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Check whether the given fractions are equivalent or not.

a) [tex]\frac{4}{5}[/tex] and [tex]\frac{24}{30}[/tex]

b) [tex]\frac{7}{11}[/tex] and [tex]\frac{21}{32}[/tex]

c) [tex]\frac{12}{35}[/tex] and [tex]\frac{3}{5}[/tex]

d) [tex]\frac{45}{81}[/tex] and [tex]\frac{5}{7}[/tex]


Sagot :

Certainly! Let's check each pair of fractions to see if they are equivalent.

### Step-by-Step Solution:

#### a) [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex]

To determine if these fractions are equivalent, we can cross-multiply and compare the products.

For [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex]:

[tex]\[ 4 \times 30 = 120 \\ 5 \times 24 = 120 \][/tex]

Since [tex]\(120 = 120\)[/tex], [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex] are equivalent.

#### b) [tex]\(\frac{7}{11}\)[/tex] and [tex]\(\frac{21}{32}\)[/tex]

For [tex]\(\frac{7}{11}\)[/tex] and [tex]\(\frac{21}{32}\)[/tex]:

[tex]\[ 7 \times 32 = 224 \\ 11 \times 21 = 231 \][/tex]

Since [tex]\(224 \neq 231\)[/tex], [tex]\(\frac{7}{11}\)[/tex] and [tex]\(\frac{21}{32}\)[/tex] are not equivalent.

#### c) [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]

For [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:

[tex]\[ 12 \times 5 = 60 \\ 35 \times 3 = 105 \][/tex]

Since [tex]\(60 \neq 105\)[/tex], [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] are not equivalent.

#### d) [tex]\(\frac{45}{81}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex]

For [tex]\(\frac{45}{81}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex]:

[tex]\[ 45 \times 7 = 315 \\ 81 \times 5 = 405 \][/tex]

Since [tex]\(315 \neq 405\)[/tex], [tex]\(\frac{45}{81}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex] are not equivalent.

### Summary:

- [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex] are equivalent (True)
- [tex]\(\frac{7}{11}\)[/tex] and [tex]\(\frac{21}{32}\)[/tex] are not equivalent (False)
- [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] are not equivalent (False)
- [tex]\(\frac{45}{81}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex] are not equivalent (False)

Hence, the results are [tex]\([True, False, False, False]\)[/tex].