Order of Operations: Practice

Exponents are on a higher tier than addition, so square first.

$2 + 3^2 = 2 + 9$

Then add.

$2 + 9 = 11$

The exponent goes before the multiplication.

$5 \times 2^2 = 5 \times 4$

Then multiply.

$5 \times 4 = 20$

Grouping settles before the exponent.

$(2 + 3)^2 = 5^2$

Then square.

$5^2 = 25$

This differs from $2 + 3^2 = 11$, where only the $3$ is squared.

Square first, then multiply, then subtract.

$4^2 - 2 \times 5 = 16 - 2 \times 5$

Do the multiplication next.

$16 - 2 \times 5 = 16 - 10 = 6$

Cube first, then divide, then add.

$2^3 + 4 \div 2 = 8 + 4 \div 2$

Division outranks the addition.

$8 + 4 \div 2 = 8 + 2 = 10$

Settle the group, then square, then divide.

$(6 - 2)^2 \div 4 = 4^2 \div 4$

Square, then divide.

$4^2 \div 4 = 16 \div 4 = 4$

The exponent goes before the division.

$100 \div 5^2 = 100 \div 25$

Then divide.

$100 \div 25 = 4$

The fraction bar groups the numerator and the denominator, so settle each first.

$\frac{8 + 4}{2 + 1} = \frac{12}{3}$

Then divide.

$\frac{12}{3} = 4$

Settle the group, then square, then subtract.

$(3 + 1)^2 - 5 = 4^2 - 5$

Square, then subtract.

$4^2 - 5 = 16 - 5 = 11$

Settle the group first.

$50 \div (2 + 3) = 50 \div 5$

Then divide.

$50 \div 5 = 10$

Settle the numerator and the denominator separately.

$\frac{6^2}{2 + 1} = \frac{36}{3}$

Then divide.

$\frac{36}{3} = 12$

Inside the group, multiply before subtracting, then apply the exponent.

$(10 - 2 \times 3)^2 = (10 - 6)^2 = 4^2$

Then square.

$4^2 = 16$