Order of Operations: Practice

Work from the innermost group outward, applying the tiers inside each group.

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

Inside the bracket, multiply before adding.

$2 \times [\,3 + 6\,] = 2 \times 9 = 18$

Group the addition so it happens before the multiplication.

$(2 + 3) \times 4 = 5 \times 4 = 20$

Without parentheses the value is $14$, and $2 + (3 \times 4)$ is also $14$.

Division and multiplication share one tier, so work left to right.

$20 \div 4 \times 5 = 5 \times 5 = 25$

The student did $4 \times 5 = 20$ first, then $20 \div 20 = 1$, treating multiplication as if it always came before division.

Settle the group, then divide, then add.

$48 \div (2 \times 4) + 1 = 48 \div 8 + 1$

Divide, then add.

$48 \div 8 + 1 = 6 + 1 = 7$

Work from the innermost group outward; the exponent goes before the addition inside it.

$3 + 2 \times [\,10 - (2^2 + 3)\,] = 3 + 2 \times [\,10 - 7\,]$

Finish the bracket, then multiply, then add.

$3 + 2 \times 3 = 3 + 6 = 9$

Group the subtraction so it happens before the division.

$(12 - 6) \div 3 = 6 \div 3 = 2$

Without parentheses the value is $10$, and $12 - (6 \div 3)$ is also $10$.

The bar groups the whole numerator, so settle it first; the exponent goes before the addition.

$\frac{4^2 + 8}{3} \times 2 = \frac{16 + 8}{3} \times 2 = \frac{24}{3} \times 2$

The line is now $24 \div 3 \times 2$. Division and multiplication share one tier, so work left to right: divide, then multiply.

$8 \times 2 = 16$

Settle the group, then square, then multiply, then subtract.

$100 - 2 \times (3 + 2)^2 = 100 - 2 \times 5^2 = 100 - 2 \times 25$

Multiply, then subtract.

$100 - 50 = 50$

The bar groups the denominator, so settle the fraction; handle the exponent and multiplication separately.

$\frac{30}{2 + 3} + 2 \times 3^2 = \frac{30}{5} + 2 \times 9 = 6 + 18$

Then add.

$6 + 18 = 24$

The fraction bar groups the whole numerator and the whole denominator, so it must be written $(8 + 4) \div (2 + 2)$.

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

Dropping the grouping turned the line into $8 + 4 \div 2 + 2$, where the division acts on only the $4$. That gives $4 \div 2 = 2$, then $8 + 2 + 2 = 12$, dividing one term instead of the whole top by the whole bottom.

Settle the group, then the exponents, then the multiplication and division, then add.

$2^3 \div 4 + 3 \times (5 - 2)^2 = 8 \div 4 + 3 \times 3^2 = 2 + 3 \times 9 = 2 + 27$

Then add.

$2 + 27 = 29$

Settle the fraction, whose bar groups its numerator, then add the squared term.

$\frac{(8 - 3)^2 - 1}{4} + 2^2 = \frac{5^2 - 1}{4} + 4 = \frac{24}{4} + 4 = 6 + 4$

Then add.

$6 + 4 = 10$