Question

EXPRESSIONS WITH FRACTION BARS Evaluate the expression. $$ \frac{(3 \cdot 7)+9}{2^{3}+5-3} $$

Short answer

The evaluated expression is 3.

Step-by-step solution

Simplify the expression inside the brackets in both numerator and denominator

According to PEMDAS rule, first evaluate the expressions inside parentheses and then proceed with other operators. \( \frac{(3 \cdot 7)+9}{2^{3}+5-3} \) becomes \( \frac{21+9}{8+5-3} \).

Carry out the operations in numerator and denominator

Now perform the addition and subtraction operation in both the numerator and denominator. The expression \( \frac{21+9}{8+5-3} \) simplifies to \( \frac{30}{10} \).

Simplify the fraction

Finally, simplify the fraction \( \frac{30}{10} \) by dividing both the numerator and denominator by their greatest common factor, which is 10. Thus, the expression \( \frac{30}{10} \) simplifies to \( 3 \).