Solve 25 + 45/9: Mixed Operations with Whole Numbers and Fractions

Order of Operations with Fraction Division

25+459=? 25+\frac{45}{9}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Multiplication and division precede addition and subtraction, so we'll start with them
00:08 Let's reduce the fraction
00:10 We're left with a simple addition exercise
00:12 That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

25+459=? 25+\frac{45}{9}=\text{?}

2

Step-by-step solution

According to the order of operations, first we'll solve the fraction:

459=5 \frac{45}{9}=5

25+5=30 25+5=30

3

Final Answer

30 30

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always perform division before addition in mixed operations
  • Technique: First calculate 459=5 \frac{45}{9} = 5 , then add to whole number
  • Check: Verify: 459=5 \frac{45}{9} = 5 and 25+5=30 25 + 5 = 30

Common Mistakes

Avoid these frequent errors
  • Adding before dividing the fraction
    Don't add 25 + 45 = 70, then divide by 9 = 7.78! This ignores the order of operations and gives completely wrong results. Always calculate the fraction 459 \frac{45}{9} first, then add to the whole number.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( 12+3\cdot0= \)

FAQ

Everything you need to know about this question

Why can't I just add 25 + 45 first?

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Because of the order of operations (PEMDAS/BODMAS)! Division comes before addition, so you must calculate 459 \frac{45}{9} first, then add the result to 25.

How do I know when to simplify fractions?

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Always check if the numerator divides evenly by the denominator first. Since 45÷9=5 45 ÷ 9 = 5 exactly, this fraction simplifies to a whole number!

What if the fraction doesn't divide evenly?

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Then you would add the decimal form of the fraction to the whole number. For example, 25+469=25+5.11...=30.11... 25 + \frac{46}{9} = 25 + 5.11... = 30.11...

Can I convert 25 to a fraction instead?

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Yes! You could write 2259+459=2709=30 \frac{225}{9} + \frac{45}{9} = \frac{270}{9} = 30 . Both methods work, but converting the fraction to a whole number is usually easier.

How do I check my answer is correct?

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Substitute back: Does 25+459=30 25 + \frac{45}{9} = 30 ? Yes, because 25+5=30 25 + 5 = 30

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