Order of Operations

Follow this simple rule: “PMDAS”
where:
P = Parentheses
MD = Multiplication and Division
AS = Addition and Subtraction

The order of operations is read from left to right. Parentheses have the highest precedence. Multiplication and Division are next followed by Addition and Subtraction as the lowest precedence.

MD have equal precedence meaning you have to calculate whoever comes first as you solve the equations. The same rule of equal precedence applies to Addition and Subtraction (AS) as well.

Let’s try some examples. Fill in the missing operators $\left( +,\;-,\;\times \; \mathrm{or}\; \div \right)$ in each of the boxes below.

$\quad 1.\quad 51\enspace \square \enspace 7\; \times \; 5 \; + \; 11 \; = \; 97$

Show answer:

$\enspace+$

$\quad 2.\quad 72\enspace \square \enspace 2\; +\; 6\; \times \; 4\; =\; 60$

Show answer:

$\enspace\div$

$\quad 3.\quad 24\; \div \; 2 \;+ \;4 \enspace \square \enspace 6\; +\; 11\; =\; 47$

Show answer:

$\enspace\times$

$\quad 4.\quad 31\enspace \square \enspace 10\; \div \; 5\; =\; 29$

Show answer:

$\enspace-$

$\quad 5.\quad 6\; +\; 42\;\div \;2 \enspace \square \enspace 15\; = \;12$

Show answer:

$\enspace-$

$\quad 6.\quad 25\enspace \square \enspace 2\; -\; 42\; \div \;6\;+\;18\;=\;61$

Show answer:

$\enspace\times$

$\quad 7.\quad 58\; \times \;2\enspace \square \enspace 85 \;= \;31$

Show answer:

$\enspace-$

$\quad 8.\quad 63\enspace \square \enspace 7\; \times\; 3 \;- \;4 \;= \;23$

Show answer:

$\enspace\div$

$\quad 9.\quad 36\;- \;10\enspace \square \enspace 2\; \div \;5 \;- \;11 \;= \;21$

Show answer:

$\enspace\times$

$\quad 10.\quad 10\enspace \square \enspace 3\; \times \;6 \;= \;28$

Show answer:

$\enspace+$

$\\[1pt]$
Too easy? Well done! Try some of these “more challenging” questions below . Fill in each of the squares with the missing numbers or operators.

$\quad 1.\quad 50 \;-\;18\;\div \; \square \; \times \; 6\; =\; 14$

Show Answer:

$\enspace 3$

$\quad 2.\quad 24\; \times\; 3\;-\;\square\;\times\; 9\; =\; 9$

Show Answer:

$\enspace 7$

$\quad 3. \quad 7\; -\; 12\; \div\; \square\; +\; 6\; =\; 10$

Show Answer:

$\enspace 4$

$\quad 4. \quad 5\enspace \square\enspace \left(5\enspace \square\enspace 3\right)\enspace \square\enspace 5\enspace \square\enspace 35\; =\; 10$

Show Answer:

$\enspace \times,\; +,\; +,\; –$

$\quad 5. \quad 2\enspace \square \enspace 4 \enspace \square \enspace 5 \enspace \square \enspace 9 \enspace \square \enspace 3\; =\; 19$

Show Answer:

$\enspace\times,\; +,\; +,\; –$

$\quad 6. \quad 42 \enspace \square \enspace \left(4 \enspace \square \enspace 2\right) \enspace \square \enspace 5 \enspace \square \enspace 10\; =25$

Show Answer:

$\enspace\div,\; +,\; \times,\; –$

$\\[1pt]$
Feel free to comment below if you have questions or difficulties and I’ll get right back to you!