Answer :
To simplify the fractions provided in your question, we need to reduce them by finding the greatest common divisor (GCD) of the numerator and the denominator of each fraction and then dividing both by this number. Let's go through each fraction one by one:
1. [tex]\(\frac{6}{9}\)[/tex]:
- The GCD of 6 and 9 is 3.
- Dividing the numerator and denominator by 3, we get [tex]\(\frac{6 \div 3}{9 \div 3} = \frac{2}{3}\)[/tex].
2. [tex]\(\frac{2}{3}\)[/tex]:
- The GCD of 2 and 3 is 1 (since they are already simplified).
- Therefore, [tex]\(\frac{2}{3}\)[/tex] is already in its simplest form.
3. [tex]\(\frac{12}{18}\)[/tex]:
- The GCD of 12 and 18 is 6.
- Dividing the numerator and denominator by 6, we get [tex]\(\frac{12 \div 6}{18 \div 6} = \frac{2}{3}\)[/tex].
4. [tex]\(\frac{5}{7}\)[/tex]:
- The GCD of 5 and 7 is 1 (they are prime to each other).
- Therefore, [tex]\(\frac{5}{7}\)[/tex] is already in its simplest form.
5. [tex]\(\frac{9}{10}\)[/tex]:
- The GCD of 9 and 10 is 1 (since they have no common factors other than 1).
- Therefore, [tex]\(\frac{9}{10}\)[/tex] is already in its simplest form.
6. [tex]\(\frac{32}{40}\)[/tex]:
- The GCD of 32 and 40 is 8.
- Dividing the numerator and denominator by 8, we get [tex]\(\frac{32 \div 8}{40 \div 8} = \frac{4}{5}\)[/tex].
7. [tex]\(\frac{28}{36}\)[/tex]:
- The GCD of 28 and 36 is 4.
- Dividing the numerator and denominator by 4, we get [tex]\(\frac{28 \div 4}{36 \div 4} = \frac{7}{9}\)[/tex].
8. [tex]\(\frac{1}{1000}\)[/tex]:
- The GCD of 1 and 1000 is 1.
- Therefore, [tex]\(\frac{1}{1000}\)[/tex] is already in its simplest form.
So, the simplified forms of the given fractions are:
- [tex]\(\frac{6}{9} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{2}{3} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{12}{18} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{5}{7} = \frac{5}{7}\)[/tex]
- [tex]\(\frac{9}{10} = \frac{9}{10}\)[/tex]
- [tex]\(\frac{32}{40} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{28}{36} = \frac{7}{9}\)[/tex]
- [tex]\(\frac{1}{1000} = \frac{1}{1000}\)[/tex]
1. [tex]\(\frac{6}{9}\)[/tex]:
- The GCD of 6 and 9 is 3.
- Dividing the numerator and denominator by 3, we get [tex]\(\frac{6 \div 3}{9 \div 3} = \frac{2}{3}\)[/tex].
2. [tex]\(\frac{2}{3}\)[/tex]:
- The GCD of 2 and 3 is 1 (since they are already simplified).
- Therefore, [tex]\(\frac{2}{3}\)[/tex] is already in its simplest form.
3. [tex]\(\frac{12}{18}\)[/tex]:
- The GCD of 12 and 18 is 6.
- Dividing the numerator and denominator by 6, we get [tex]\(\frac{12 \div 6}{18 \div 6} = \frac{2}{3}\)[/tex].
4. [tex]\(\frac{5}{7}\)[/tex]:
- The GCD of 5 and 7 is 1 (they are prime to each other).
- Therefore, [tex]\(\frac{5}{7}\)[/tex] is already in its simplest form.
5. [tex]\(\frac{9}{10}\)[/tex]:
- The GCD of 9 and 10 is 1 (since they have no common factors other than 1).
- Therefore, [tex]\(\frac{9}{10}\)[/tex] is already in its simplest form.
6. [tex]\(\frac{32}{40}\)[/tex]:
- The GCD of 32 and 40 is 8.
- Dividing the numerator and denominator by 8, we get [tex]\(\frac{32 \div 8}{40 \div 8} = \frac{4}{5}\)[/tex].
7. [tex]\(\frac{28}{36}\)[/tex]:
- The GCD of 28 and 36 is 4.
- Dividing the numerator and denominator by 4, we get [tex]\(\frac{28 \div 4}{36 \div 4} = \frac{7}{9}\)[/tex].
8. [tex]\(\frac{1}{1000}\)[/tex]:
- The GCD of 1 and 1000 is 1.
- Therefore, [tex]\(\frac{1}{1000}\)[/tex] is already in its simplest form.
So, the simplified forms of the given fractions are:
- [tex]\(\frac{6}{9} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{2}{3} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{12}{18} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{5}{7} = \frac{5}{7}\)[/tex]
- [tex]\(\frac{9}{10} = \frac{9}{10}\)[/tex]
- [tex]\(\frac{32}{40} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{28}{36} = \frac{7}{9}\)[/tex]
- [tex]\(\frac{1}{1000} = \frac{1}{1000}\)[/tex]
