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------------------------------------------------ Reduce to lowest terms:

36) [tex]\frac{9}{12}[/tex]

37) [tex]\frac{24}{30}[/tex]

38) Write as a mixed number: [tex]\frac{12}{5}[/tex]

Sure! Let's simplify these fractions and convert the improper fraction into a mixed number step by step.

36) Simplify the fraction [tex]\(\frac{9}{12}\)[/tex]:

1. Find the greatest common divisor (GCD) of both the numerator and the denominator. For 9 and 12, the GCD is 3.
2. Divide both the numerator and the denominator by their GCD (3):
- [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex].

The fraction [tex]\(\frac{9}{12}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].

37) Simplify the fraction [tex]\(\frac{24}{30}\)[/tex]:

1. Find the greatest common divisor (GCD) of 24 and 30. The GCD is 6.
2. Divide both the numerator and the denominator by their GCD (6):
- [tex]\(\frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex].

The fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

38) Write the improper fraction [tex]\(\frac{12}{5}\)[/tex] as a mixed number:

1. Divide the numerator (12) by the denominator (5) to find the whole number part:
- 12 divided by 5 equals 2 with a remainder of 2.
2. The whole number part is 2.
3. The remainder becomes the new numerator, and the original denominator stays the same:
- This gives us [tex]\(\frac{2}{5}\)[/tex].

So, when [tex]\(\frac{12}{5}\)[/tex] is written as a mixed number, it becomes [tex]\(2 \frac{2}{5}\)[/tex].

I hope this helps! Let me know if you have any more questions.