Sure, let's tackle this problem step by step to determine whether [tex]\(\left(1=\frac{1}{13}\right)\left(\frac{4}{52}\right)\)[/tex] holds true.
Firstly, let's calculate each fraction separately:
1. Calculate [tex]\(\frac{1}{13}\)[/tex]:
[tex]\[\frac{1}{13} = 0.07692307692307693\][/tex]
2. Calculate [tex]\(\frac{4}{52}\)[/tex]:
[tex]\[\frac{4}{52} = \frac{4}{4 \times 13}\][/tex]
[tex]\[\frac{4}{52} = \frac{1}{13}\][/tex]
[tex]\[\frac{1}{13} = 0.07692307692307693\][/tex]
Therefore, we now have the values:
[tex]\[\frac{1}{13} = 0.07692307692307693 \quad \text{and} \quad \frac{4}{52} = 0.07692307692307693\][/tex]
Next, we need to multiply these fractional values together:
[tex]\[ \text{Result} = \left(\frac{1}{13}\right) \times \left(\frac{4}{52}\right) = 0.07692307692307693 \times 0.07692307692307693 \][/tex]
When we multiply these two values, we get:
[tex]\[0.07692307692307693 \times 0.07692307692307693 = 0.00591715976331361\][/tex]
Now, let's compare the result to see if it is equal to 1:
[tex]\[0.00591715976331361 \neq 1\][/tex]
Therefore, [tex]\(\left(1=\frac{1}{13}\right)\left(\frac{4}{52}\right)\)[/tex] does not hold true. The comparison results indicate that the expression [tex]\(\left(\frac{1}{13}\right)\left(\frac{4}{52}\right)\)[/tex] is not equal to 1.
