Answer :
To determine which number is not equivalent to [tex]\(\frac{3}{4}\)[/tex], we will simplify each fraction to see if it matches [tex]\(\frac{3}{4}\)[/tex].
Step 1: Simplify [tex]\(\frac{12}{16}\)[/tex]
- Find the greatest common divisor (GCD) of 12 and 16, which is 4.
- Divide both the numerator and the denominator by 4:
[tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex]
Step 2: Simplify [tex]\(\frac{18}{24}\)[/tex]
- Find the GCD of 18 and 24, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\(\frac{18 \div 6}{24 \div 6} = \frac{3}{4}\)[/tex]
Step 3: Simplify [tex]\(\frac{24}{30}\)[/tex]
- Find the GCD of 24 and 30, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\(\frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex]
This fraction simplifies to [tex]\(\frac{4}{5}\)[/tex], which is not equivalent to [tex]\(\frac{3}{4}\)[/tex].
Step 4: Simplify [tex]\(\frac{75}{100}\)[/tex]
- Find the GCD of 75 and 100, which is 25.
- Divide both the numerator and the denominator by 25:
[tex]\(\frac{75 \div 25}{100 \div 25} = \frac{3}{4}\)[/tex]
Upon simplification, [tex]\(\frac{24}{30}\)[/tex] is the only fraction that does not simplify to [tex]\(\frac{3}{4}\)[/tex]. Therefore, the number that is not equivalent to [tex]\(\frac{3}{4}\)[/tex] is:
C) [tex]\(\frac{24}{30}\)[/tex]
Step 1: Simplify [tex]\(\frac{12}{16}\)[/tex]
- Find the greatest common divisor (GCD) of 12 and 16, which is 4.
- Divide both the numerator and the denominator by 4:
[tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex]
Step 2: Simplify [tex]\(\frac{18}{24}\)[/tex]
- Find the GCD of 18 and 24, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\(\frac{18 \div 6}{24 \div 6} = \frac{3}{4}\)[/tex]
Step 3: Simplify [tex]\(\frac{24}{30}\)[/tex]
- Find the GCD of 24 and 30, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\(\frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex]
This fraction simplifies to [tex]\(\frac{4}{5}\)[/tex], which is not equivalent to [tex]\(\frac{3}{4}\)[/tex].
Step 4: Simplify [tex]\(\frac{75}{100}\)[/tex]
- Find the GCD of 75 and 100, which is 25.
- Divide both the numerator and the denominator by 25:
[tex]\(\frac{75 \div 25}{100 \div 25} = \frac{3}{4}\)[/tex]
Upon simplification, [tex]\(\frac{24}{30}\)[/tex] is the only fraction that does not simplify to [tex]\(\frac{3}{4}\)[/tex]. Therefore, the number that is not equivalent to [tex]\(\frac{3}{4}\)[/tex] is:
C) [tex]\(\frac{24}{30}\)[/tex]
