Answer :
To solve for the missing quantity in the given fractions, let's follow a step-by-step approach:
1. Understanding the given fractions:
We need to find an equivalent fraction for [tex]\(\frac{40}{100}\)[/tex] and [tex]\(\frac{1}{20}\)[/tex].
2. Simplifying the known fractions:
- Simplify [tex]\(\frac{40}{100}\)[/tex]:
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]
- Check for equivalence with [tex]\(\frac{1}{20}\)[/tex]:
When [tex]\(\frac{40}{100}\)[/tex] is simplified, it becomes [tex]\(\frac{2}{5}\)[/tex], not [tex]\(\frac{1}{20}\)[/tex]. There seems to be an error in equating these fractions since [tex]\(\frac{1}{20}\)[/tex] simplifies in decimal to 0.05, whereas [tex]\(\frac{2}{5}\)[/tex] simplifies to 0.4, like [tex]\(\frac{40}{100}\)[/tex].
3. Fill the missing fraction:
Given that [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex], and noting that [tex]\(\frac{40}{100}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex], the missing equivalent fraction for the blank should also be [tex]\(\frac{2}{5}\)[/tex].
So, the final equivalent fraction to [tex]\(\frac{40}{100}\)[/tex] and [tex]\(\frac{1}{20}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex]. Therefore, the missing quantity is:
[tex]\[
\frac{40}{100}=\frac{1}{20}=\frac{2}{5}
\][/tex]
1. Understanding the given fractions:
We need to find an equivalent fraction for [tex]\(\frac{40}{100}\)[/tex] and [tex]\(\frac{1}{20}\)[/tex].
2. Simplifying the known fractions:
- Simplify [tex]\(\frac{40}{100}\)[/tex]:
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]
- Check for equivalence with [tex]\(\frac{1}{20}\)[/tex]:
When [tex]\(\frac{40}{100}\)[/tex] is simplified, it becomes [tex]\(\frac{2}{5}\)[/tex], not [tex]\(\frac{1}{20}\)[/tex]. There seems to be an error in equating these fractions since [tex]\(\frac{1}{20}\)[/tex] simplifies in decimal to 0.05, whereas [tex]\(\frac{2}{5}\)[/tex] simplifies to 0.4, like [tex]\(\frac{40}{100}\)[/tex].
3. Fill the missing fraction:
Given that [tex]\(\frac{40}{100} = \frac{2}{5}\)[/tex], and noting that [tex]\(\frac{40}{100}\)[/tex] simplifies to [tex]\(\frac{2}{5}\)[/tex], the missing equivalent fraction for the blank should also be [tex]\(\frac{2}{5}\)[/tex].
So, the final equivalent fraction to [tex]\(\frac{40}{100}\)[/tex] and [tex]\(\frac{1}{20}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex]. Therefore, the missing quantity is:
[tex]\[
\frac{40}{100}=\frac{1}{20}=\frac{2}{5}
\][/tex]
