SSAT Upper Level

Order of Operations

Evaluating expressions using PEMDAS — includes custom operation symbol problems (e.g., a◆b = a − 3b)

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Imagine trying to build a giant LEGO spaceship, but you decide to put the roof on before building the walls. Crash! Disaster! 🚀 Math is exactly the same way. If you try to solve a math problem in the wrong order, the whole thing falls apart. That’s why we have the Order of Operations!

Think of the Order of Operations like a recipe for baking the perfect math pizza. 🍕 If you put the cheese in the box, then bake the dough, then throw sauce on top... yuck! You have to follow the steps in the exact right order. In math, our recipe is called PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

On the SSAT, the test-makers love to try and trick you by giving you a long string of numbers and hoping you just read it left-to-right like a regular book. But you know better! You'll hunt down those parentheses first, blast the exponents, and then tackle the rest.

Sometimes, the SSAT will even invent funny, made-up symbols like a diamond or a star. Don't panic! 🎮 These are just custom recipes. They will tell you exactly what the symbol means, and all you have to do is plug your numbers into their secret formula, following PEMDAS of course. You've got this!

Key Formula

PEMDAS: Parentheses \to Exponents \to Multiply/Divide (left to right) \to Add/Subtract (left to right)

Practice Questions

4 practice questions for SSAT Upper Level

Q1 Hard

What is the value of

12 + 18 \div 3 - 4 \times 2

A 2

B 8

C 10

D 12

E 22

Show Solution

According to the order of operations (PEMDAS/BODMAS), perform multiplication and division from left to right before addition and subtraction.

First, evaluate $18 \div 3 = 6$ and $4 \times 2 = 8$ .
Substitute these values back into the expression: $12 + 6 - 8$ .
Next, perform addition and subtraction from left to right.
$12 + 6 = 18$
$18 - 8 = 10$

Answer: C

Q2 Hard

30 - 2 \times (7 - 4)^{2} + 8 \div 4

Which of the following is the value of the expression above?

A -4

B 10

C 12

D 14

E 254

Show Solution

Follow the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

First, simplify inside the parentheses: $7 - 4 = 3$ .
The expression becomes $30 - 2 \times 3^{2} + 8 \div 4$ .
Next, evaluate the exponent: $3^{2} = 9$ .
The expression becomes $30 - 2 \times 9 + 8 \div 4$ .
Perform multiplication and division from left to right: $2 \times 9 = 18$ and $8 \div 4 = 2$ .
The expression is now $30 - 18 + 2$ .
Finally, perform addition and subtraction from left to right: $30 - 18 = 12$ , and $12 + 2 = 14$ .

Answer: D

Q3 Hard

Simplify:

\frac{36 - 3 \times 4}{2 ^{3} - 2}

A 2

B 4

C 6

D 12

E 22

Show Solution

A fraction bar acts as a grouping symbol, meaning you must simplify the numerator and the denominator completely before dividing.

Numerator: $36 - 3 \times 4$ . Multiply first to get $36 - 12 = 24$ .
Denominator: $2^{3} - 2$ . Evaluate the exponent first to get $8 - 2 = 6$ .
Now substitute the simplified values back into the fraction: $\frac{24}{6}$ .
Divide to find the final answer: $24 \div 6 = 4$ .

Answer: B

Q4 Hard

What is the value of

40 \div 4 \times 2 - 3 (5 - 2)

A 11

B 17

C 20

D 29

E 51

Show Solution

Follow the order of operations.

First, simplify the parentheses: $(5 - 2) = 3$ .
The expression becomes $40 \div 4 \times 2 - 3 (3)$ .
Next, perform all multiplication and division strictly from left to right.
$40 \div 4 = 10$
$10 \times 2 = 20$
And for the second part, $3 \times 3 = 9$ .
The expression is now $20 - 9$ .
Finally, subtract to get $11$ .

Answer: A

Tips & Strategies

Write PEMDAS at the top of your scratch paper as soon as the test starts! Cross off each letter as you finish that step in a long problem. 📝
Multiplication and Division are twins! They happen at the exact same time, from left to right. Same goes for Addition and Subtraction. Don't automatically multiply before dividing if the division sign comes first! 👯‍♀️
For made-up symbol problems (like x ♥ y), underline what $x$ is and what $y$ is before plugging them in. It stops you from putting the numbers in backward! 🔍

Common Mistakes

Watch out for reading math like a book! 📚 Many students just read left to right and would solve $2 + 3 \times 4$ as $5 \times 4 = 20$ . Remember, multiplication cuts in line! It should be $2 + 12 = 14$ .
Don't forget that negative signs belong to the number after them! If you have $10 - 2 \times 3$ , you multiply $2 \times 3$ to get $6$ , making it $10 - 6$ . Be careful not to lose that minus sign! ➖

Frequently Asked Questions

What does PEMDAS stand for?

It stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. A fun way to remember it is 'Please Excuse My Dear Aunt Sally'! 👵

What if a problem has a weird symbol I've never seen, like a smiley face?

Don't worry! The SSAT invents symbols to test if you can follow directions. They will always give you the 'recipe' for the symbol right there in the question. Just plug your numbers in! 😃

Do I always multiply before I divide?

Nope! Multiplication and Division are on the same team. You just solve them from left to right, like reading a sentence. If you see a fraction like $\frac{10}{2}$ , remember that a fraction bar is just a division sign in disguise! ⚖️

How many order of operations questions are on the SSAT?

You'll usually see 2 or 3 of these directly, but PEMDAS is the secret code you need to solve almost every other math question on the test! 🕵️‍♂️

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