Order of Operations: Additional Practice (Set 1)

Settle the group first, then the exponent, then the two products, then subtract left to right.

$3 \times (2 + 4)^2 - 5 \times 4 = 3 \times 6^2 - 5 \times 4 = 3 \times 36 - 5 \times 4$

Do both multiplications, which outrank the subtraction.

$108 - 20 = 88$

The bar groups the whole numerator, so settle it before dividing; inside it the exponent and the product go before the addition.

$\frac{4^2 + 2 \times 7}{3} + 2^3 = \frac{16 + 14}{3} + 8 = \frac{30}{3} + 8$

Divide, then add the term outside the fraction.

$10 + 8 = 18$

Work the innermost group first, where the exponent precedes the addition.

$100 - [\,2 \times (3^2 + 1) + 4\,] = 100 - [\,2 \times 10 + 4\,]$

Inside the bracket, multiply before adding, then subtract.

$100 - [\,20 + 4\,] = 100 - 24 = 76$

Group the subtraction so it happens before the division.

$(12 - 8) \div 2 = 4 \div 2 = 2$

Without parentheses the value is $12 - 4 = 8$, and $12 - (8 \div 2)$ is also $8$, so only grouping the difference first reaches $2$.

The bar groups the numerator, so settle it before dividing; the exponent and product on the right are handled separately.

$\frac{6 \times 5 - 2}{4} + 3 \times 2^2 = \frac{30 - 2}{4} + 3 \times 4 = \frac{28}{4} + 12$

Divide, then add.

$7 + 12 = 19$

Evaluate each option under the tiers.

$(2 + 3) \times 6 = 30, \quad 4 \times 5 - 1 = 19, \quad 30 - 2 \times 4 = 22, \quad 2 + 3 \times 6 = 20$

Only the last reaches $20$, because the multiplication outranks the addition.

$2 + 3 \times 6 = 2 + 18 = 20$

Each bar groups its own numerator and denominator, so settle both fractions before adding.

$\frac{(2 + 4)^2}{4} + \frac{18}{3 + 3} = \frac{6^2}{4} + \frac{18}{6} = \frac{36}{4} + \frac{18}{6}$

Divide each, then add.

$9 + 3 = 12$

Square first, then run the division and multiplication strictly left to right.

$48 \div 2^2 \div 3 \times 2 = 48 \div 4 \div 3 \times 2 = 12 \div 3 \times 2$

Continue left to right.

$12 \div 3 \times 2 = 4 \times 2 = 8$

Evaluate each option under the tiers.

$2 \times 3^2 + 18 = 18 + 18 = 36, \quad (4 + 2)^2 = 6^2 = 36, \quad 3 \times 4 \times 3 = 36$

The outlier evaluates the exponent before subtracting.

$50 - 4^2 = 50 - 16 = 34$

That value is $34$, which is not $36$, so $50 - 4^2$ is the one that is not equal to $36$.

The bar groups the whole numerator and the whole denominator, so settle each; the right term handles its own exponent before dividing.

$\frac{8^2 - 4}{2 \times 5} + 4^2 \div 8 = \frac{64 - 4}{10} + 16 \div 8 = \frac{60}{10} + 2$

Divide, then add.

$6 + 2 = 8$

Settle the innermost group, then the bracket, then the brace, and only then apply the exponent and divide.

$\{\,4 + [\,2 \times (6 - 3)\,]\,\}^2 \div 4 = \{\,4 + [\,2 \times 3\,]\,\}^2 \div 4 = \{\,4 + 6\,\}^2 \div 4$

Finish the brace, square it, then divide.

$10^2 \div 4 = 100 \div 4 = 25$

Handle the standalone exponent and its product, settle the fraction whose bar groups the numerator, then work the bottom tier left to right.

$2 \times 3^2 + \frac{20 - 2 \times 4}{6} - 5 = 2 \times 9 + \frac{20 - 8}{6} - 5 = 18 + \frac{12}{6} - 5$

Divide, then add and subtract left to right.

$18 + 2 - 5 = 20 - 5 = 15$