Solve for ?: (45-22)×19+25÷5+?×3=82 Order of Operations

Q: Why do I get the wrong answer when I solve from left to right?

Order of operations matters! You must do multiplication and division before addition and subtraction. Otherwise, you're solving a completely different equation.

Q: What does the colon symbol mean in 25÷5?

The colon (:) means division, just like the ÷ symbol. So $ 25\colon5 = 25÷5 = 5 $.

Q: What if I forget to do parentheses first?

You'll get the wrong answer! Always solve what's in parentheses first: $ (45-22) = 23 $, then multiply by 19.

Q: How can I check if my final answer is correct?

Substitute your answer back into the original equation. If the left side equals 82, you're right! For example: $ 23×19+5+(-120)×3 = 437+5-360 = 82 $ ✓

Order of Operations with Missing Variables

Calculate the missing number in the equation:

$(45-22)\times19+25\colon5+?\times3=82$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's start by focusing on the expression inside the parentheses.

00:30 Next, we do the multiplication and division steps.

00:47 Keep going as we solve the problem step by step.

00:57 Now subtract four hundred forty-two from both sides to isolate the variable.

01:15 Finally, divide both sides by three. And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the missing number in the equation:

$(45-22)\times19+25\colon5+?\times3=82$

Step-by-step solution

We solve the exercise in parentheses:

$23\times19+25\colon5+?\times3=82$

We place the multiplication and division exercises inside parentheses:

$(23\times19)+(25\colon5)+?\times3=82$

We solve the exercise in parentheses:

$437+5+?\times3=82$

We simplify:

$442+?\times3=82$

We swap sections:

$?\times3=82-442$

$?\times3=-360$

We divide by 3

$?=-120$

Final Answer

$?=-120$

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS - parentheses, then multiplication/division left to right
Technique: Calculate (45-22)×19 = 23×19 = 437, then 25÷5 = 5
Check: Substitute ?=-120: 437+5+(-120)×3 = 442-360 = 82 ✓

Common Mistakes

Avoid these frequent errors

Solving left to right without following order of operations
Don't solve 45-22+19×25÷5 from left to right = wrong operations order! This ignores multiplication and division priority, giving completely wrong results. Always follow PEMDAS: parentheses first, then multiplication and division before addition and subtraction.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why do I get the wrong answer when I solve from left to right?

Order of operations matters! You must do multiplication and division before addition and subtraction. Otherwise, you're solving a completely different equation.

What does the colon symbol mean in 25÷5?

The colon (:) means division, just like the ÷ symbol. So $25\colon5 = 25÷5 = 5$ .

How do I isolate the unknown variable ?

After following order of operations, you'll have a simple equation like $?×3 = -360$ . Then just divide both sides by 3 to get $? = -120$ .

Can the answer be negative?

Yes! Negative numbers are perfectly valid answers. In this problem, $? = -120$ because $(-120)×3 = -360$ .

What if I forget to do parentheses first?

You'll get the wrong answer! Always solve what's in parentheses first: $(45-22) = 23$ , then multiply by 19.

How can I check if my final answer is correct?

Substitute your answer back into the original equation. If the left side equals 82, you're right! For example: $23×19+5+(-120)×3 = 437+5-360 = 82$ ✓

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Solve for ?: (45-22)×19+25÷5+?×3=82 Order of Operations

Order of Operations with Missing Variables

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I get the wrong answer when I solve from left to right?

What does the colon symbol mean in 25÷5?

How do I isolate the unknown variable ?

Can the answer be negative?

What if I forget to do parentheses first?

How can I check if my final answer is correct?

🌟 Unlock Your Math Potential

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