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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (7)/(12)-(1)/(7) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{7}{12}-\frac{1}{7}$ $\newline$ Answer:

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Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

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\frac{7}{12}-\frac{1}{7}

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Answer:

Find Common Denominator: To subtract the two fractions, we need to find a common denominator. The denominators are $12$ and $7$ , which are both prime to each other, so the common denominator will be their product, $12 \times 7 = 84$ .
Convert to Equivalent Fractions: Now we convert each fraction to an equivalent fraction with the common denominator of $84$ . For the first fraction, $\frac{7}{12}$ , we multiply both the numerator and the denominator by $7$ to get $\left(\frac{7\times7}{12\times7}\right) = \frac{49}{84}$ . For the second fraction, $\frac{1}{7}$ , we multiply both the numerator and the denominator by $12$ to get $\left(\frac{1\times12}{7\times12}\right) = \frac{12}{84}$ .
Subtract Fractions: With both fractions having the common denominator of $84$ , we can now subtract them: $(\frac{49}{84}) - (\frac{12}{84})$ .
Perform Numerical Subtraction: Subtracting the numerators while keeping the common denominator gives us $(49 - 12)/84$ .
Check for Simplification: Performing the subtraction in the numerator gives us $\frac{37}{84}.$
Check for Simplification: Performing the subtraction in the numerator gives us $\frac{37}{84}$ .We now check if the fraction $\frac{37}{84}$ can be simplified further. Since $37$ is a prime number and does not share any common factors with $84$ other than $1$ , the fraction is already in its simplest form.