Order-of-operations trap sprint

Evaluate left-to-right instead of following PEMDAS.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

Loading questions…

How to avoid order-of-operations mistakes

What is \(3 + 4 \times 5\)? If you go left to right, you get \(7 \times 5 = 35\). The right answer is \(3 + 20 = 23\), because multiplication comes before addition.

Students fall for this because we read left to right, and our hands want to compute the same way. SHSAT problems also hide the trap inside formulas:

Check habits:

Worked examples

Example 1.
What is the value of \(12 + 4 \times 6 - 1\)?
Show answer and explanation
Answer:
A

Follow the order of operations: \(4 \times 6 = 24\), then \(12 + 24 - 1 = 35\). Working left to right (adding before multiplying) gives \(95\). Subtracting before multiplying gives \(32\). Doing the addition and the subtraction before the multiplication gives \(80\).

Example 2.
The operation \(\blacksquare\) is defined for all numbers \(x\) by \(\blacksquare x = x^2 + 2\). What is the value of \(\blacksquare 5\)?
Show answer and explanation
Answer:
A

Replace every \(x\) in the rule with \(5\): \(\blacksquare 5 = 5^2 + 2 = 25 + 2 = 27\). Square first, then add the constant. (Reading \(5^2\) as \(5 \times 2\) gives \(12\). Forgetting the square gives \(7\). Adding the \(2\) before squaring gives \(49\).)

Example 3.
A washer-shaped ring is formed by cutting a circle of radius 8 cm out of the center of a larger circle of radius 14 cm. What is the area of the ring, in terms of \(\pi\)?
Show answer and explanation
Answer:
C

Ring area \(= \pi R^2 - \pi r^2 = \pi(14^2 - 8^2) = 132\pi\) sq cm. (Subtracting the radii first and then squaring, \(\pi(14 - 8)^2\), gives \(36\pi\). Adding the two circles instead of subtracting gives \(260\pi\). Forgetting to take out the hole gives the large circle's area, \(196\pi\).)