Answer :
Sure! Let's simplify each of the given fractions step by step by using their prime factorization:
26. [tex]\(\frac{40}{60}\)[/tex]
To simplify [tex]\(\frac{40}{60}\)[/tex], we find the prime factorization of both the numerator and the denominator.
- The prime factors of 40 are [tex]\(2 \times 2 \times 2 \times 5\)[/tex].
- The prime factors of 60 are [tex]\(2 \times 2 \times 3 \times 5\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(2 \times 2\)[/tex] and [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{40}{60} = \frac{2}{3}
\][/tex]
27. [tex]\(\frac{18}{48}\)[/tex]
Prime factorize both numbers:
- The prime factors of 18 are [tex]\(2 \times 3 \times 3\)[/tex].
- The prime factors of 48 are [tex]\(2 \times 2 \times 2 \times 2 \times 3\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(2\)[/tex] and [tex]\(3\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{18}{48} = \frac{3}{8}
\][/tex]
28. [tex]\(\frac{25}{45}\)[/tex]
Prime factorize both numbers:
- The prime factors of 25 are [tex]\(5 \times 5\)[/tex].
- The prime factors of 45 are [tex]\(3 \times 3 \times 5\)[/tex].
Cancel the common prime factor:
- Both have [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{25}{45} = \frac{5}{9}
\][/tex]
29. [tex]\(\frac{40}{45}\)[/tex]
Prime factorize both numbers:
- The prime factors of 40 are [tex]\(2 \times 2 \times 2 \times 5\)[/tex].
- The prime factors of 45 are [tex]\(3 \times 3 \times 5\)[/tex].
Cancel the common prime factor:
- Both have [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{40}{45} = \frac{8}{9}
\][/tex]
30. [tex]\(\frac{45}{60}\)[/tex]
Prime factorize both numbers:
- The prime factors of 45 are [tex]\(3 \times 3 \times 5\)[/tex].
- The prime factors of 60 are [tex]\(2 \times 2 \times 3 \times 5\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(3\)[/tex] and [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
31. [tex]\(\frac{24}{36}\)[/tex]
Prime factorize both numbers:
- The prime factors of 24 are [tex]\(2 \times 2 \times 2 \times 3\)[/tex].
- The prime factors of 36 are [tex]\(2 \times 2 \times 3 \times 3\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(2 \times 2\)[/tex] and [tex]\(3\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{24}{36} = \frac{2}{3}
\][/tex]
So, the fractions simplified to their lowest terms are:
1. [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex]
2. [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
3. [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
4. [tex]\(\frac{40}{45} = \frac{8}{9}\)[/tex]
5. [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex]
6. [tex]\(\frac{24}{36} = \frac{2}{3}\)[/tex]
26. [tex]\(\frac{40}{60}\)[/tex]
To simplify [tex]\(\frac{40}{60}\)[/tex], we find the prime factorization of both the numerator and the denominator.
- The prime factors of 40 are [tex]\(2 \times 2 \times 2 \times 5\)[/tex].
- The prime factors of 60 are [tex]\(2 \times 2 \times 3 \times 5\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(2 \times 2\)[/tex] and [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{40}{60} = \frac{2}{3}
\][/tex]
27. [tex]\(\frac{18}{48}\)[/tex]
Prime factorize both numbers:
- The prime factors of 18 are [tex]\(2 \times 3 \times 3\)[/tex].
- The prime factors of 48 are [tex]\(2 \times 2 \times 2 \times 2 \times 3\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(2\)[/tex] and [tex]\(3\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{18}{48} = \frac{3}{8}
\][/tex]
28. [tex]\(\frac{25}{45}\)[/tex]
Prime factorize both numbers:
- The prime factors of 25 are [tex]\(5 \times 5\)[/tex].
- The prime factors of 45 are [tex]\(3 \times 3 \times 5\)[/tex].
Cancel the common prime factor:
- Both have [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{25}{45} = \frac{5}{9}
\][/tex]
29. [tex]\(\frac{40}{45}\)[/tex]
Prime factorize both numbers:
- The prime factors of 40 are [tex]\(2 \times 2 \times 2 \times 5\)[/tex].
- The prime factors of 45 are [tex]\(3 \times 3 \times 5\)[/tex].
Cancel the common prime factor:
- Both have [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{40}{45} = \frac{8}{9}
\][/tex]
30. [tex]\(\frac{45}{60}\)[/tex]
Prime factorize both numbers:
- The prime factors of 45 are [tex]\(3 \times 3 \times 5\)[/tex].
- The prime factors of 60 are [tex]\(2 \times 2 \times 3 \times 5\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(3\)[/tex] and [tex]\(5\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
31. [tex]\(\frac{24}{36}\)[/tex]
Prime factorize both numbers:
- The prime factors of 24 are [tex]\(2 \times 2 \times 2 \times 3\)[/tex].
- The prime factors of 36 are [tex]\(2 \times 2 \times 3 \times 3\)[/tex].
Cancel the common prime factors:
- Both have [tex]\(2 \times 2\)[/tex] and [tex]\(3\)[/tex] in common.
After canceling, we are left with:
[tex]\[
\frac{24}{36} = \frac{2}{3}
\][/tex]
So, the fractions simplified to their lowest terms are:
1. [tex]\(\frac{40}{60} = \frac{2}{3}\)[/tex]
2. [tex]\(\frac{18}{48} = \frac{3}{8}\)[/tex]
3. [tex]\(\frac{25}{45} = \frac{5}{9}\)[/tex]
4. [tex]\(\frac{40}{45} = \frac{8}{9}\)[/tex]
5. [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex]
6. [tex]\(\frac{24}{36} = \frac{2}{3}\)[/tex]
