College

7. What is the lowest term of [tex]\frac{18}{80}[/tex]?

A. [tex]\frac{9}{40}[/tex]
B. [tex]\frac{9}{20}[/tex]
C. [tex]\frac{1}{2}[/tex]
D. [tex]\frac{18}{20}[/tex]

8. What is [tex]2 \frac{2}{3}[/tex] as an improper fraction?

A. [tex]\frac{8}{3}[/tex]
B. [tex]\frac{12}{3}[/tex]
C. [tex]\frac{14}{3}[/tex]
D. [tex]\frac{24}{3}[/tex]

Answer :

Certainly! Let's solve each question step by step.

Question 7: What is the lowest terms of [tex]\(\frac{18}{80}\)[/tex]?

To simplify the fraction [tex]\(\frac{18}{80}\)[/tex] to its lowest terms, we need to find the greatest common divisor (GCD) of 18 and 80. The GCD is the largest number that divides both 18 and 80 without leaving a remainder.

1. The GCD of 18 and 80 is 2.
2. Now, divide both the numerator (18) and the denominator (80) by their GCD (which is 2):

[tex]\[
\frac{18 \div 2}{80 \div 2} = \frac{9}{40}
\][/tex]

Therefore, the fraction [tex]\(\frac{18}{80}\)[/tex] in its lowest terms is [tex]\(\frac{9}{40}\)[/tex].

Answer: (A.) [tex]\(\frac{9}{40}\)[/tex]

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Question 8: What is [tex]\(2 \frac{2}{3}\)[/tex] as an improper fraction?

To convert the mixed number [tex]\(2 \frac{2}{3}\)[/tex] into an improper fraction, follow these steps:

1. Multiply the whole number part (2) by the denominator of the fraction (3):
[tex]\[
2 \times 3 = 6
\][/tex]

2. Add the result to the numerator of the fraction part, which is 2:
[tex]\[
6 + 2 = 8
\][/tex]

3. Place this result over the original denominator (3) to form the improper fraction:
[tex]\[
\frac{8}{3}
\][/tex]

Thus, the mixed number [tex]\(2 \frac{2}{3}\)[/tex] as an improper fraction is [tex]\(\frac{8}{3}\)[/tex].

Answer: (A.) [tex]\(\frac{8}{3}\)[/tex]