Problem 20 - Elementary Algebra

Question

For the following problems, use the order of operations to find each value. $$\frac{8(6+20)}{8}+\frac{3(6+16)}{22}$$

Step-by-Step Solution

Answer

Question: Evaluate the given expression: $$\frac{8(6 + 20)}{8}+\frac{3(6 + 16)}{22}$$ Answer: 29

Step 1: Simplify the expressions within the parentheses.

Add the numbers inside each pair of parentheses. $$6 + 20 = 26$$ $$6 + 16 = 22$$ Now, the expression becomes: $$\frac{8(26)}{8}+\frac{3(22)}{22}$$

Step 2: Perform multiplication.

Multiply the coefficients of each respective term with the result obtained in the parentheses. $$8 \times 26 = 208$$ $$3 \times 22 = 66$$ Now, the expression becomes: $$\frac{208}{8}+\frac{66}{22}$$

Step 3: Simplify each fraction.

Divide the numerators by the denominators in each fraction. $$\frac{208}{8} = 26$$ $$\frac{66}{22} = 3$$ Now, the expression becomes: $$26+3$$

Step 4: Add the simplified fractions.

Add the two values obtained in Step 3. $$26 + 3 = 29$$ Thus, the final value of the expression is 29.