Solve '75 - 54 ÷ 3 + 9': Order of Operations Practice

Q: Why can't I just work from left to right like reading?

Mathematics has special rules called the order of operations (PEMDAS) that override left-to-right reading. Division and multiplication are stronger operations that must be done first, just like in real-world situations.

Q: How do I remember to do division before subtraction?

Think of division as grouping things together first. In $ 75 - 54 ÷ 3 + 9 $, you must figure out what $ 54 ÷ 3 $ equals before you can subtract it from 75!

Q: What if I get a different answer than the choices?

Double-check your order of operations! The most common error is working left to right. Write out each step clearly: first $ 54 ÷ 3 = 18 $, then $ 75 - 18 + 9 $.

Q: Is there an easy way to avoid mistakes?

Yes! Underline or circle the multiplication and division operations first. Do those calculations, then rewrite the expression with your answers before doing addition and subtraction left to right.

Order of Operations with Mixed Arithmetic

Calculate the following expression:

$75 - 54 \div 3 + 9$

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Understand the problem

Calculate the following expression:

$75 - 54 \div 3 + 9$

Step-by-step solution

First, perform the division: $54 \div 3 = 18$ .

Next, perform the subtraction: $75 - 18 = 57$

Finally, perform the addition: $57 + 9 = 66$

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Division comes before subtraction and addition
Technique: Calculate $54 ÷ 3 = 18$ first, then left to right
Check: Verify each step: 75 - 18 + 9 = 57 + 9 = 66 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't calculate 75 - 54 = 21 first, then 21 ÷ 3 + 9 = 16! This ignores the rule that division must be done before subtraction. Always perform division first, then work left to right for addition and subtraction.

Practice Quiz

Test your knowledge with interactive questions

$8 + 3 \times 2 =$

FAQ

Everything you need to know about this question

Why can't I just work from left to right like reading?

Mathematics has special rules called the order of operations (PEMDAS) that override left-to-right reading. Division and multiplication are stronger operations that must be done first, just like in real-world situations.

What does PEMDAS stand for again?

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Remember: MD and AS have equal priority within their groups!

How do I remember to do division before subtraction?

Think of division as grouping things together first. In $75 - 54 ÷ 3 + 9$ , you must figure out what $54 ÷ 3$ equals before you can subtract it from 75!

What if I get a different answer than the choices?

Double-check your order of operations! The most common error is working left to right. Write out each step clearly: first $54 ÷ 3 = 18$ , then $75 - 18 + 9$ .

Is there an easy way to avoid mistakes?

Yes! Underline or circle the multiplication and division operations first. Do those calculations, then rewrite the expression with your answers before doing addition and subtraction left to right.

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