Answer :
Sure! Let's go through each of these questions and simplify the fractions or make comparisons as required:
9. Simplify [tex]\(\frac{5}{10}\)[/tex]:
To simplify, we divide both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 5 and 10 is 5.
- [tex]\(\frac{5 \div 5}{10 \div 5} = \frac{1}{2}\)[/tex]
10. Simplify the fractions [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{3}{8}\)[/tex] is already in its simplest form because 3 and 8 have no common divisors other than 1.
For [tex]\(\frac{6}{12}\)[/tex]:
- The greatest common divisor of 6 and 12 is 6.
- [tex]\(\frac{6 \div 6}{12 \div 6} = \frac{1}{2}\)[/tex]
So, [tex]\(\frac{3}{8}\)[/tex] stays the same, and [tex]\(\frac{6}{12}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
13. Simplify [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
Both fractions represent a whole number:
- [tex]\(\frac{5}{5} = 1\)[/tex]
- [tex]\(\frac{4}{4} = 1\)[/tex]
14. Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
First, simplify [tex]\(\frac{4}{6}\)[/tex]:
- The greatest common divisor of 4 and 6 is 2.
- [tex]\(\frac{4 \div 2}{6 \div 2} = \frac{2}{3}\)[/tex]
Now compare:
- [tex]\(\frac{2}{3}\)[/tex] is not equal to [tex]\(\frac{1}{3}\)[/tex].
- So, [tex]\(\frac{4}{6} \bigcirc \frac{1}{3}\)[/tex] is False (they are not equal).
17. Simplify [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- [tex]\(\frac{48}{12}\)[/tex]: The greatest common divisor of 48 and 12 is 12. So, [tex]\(\frac{48 \div 12}{12 \div 12} = 4\)[/tex].
- [tex]\(\frac{10}{5}\)[/tex]: The greatest common divisor of 10 and 5 is 5. So, [tex]\(\frac{10 \div 5}{5 \div 5} = 2\)[/tex].
18. Simplify [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
First, simplify [tex]\(\frac{9}{12}\)[/tex]:
- The greatest common divisor of 9 and 12 is 3.
- [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex] is already in its simplest form as 5 and 6 have no common divisors other than 1.
In summary, the simplified results are:
- For question 9: [tex]\(\frac{1}{2}\)[/tex]
- For question 10: [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]
- For question 13: Both simplify to 1
- For question 14: [tex]\(\frac{2}{3} \neq \frac{1}{3}\)[/tex]
- For question 17: 4 and 2
- For question 18: [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]
9. Simplify [tex]\(\frac{5}{10}\)[/tex]:
To simplify, we divide both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 5 and 10 is 5.
- [tex]\(\frac{5 \div 5}{10 \div 5} = \frac{1}{2}\)[/tex]
10. Simplify the fractions [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{6}{12}\)[/tex]:
- [tex]\(\frac{3}{8}\)[/tex] is already in its simplest form because 3 and 8 have no common divisors other than 1.
For [tex]\(\frac{6}{12}\)[/tex]:
- The greatest common divisor of 6 and 12 is 6.
- [tex]\(\frac{6 \div 6}{12 \div 6} = \frac{1}{2}\)[/tex]
So, [tex]\(\frac{3}{8}\)[/tex] stays the same, and [tex]\(\frac{6}{12}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
13. Simplify [tex]\(\frac{5}{5}\)[/tex] and [tex]\(\frac{4}{4}\)[/tex]:
Both fractions represent a whole number:
- [tex]\(\frac{5}{5} = 1\)[/tex]
- [tex]\(\frac{4}{4} = 1\)[/tex]
14. Compare [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
First, simplify [tex]\(\frac{4}{6}\)[/tex]:
- The greatest common divisor of 4 and 6 is 2.
- [tex]\(\frac{4 \div 2}{6 \div 2} = \frac{2}{3}\)[/tex]
Now compare:
- [tex]\(\frac{2}{3}\)[/tex] is not equal to [tex]\(\frac{1}{3}\)[/tex].
- So, [tex]\(\frac{4}{6} \bigcirc \frac{1}{3}\)[/tex] is False (they are not equal).
17. Simplify [tex]\(\frac{48}{12}\)[/tex] and [tex]\(\frac{10}{5}\)[/tex]:
- [tex]\(\frac{48}{12}\)[/tex]: The greatest common divisor of 48 and 12 is 12. So, [tex]\(\frac{48 \div 12}{12 \div 12} = 4\)[/tex].
- [tex]\(\frac{10}{5}\)[/tex]: The greatest common divisor of 10 and 5 is 5. So, [tex]\(\frac{10 \div 5}{5 \div 5} = 2\)[/tex].
18. Simplify [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]:
First, simplify [tex]\(\frac{9}{12}\)[/tex]:
- The greatest common divisor of 9 and 12 is 3.
- [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex] is already in its simplest form as 5 and 6 have no common divisors other than 1.
In summary, the simplified results are:
- For question 9: [tex]\(\frac{1}{2}\)[/tex]
- For question 10: [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]
- For question 13: Both simplify to 1
- For question 14: [tex]\(\frac{2}{3} \neq \frac{1}{3}\)[/tex]
- For question 17: 4 and 2
- For question 18: [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]
