Answer :
To determine which fraction is equivalent to [tex]\(\frac{8}{10}\)[/tex], we start by simplifying [tex]\(\frac{8}{10}\)[/tex].
1. Simplify the fraction [tex]\(\frac{8}{10}\)[/tex]:
- Both the numerator (8) and the denominator (10) can be divided by their greatest common divisor, which is 2.
- Divide the numerator by 2: [tex]\(8 \div 2 = 4\)[/tex]
- Divide the denominator by 2: [tex]\(10 \div 2 = 5\)[/tex]
- So, [tex]\(\frac{8}{10}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
2. Compare with the given options:
We need to see if any of the given fractions also simplify to [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{24}{28}\)[/tex]:
- Greatest common divisor of 24 and 28 is 4.
- Simplifying:
[tex]\[
24 \div 4 = 6 \quad \text{and} \quad 28 \div 4 = 7
\][/tex]
- So, [tex]\(\frac{24}{28} = \frac{6}{7}\)[/tex] (not equivalent to [tex]\(\frac{4}{5}\)[/tex]).
- [tex]\(\frac{24}{30}\)[/tex]:
- Greatest common divisor of 24 and 30 is 6.
- Simplifying:
[tex]\[
24 \div 6 = 4 \quad \text{and} \quad 30 \div 6 = 5
\][/tex]
- So, [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex] (equivalent to [tex]\(\frac{4}{5}\)[/tex]).
- [tex]\(\frac{43}{48}\)[/tex]:
- This fraction doesn't simplify neatly to [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{46}{50}\)[/tex]:
- Greatest common divisor of 46 and 50 is 2.
- Simplifying:
[tex]\[
46 \div 2 = 23 \quad \text{and} \quad 50 \div 2 = 25
\][/tex]
- So, [tex]\(\frac{46}{50} = \frac{23}{25}\)[/tex] (not equivalent to [tex]\(\frac{4}{5}\)[/tex]).
The fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex], which is equivalent to [tex]\(\frac{8}{10}\)[/tex]. Therefore, the correct answer is [tex]\(\frac{24}{30}\)[/tex].
1. Simplify the fraction [tex]\(\frac{8}{10}\)[/tex]:
- Both the numerator (8) and the denominator (10) can be divided by their greatest common divisor, which is 2.
- Divide the numerator by 2: [tex]\(8 \div 2 = 4\)[/tex]
- Divide the denominator by 2: [tex]\(10 \div 2 = 5\)[/tex]
- So, [tex]\(\frac{8}{10}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
2. Compare with the given options:
We need to see if any of the given fractions also simplify to [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{24}{28}\)[/tex]:
- Greatest common divisor of 24 and 28 is 4.
- Simplifying:
[tex]\[
24 \div 4 = 6 \quad \text{and} \quad 28 \div 4 = 7
\][/tex]
- So, [tex]\(\frac{24}{28} = \frac{6}{7}\)[/tex] (not equivalent to [tex]\(\frac{4}{5}\)[/tex]).
- [tex]\(\frac{24}{30}\)[/tex]:
- Greatest common divisor of 24 and 30 is 6.
- Simplifying:
[tex]\[
24 \div 6 = 4 \quad \text{and} \quad 30 \div 6 = 5
\][/tex]
- So, [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex] (equivalent to [tex]\(\frac{4}{5}\)[/tex]).
- [tex]\(\frac{43}{48}\)[/tex]:
- This fraction doesn't simplify neatly to [tex]\(\frac{4}{5}\)[/tex].
- [tex]\(\frac{46}{50}\)[/tex]:
- Greatest common divisor of 46 and 50 is 2.
- Simplifying:
[tex]\[
46 \div 2 = 23 \quad \text{and} \quad 50 \div 2 = 25
\][/tex]
- So, [tex]\(\frac{46}{50} = \frac{23}{25}\)[/tex] (not equivalent to [tex]\(\frac{4}{5}\)[/tex]).
The fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex], which is equivalent to [tex]\(\frac{8}{10}\)[/tex]. Therefore, the correct answer is [tex]\(\frac{24}{30}\)[/tex].
