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Answer :
To find which fractions are equivalent, we need to simplify each fraction to its lowest terms and compare them. Fractions are equivalent if they simplify to the same fraction. Let's take a closer look at each of the given fractions:
1. Fraction [tex]\(\frac{24}{36}\)[/tex]:
- Simplify it by finding the greatest common divisor (GCD) of 24 and 36, which is 12.
- Divide both numerator and denominator by 12:
[tex]\(\frac{24 \div 12}{36 \div 12} = \frac{2}{3}\)[/tex].
2. Fraction [tex]\(\frac{8}{12}\)[/tex]:
- Simplify it by finding the GCD of 8 and 12, which is 4.
- Divide both numerator and denominator by 4:
[tex]\(\frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)[/tex].
3. Fraction [tex]\(\frac{12}{16}\)[/tex]:
- Simplify it by finding the GCD of 12 and 16, which is 4.
- Divide both numerator and denominator by 4:
[tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex].
4. Fraction [tex]\(\frac{4}{6}\)[/tex]:
- Simplify it by finding the GCD of 4 and 6, which is 2.
- Divide both numerator and denominator by 2:
[tex]\(\frac{4 \div 2}{6 \div 2} = \frac{2}{3}\)[/tex].
5. Fraction [tex]\(\frac{18}{20}\)[/tex]:
- Simplify it by finding the GCD of 18 and 20, which is 2.
- Divide both numerator and denominator by 2:
[tex]\(\frac{18 \div 2}{20 \div 2} = \frac{9}{10}\)[/tex].
Now, let's compare the simplified forms:
- [tex]\(\frac{24}{36}\)[/tex], [tex]\(\frac{8}{12}\)[/tex], and [tex]\(\frac{4}{6}\)[/tex] all simplify to [tex]\(\frac{2}{3}\)[/tex]. Therefore, these fractions are equivalent to each other.
The equivalent fractions from the list are:
- [tex]\(\frac{24}{36}\)[/tex]
- [tex]\(\frac{8}{12}\)[/tex]
- [tex]\(\frac{4}{6}\)[/tex]
These correspond to the first, second, and fourth fractions in the original question.
1. Fraction [tex]\(\frac{24}{36}\)[/tex]:
- Simplify it by finding the greatest common divisor (GCD) of 24 and 36, which is 12.
- Divide both numerator and denominator by 12:
[tex]\(\frac{24 \div 12}{36 \div 12} = \frac{2}{3}\)[/tex].
2. Fraction [tex]\(\frac{8}{12}\)[/tex]:
- Simplify it by finding the GCD of 8 and 12, which is 4.
- Divide both numerator and denominator by 4:
[tex]\(\frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)[/tex].
3. Fraction [tex]\(\frac{12}{16}\)[/tex]:
- Simplify it by finding the GCD of 12 and 16, which is 4.
- Divide both numerator and denominator by 4:
[tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex].
4. Fraction [tex]\(\frac{4}{6}\)[/tex]:
- Simplify it by finding the GCD of 4 and 6, which is 2.
- Divide both numerator and denominator by 2:
[tex]\(\frac{4 \div 2}{6 \div 2} = \frac{2}{3}\)[/tex].
5. Fraction [tex]\(\frac{18}{20}\)[/tex]:
- Simplify it by finding the GCD of 18 and 20, which is 2.
- Divide both numerator and denominator by 2:
[tex]\(\frac{18 \div 2}{20 \div 2} = \frac{9}{10}\)[/tex].
Now, let's compare the simplified forms:
- [tex]\(\frac{24}{36}\)[/tex], [tex]\(\frac{8}{12}\)[/tex], and [tex]\(\frac{4}{6}\)[/tex] all simplify to [tex]\(\frac{2}{3}\)[/tex]. Therefore, these fractions are equivalent to each other.
The equivalent fractions from the list are:
- [tex]\(\frac{24}{36}\)[/tex]
- [tex]\(\frac{8}{12}\)[/tex]
- [tex]\(\frac{4}{6}\)[/tex]
These correspond to the first, second, and fourth fractions in the original question.
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