31}\)[/tex]
- [tex]\(\frac{35}{15} = \frac{7}{3}\)[/tex]
- [tex]\(\frac{-14}{-49} = \frac{2}{7}\)[/tex]

Thanks for taking the time to read Reduce these rational numbers to their standard form A tex frac 27 15 tex B tex frac 100 18 tex C tex frac 36 124. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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