To determine which of the given fractions is equivalent to [tex]\( \frac{24}{10} \)[/tex], we need to find a fraction from the list that simplifies to the same value as [tex]\( \frac{24}{10} \)[/tex].
Let's analyze each fraction step-by-step.
1. Fraction [tex]\( \frac{22}{8} \)[/tex]:
- Simplify [tex]\( \frac{22}{8} \)[/tex]:
- Greatest common divisor (GCD) of 22 and 8 is 2.
- [tex]\( \frac{22}{8} = \frac{22 \div 2}{8 \div 2} = \frac{11}{4} \)[/tex].
- [tex]\( \frac{11}{4} \)[/tex] is not equivalent to [tex]\( \frac{24}{10} \)[/tex].
2. Fraction [tex]\( \frac{11}{5} \)[/tex]:
- Simplify [tex]\( \frac{11}{5} \)[/tex]:
- This fraction is already in simplest form.
- Compare it directly with [tex]\( \frac{24}{10} \)[/tex]:
- [tex]\( \frac{24 \div 2.4}{10 \div 2.4} = \frac{10}{5} = 2 \)[/tex], and [tex]\( 11 \neq 10 \)[/tex], so they are not equivalent.
3. Fraction [tex]\( \frac{48}{20} \)[/tex]:
- Simplify [tex]\( \frac{48}{20} \)[/tex]:
- Greatest common divisor (GCD) of 48 and 20 is 4.
- [tex]\( \frac{48}{20} = \frac{48 \div 4}{20 \div 4} = \frac{12}{5} \)[/tex].
- Compare it directly with [tex]\( \frac{24}{10} \)[/tex]:
- [tex]\( \frac{24}{10} = \frac{24 \div 2}{10 \div 2} = \frac{12}{5} \)[/tex], so these fractions are equivalent.
4. Fraction [tex]\( \frac{46}{18} \)[/tex]:
- Simplify [tex]\( \frac{46}{18} \)[/tex]:
- Greatest common divisor (GCD) of 46 and 18 is 2.
- [tex]\( \frac{46}{18} = \frac{46 \div 2}{18 \div 2} = \frac{23}{9} \)[/tex].
- [tex]\( \frac{23}{9} \)[/tex] is not equivalent to [tex]\( \frac{24}{10} \)[/tex].
After reviewing all the fractions, the only fraction that is equivalent to [tex]\( \frac{24}{10} \)[/tex] is [tex]\( \frac{48}{20} \)[/tex].
Therefore, the fraction that is equivalent to [tex]\( \frac{24}{10} \)[/tex] is:
○ 48/20
