Answer :
To find which fractions are equivalent to 40%, we need to understand what 40% means as a fraction and then compare it to the given options.
### Step-by-Step Solution:
1. Convert 40% to a Fraction:
- Percent means "per hundred," so 40% is the same as 40 out of 100.
- Thus, 40% as a fraction is [tex]\( \frac{40}{100} \)[/tex].
2. Simplify [tex]\( \frac{40}{100} \)[/tex]:
- To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 20:
[tex]\[
\frac{40 \div 20}{100 \div 20} = \frac{2}{5}
\][/tex]
- So, 40% as a simplified fraction is [tex]\( \frac{2}{5} \)[/tex].
3. Evaluate Each Option:
- [tex]\( \frac{1}{40} \)[/tex]: This is not equivalent to [tex]\( \frac{2}{5} \)[/tex] as it is much smaller.
- [tex]\( \frac{2}{20} \)[/tex]: Simplify [tex]\( \frac{2}{20} \)[/tex] to [tex]\( \frac{1}{10} \)[/tex], which is not equivalent to [tex]\( \frac{2}{5} \)[/tex].
- [tex]\( \frac{2}{5} \)[/tex]: This is exactly equivalent to 40% because it's the simplified form of [tex]\( \frac{40}{100} \)[/tex].
- [tex]\( \frac{40}{10} \)[/tex]: Simplify [tex]\( \frac{40}{10} \)[/tex] to 4, which is not equivalent to [tex]\( \frac{2}{5} \)[/tex].
- [tex]\( \frac{40}{100} \)[/tex]: This fraction is not yet simplified, but it represents 40% directly.
- [tex]\( \frac{20}{50} \)[/tex]: Simplify [tex]\( \frac{20}{50} \)[/tex] by dividing both numerator and denominator by 10, getting [tex]\( \frac{2}{5} \)[/tex], which is equivalent to 40%.
### Conclusion:
The fractions that are equivalent to 40% are:
- [tex]\( \frac{2}{5} \)[/tex]
- [tex]\( \frac{40}{100} \)[/tex]
- [tex]\( \frac{20}{50} \)[/tex]
These fractions either represent 40% directly or simplify to the same value as 40%.
### Step-by-Step Solution:
1. Convert 40% to a Fraction:
- Percent means "per hundred," so 40% is the same as 40 out of 100.
- Thus, 40% as a fraction is [tex]\( \frac{40}{100} \)[/tex].
2. Simplify [tex]\( \frac{40}{100} \)[/tex]:
- To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 20:
[tex]\[
\frac{40 \div 20}{100 \div 20} = \frac{2}{5}
\][/tex]
- So, 40% as a simplified fraction is [tex]\( \frac{2}{5} \)[/tex].
3. Evaluate Each Option:
- [tex]\( \frac{1}{40} \)[/tex]: This is not equivalent to [tex]\( \frac{2}{5} \)[/tex] as it is much smaller.
- [tex]\( \frac{2}{20} \)[/tex]: Simplify [tex]\( \frac{2}{20} \)[/tex] to [tex]\( \frac{1}{10} \)[/tex], which is not equivalent to [tex]\( \frac{2}{5} \)[/tex].
- [tex]\( \frac{2}{5} \)[/tex]: This is exactly equivalent to 40% because it's the simplified form of [tex]\( \frac{40}{100} \)[/tex].
- [tex]\( \frac{40}{10} \)[/tex]: Simplify [tex]\( \frac{40}{10} \)[/tex] to 4, which is not equivalent to [tex]\( \frac{2}{5} \)[/tex].
- [tex]\( \frac{40}{100} \)[/tex]: This fraction is not yet simplified, but it represents 40% directly.
- [tex]\( \frac{20}{50} \)[/tex]: Simplify [tex]\( \frac{20}{50} \)[/tex] by dividing both numerator and denominator by 10, getting [tex]\( \frac{2}{5} \)[/tex], which is equivalent to 40%.
### Conclusion:
The fractions that are equivalent to 40% are:
- [tex]\( \frac{2}{5} \)[/tex]
- [tex]\( \frac{40}{100} \)[/tex]
- [tex]\( \frac{20}{50} \)[/tex]
These fractions either represent 40% directly or simplify to the same value as 40%.
