To convert percentages to fractions in their lowest form, we shall follow these steps:
1. Understand the percentage: A percentage is a number out of 100. For instance, [tex]\(70 \%\)[/tex] is [tex]\(70\)[/tex] out of [tex]\(100\)[/tex].
2. Form the initial fraction: Write the percentage as a fraction with the denominator [tex]\(100\)[/tex].
3. Simplify the fraction: Reduce the fraction to its lowest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Let's go through each part of the question step by step.
### (a) [tex]\(70 \%\)[/tex]
1. Write as a fraction:
[tex]\[
70 \% = \frac{70}{100}
\][/tex]
2. Simplify the fraction:
- The greatest common divisor (GCD) of [tex]\(70\)[/tex] and [tex]\(100\)[/tex] is [tex]\(10\)[/tex].
- Divide both the numerator and the denominator by [tex]\(10\)[/tex]:
[tex]\[
\frac{70 \div 10}{100 \div 10} = \frac{7}{10}
\][/tex]
So, [tex]\(70\% = \frac{7}{10}\)[/tex].
### (b) [tex]\(100 \%\)[/tex]
1. Write as a fraction:
[tex]\[
100 \% = \frac{100}{100}
\][/tex]
2. Simplify the fraction:
- The greatest common divisor (GCD) of [tex]\(100\)[/tex] and [tex]\(100\)[/tex] is [tex]\(100\)[/tex].
- Divide both the numerator and the denominator by [tex]\(100\)[/tex]:
[tex]\[
\frac{100 \div 100}{100 \div 100} = \frac{1}{1}
\][/tex]
So, [tex]\(100\% = 1\)[/tex].
### (c) [tex]\(55 \%\)[/tex]
1. Write as a fraction:
[tex]\[
55 \% = \frac{55}{100}
\][/tex]
2. Simplify the fraction:
- The greatest common divisor (GCD) of [tex]\(55\)[/tex] and [tex]\(100\)[/tex] is [tex]\(5\)[/tex].
- Divide both the numerator and the denominator by [tex]\(5\)[/tex]:
[tex]\[
\frac{55 \div 5}{100 \div 5} = \frac{11}{20}
\][/tex]
So, [tex]\(55\% = \frac{11}{20}\)[/tex].
### Summary
- [tex]\(70\% = \frac{7}{10}\)[/tex]
- [tex]\(100\% = 1\)[/tex]
- [tex]\(55\% = \frac{11}{20}\)[/tex]
Thus, the fractions in their lowest form are:
[tex]\[
\left(\frac{7}{10}, 1, \frac{11}{20}\right)
\][/tex]
