Order of Operations

Simplifying expressions following the order of operations. Start by selecting an expression to simplify and then click "Given".

Step	Operation	Perform	Result
Given			$16 - 32 \div 8 + 1$
	Divide	$16 - 32 \div 8 + 1$	$16 - 4 + 1$
	Subtract	$16 - 4 + 1$	$12 + 1$
	Add	$12 + 1$	$13$

Solution: $13$

Step	Operation	Perform	Result
Given			$3 (- 3) + 5 \cdot 4 - 7$
	Multiply	$3 (- 3) + 5 \cdot 4 - 7$	$- 9 + 5 \cdot 4 - 7$
	Multiply	$- 9 + 5 \cdot 4 - 7$	$- 9 + 20 - 7$
	Add	$- 9 + 20 - 7$	$11 - 7$
	Subtract	$11 - 7$	$4$

Solution: $4$

Step	Operation	Perform	Result
Given			$18 \div 9 \cdot 7 - 5$
	Divide	$18 \div 9 \cdot 7 - 5$	$2 \cdot 7 - 5$
	Multiply	$2 \cdot 7 - 5$	$14 - 5$
	Subtract	$14 - 5$	$9$

Solution: $9$

Step	Operation	Perform	Result
Given			$24 \div 4 \cdot 2 - 7$
	Divide	$24 \div 4 \cdot 2 - 7$	$6 \cdot 2 - 7$
	Multiply	$6 \cdot 2 - 7$	$12 - 7$
	Subtract	$12 - 7$	$5$

Solution: $5$

Step	Operation	Perform	Result
Given			$- 3 - 4 [6 + (8 - 2) \div 3]$
	Subtract within the innermost parentheses	$- 3 - 4 [6 + (8 - 2) \div 3]$	$- 3 - 4 [6 + 6 \div 3]$
	Divide within the brackets	$- 3 - 4 [6 + 6 \div 3]$	$- 3 - 4 [6 + 2]$
	Add within the brackets	$- 3 - 4 [6 + 2]$	$- 3 - 4 [8]$
	Multiply	$- 3 - 4 [8]$	$- 3 - 32$
	Subtract	$- 3 - 32$	$- 35$

Solution: $- 35$

Step	Operation	Perform	Result
Given			$8 \cdot 8 \div 2^{4} - (3 - 2)$
	Subtract within the parentheses	$8 \cdot 8 \div 2^{4} - (3 - 2)$	$8 \cdot 8 \div 2^{4} - 1$
	Evaluate the Exponent	$8 \cdot 8 \div 2^{4} - 1$	$8 \cdot 8 \div 16 - 1$
	Multiply	$8 \cdot 8 \div 16 - 1$	$64 \div 16 - 1$
	Divide	$64 \div 16 - 1$	$4 - 1$
	Subtract	$4 - 1$	$3$

Solution: $3$

Step	Operation	Perform	Result
Given			$\frac{1}{3} - \frac{2}{5} \cdot \frac{1}{4}$
	Multiply	$\frac{1}{3} - \frac{2}{5} \cdot \frac{1}{4}$	$\frac{1}{3} - \frac{2}{20}$
	Reduce	$\frac{1}{3} - \frac{2}{20}$	$\frac{1}{3} - \frac{1}{10}$
	Rewrite as equivalent fractions with common denominators	$\frac{1}{3} - \frac{1}{10}$	$\frac{10}{30} - \frac{3}{30}$
	Subtract	$\frac{10}{30} - \frac{3}{30}$	$\frac{7}{30}$

Solution: $\frac{7}{30}$

Step	Operation	Perform	Result
Given			$3^{2} \cdot (- 2 + 5) + 1 - 4 [(- 2)^{3} + 7]$
	Evaluate the Exponent within the Parentheses	$3^{2} \cdot (- 2 + 5) + 1 - 4 [(- 2)^{3} + 7]$	$3^{2} \cdot (- 2 + 5) + 1 - 4 [- 8 + 7]$
	Parentheses	$3^{2} \cdot (- 2 + 5) + 1 - 4 [- 8 + 7]$	$3^{2} \cdot (3) + 1 - 4 [- 1]$
	Evaluate the Exponent	$3^{2} \cdot (3) + 1 - 4 [- 1]$	$9 \cdot (3) + 1 - 4 [- 1]$
	Multiply	$9 \cdot (3) + 1 - 4 [- 1]$	$27 + 1 + 4$
	Add	$27 + 1 + 4$	$28 + 4$
	Add	$28 + 4$	$32$

Solution: $32$