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Answer :
Sure! Let's simplify each fraction to its lowest terms by canceling out the common prime factors.
26. [tex]\(\frac{40}{60}\)[/tex]
- Prime factorization of 40: [tex]\(2^3 \times 5\)[/tex]
- Prime factorization of 60: [tex]\(2^2 \times 3 \times 5\)[/tex]
The common factors are [tex]\(2^2\)[/tex] and 5. Cancel these out:
- [tex]\(\frac{40}{60} = \frac{2 \times 2 \times 5}{2 \times 2 \times 3 \times 5} = \frac{2}{3}\)[/tex]
27. [tex]\(\frac{18}{48}\)[/tex]
- Prime factorization of 18: [tex]\(2 \times 3^2\)[/tex]
- Prime factorization of 48: [tex]\(2^4 \times 3\)[/tex]
The common factors are [tex]\(2\)[/tex] and [tex]\(3\)[/tex]. Cancel these out:
- [tex]\(\frac{18}{48} = \frac{2 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 3} = \frac{3}{8}\)[/tex]
28. [tex]\(\frac{25}{45}\)[/tex]
- Prime factorization of 25: [tex]\(5^2\)[/tex]
- Prime factorization of 45: [tex]\(3^2 \times 5\)[/tex]
The common factor is 5. Cancel this out:
- [tex]\(\frac{25}{45} = \frac{5 \times 5}{3 \times 3 \times 5} = \frac{5}{9}\)[/tex]
29. [tex]\(\frac{40}{45}\)[/tex]
- Prime factorization of 40: [tex]\(2^3 \times 5\)[/tex]
- Prime factorization of 45: [tex]\(3^2 \times 5\)[/tex]
The common factor is 5. Cancel this out:
- [tex]\(\frac{40}{45} = \frac{2 \times 2 \times 2 \times 5}{3 \times 3 \times 5} = \frac{8}{9}\)[/tex]
30. [tex]\(\frac{45}{60}\)[/tex]
- Prime factorization of 45: [tex]\(3^2 \times 5\)[/tex]
- Prime factorization of 60: [tex]\(2^2 \times 3 \times 5\)[/tex]
The common factors are 3 and 5. Cancel these out:
- [tex]\(\frac{45}{60} = \frac{3 \times 3 \times 5}{2 \times 2 \times 3 \times 5} = \frac{3}{4}\)[/tex]
31. [tex]\(\frac{24}{36}\)[/tex]
- Prime factorization of 24: [tex]\(2^3 \times 3\)[/tex]
- Prime factorization of 36: [tex]\(2^2 \times 3^2\)[/tex]
The common factors are [tex]\(2^2\)[/tex] and [tex]\(3\)[/tex]. Cancel these out:
- [tex]\(\frac{24}{36} = \frac{2 \times 2 \times 2 \times 3}{2 \times 2 \times 3 \times 3} = \frac{2}{3}\)[/tex]
So, the fractions in simplest form are:
- [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{40}{45} = \frac{8}{9}\)[/tex]
- [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex]
- [tex]\(\frac{24}{36} = \frac{2}{3}\)[/tex]
26. [tex]\(\frac{40}{60}\)[/tex]
- Prime factorization of 40: [tex]\(2^3 \times 5\)[/tex]
- Prime factorization of 60: [tex]\(2^2 \times 3 \times 5\)[/tex]
The common factors are [tex]\(2^2\)[/tex] and 5. Cancel these out:
- [tex]\(\frac{40}{60} = \frac{2 \times 2 \times 5}{2 \times 2 \times 3 \times 5} = \frac{2}{3}\)[/tex]
27. [tex]\(\frac{18}{48}\)[/tex]
- Prime factorization of 18: [tex]\(2 \times 3^2\)[/tex]
- Prime factorization of 48: [tex]\(2^4 \times 3\)[/tex]
The common factors are [tex]\(2\)[/tex] and [tex]\(3\)[/tex]. Cancel these out:
- [tex]\(\frac{18}{48} = \frac{2 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 3} = \frac{3}{8}\)[/tex]
28. [tex]\(\frac{25}{45}\)[/tex]
- Prime factorization of 25: [tex]\(5^2\)[/tex]
- Prime factorization of 45: [tex]\(3^2 \times 5\)[/tex]
The common factor is 5. Cancel this out:
- [tex]\(\frac{25}{45} = \frac{5 \times 5}{3 \times 3 \times 5} = \frac{5}{9}\)[/tex]
29. [tex]\(\frac{40}{45}\)[/tex]
- Prime factorization of 40: [tex]\(2^3 \times 5\)[/tex]
- Prime factorization of 45: [tex]\(3^2 \times 5\)[/tex]
The common factor is 5. Cancel this out:
- [tex]\(\frac{40}{45} = \frac{2 \times 2 \times 2 \times 5}{3 \times 3 \times 5} = \frac{8}{9}\)[/tex]
30. [tex]\(\frac{45}{60}\)[/tex]
- Prime factorization of 45: [tex]\(3^2 \times 5\)[/tex]
- Prime factorization of 60: [tex]\(2^2 \times 3 \times 5\)[/tex]
The common factors are 3 and 5. Cancel these out:
- [tex]\(\frac{45}{60} = \frac{3 \times 3 \times 5}{2 \times 2 \times 3 \times 5} = \frac{3}{4}\)[/tex]
31. [tex]\(\frac{24}{36}\)[/tex]
- Prime factorization of 24: [tex]\(2^3 \times 3\)[/tex]
- Prime factorization of 36: [tex]\(2^2 \times 3^2\)[/tex]
The common factors are [tex]\(2^2\)[/tex] and [tex]\(3\)[/tex]. Cancel these out:
- [tex]\(\frac{24}{36} = \frac{2 \times 2 \times 2 \times 3}{2 \times 2 \times 3 \times 3} = \frac{2}{3}\)[/tex]
So, the fractions in simplest form are:
- [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex]
- [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
- [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
- [tex]\(\frac{40}{45} = \frac{8}{9}\)[/tex]
- [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex]
- [tex]\(\frac{24}{36} = \frac{2}{3}\)[/tex]
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