Order of Operations
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.
\(\quad 2.\quad 72\enspace \square \enspace 2\; +\; 6\; \times \; 4\; =\; 60 \)
\(\quad 3.\quad 24\; \div \; 2 \;+ \;4 \enspace \square \enspace 6\; +\; 11\; =\; 47 \)
\(\quad 4.\quad 31\enspace \square \enspace 10\; \div \; 5\; =\; 29 \)
\(\quad 5.\quad 6\; +\; 42\;\div \;2 \enspace \square \enspace 15\; = \;12 \)
\(\quad 6.\quad 25\enspace \square \enspace 2\; -\; 42\; \div \;6\;+\;18\;=\;61 \)
\(\quad 7.\quad 58\; \times \;2\enspace \square \enspace 85 \;= \;31 \)
\(\quad 8.\quad 63\enspace \square \enspace 7\; \times\; 3 \;- \;4 \;= \;23 \)
\(\quad 9.\quad 36\;- \;10\enspace \square \enspace 2\; \div \;5 \;- \;11 \;= \;21 \)
\(\quad 10.\quad 10\enspace \square \enspace 3\; \times \;6 \;= \;28 \)
\(\\[1pt]\)
Too easy? Well done! Try some of these “more challenging” questions below 😉 . Fill in each of the squares with the missing numbers or operators.
\(\quad 2.\quad 24\; \times\; 3\;-\;\square\;\times\; 9\; =\; 9 \)
\(\quad 3. \quad 7\; -\; 12\; \div\; \square\; +\; 6\; =\; 10 \)
\(\quad 4. \quad 5\enspace \square\enspace \left(5\enspace \square\enspace 3\right)\enspace \square\enspace 5\enspace \square\enspace 35\; =\; 10 \)
\(\quad 5. \quad 2\enspace \square \enspace 4 \enspace \square \enspace 5 \enspace \square \enspace 9 \enspace \square \enspace 3\; =\; 19 \)
\(\quad 6. \quad 42 \enspace \square \enspace \left(4 \enspace \square \enspace 2\right) \enspace \square \enspace 5 \enspace \square \enspace 10\; =25 \)
\(\\[1pt]\)
Feel free to comment below if you have questions or difficulties and I’ll get right back to you! 🙂