Answer :
To determine which fraction is equivalent to
$$\frac{44}{48},$$
we first simplify it.
1. Find the greatest common divisor (GCD) of 44 and 48. Since both 44 and 48 are divisible by 4, we have:
$$\text{GCD}(44,48)=4.$$
2. Divide both the numerator and the denominator by 4:
$$\frac{44}{48} = \frac{44\div4}{48\div4} = \frac{11}{12}.$$
Next, we compare this simplified result to each of the provided options:
- **Option 1:** $\frac{14}{15}$
This fraction cannot be simplified to $\frac{11}{12}$.
- **Option 2:** $\frac{27}{34}$
This fraction does not simplify to $\frac{11}{12}$.
- **Option 3:** $\frac{22}{24}$
Simplify $\frac{22}{24}$ by dividing both numerator and denominator by 2:
$$\frac{22}{24} = \frac{22\div2}{24\div2} = \frac{11}{12}.$$
This is exactly the same as the simplified form of $\frac{44}{48}$.
- **Option 4:** $\frac{18}{21}$
Simplify $\frac{18}{21}$ by dividing both numerator and denominator by 3:
$$\frac{18}{21} = \frac{18\div3}{21\div3} = \frac{6}{7},$$
which is not equal to $\frac{11}{12}$.
Since $\frac{22}{24}$ simplifies to $\frac{11}{12}$, just like $\frac{44}{48}$, the fraction equivalent to $\frac{44}{48}$ is:
$$\boxed{\frac{22}{24}}.$$
$$\frac{44}{48},$$
we first simplify it.
1. Find the greatest common divisor (GCD) of 44 and 48. Since both 44 and 48 are divisible by 4, we have:
$$\text{GCD}(44,48)=4.$$
2. Divide both the numerator and the denominator by 4:
$$\frac{44}{48} = \frac{44\div4}{48\div4} = \frac{11}{12}.$$
Next, we compare this simplified result to each of the provided options:
- **Option 1:** $\frac{14}{15}$
This fraction cannot be simplified to $\frac{11}{12}$.
- **Option 2:** $\frac{27}{34}$
This fraction does not simplify to $\frac{11}{12}$.
- **Option 3:** $\frac{22}{24}$
Simplify $\frac{22}{24}$ by dividing both numerator and denominator by 2:
$$\frac{22}{24} = \frac{22\div2}{24\div2} = \frac{11}{12}.$$
This is exactly the same as the simplified form of $\frac{44}{48}$.
- **Option 4:** $\frac{18}{21}$
Simplify $\frac{18}{21}$ by dividing both numerator and denominator by 3:
$$\frac{18}{21} = \frac{18\div3}{21\div3} = \frac{6}{7},$$
which is not equal to $\frac{11}{12}$.
Since $\frac{22}{24}$ simplifies to $\frac{11}{12}$, just like $\frac{44}{48}$, the fraction equivalent to $\frac{44}{48}$ is:
$$\boxed{\frac{22}{24}}.$$
