Solve Mixed Number Expression: 5 40/200 Step-by-Step

Mixed Number Conversion with Fraction Simplification

540200= 5\frac{40}{200}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Convert to decimal fraction
00:03 Break down the number into whole number and fraction
00:07 We want the denominator to be some multiple of 10
00:13 Reduce the fraction, make sure to divide both numerator and denominator
00:25 Convert from fraction to decimal fraction
00:35 Add
00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

540200= 5\frac{40}{200}=

2

Step-by-step solution

To solve 540200 5\frac{40}{200} , we will simplify the fraction first and convert it to a decimal:

Step 1: Simplify the fraction 40200 \frac{40}{200} .

The greatest common divisor (GCD) of 40 and 200 is 40.

Divide the numerator and the denominator by 40:

  • 40÷40200÷40=15 \frac{40 \div 40}{200 \div 40} = \frac{1}{5} .

Step 2: Convert 15 \frac{1}{5} to a decimal.

To convert 15 \frac{1}{5} to a decimal, divide 1 by 5, which gives 0.2.

Step 3: Calculate 5+0.2 5 + 0.2 .

5+0.2=5.2 5 + 0.2 = 5.2 .

Thus, the solution to the problem is 5.2 5.2 .

3

Final Answer

5.2 5.2

Key Points to Remember

Essential concepts to master this topic
  • Simplify First: Find GCD to reduce fraction before converting
  • Technique: 40200=15=0.2 \frac{40}{200} = \frac{1}{5} = 0.2 using GCD of 40
  • Check: Verify 5+15=5.2 5 + \frac{1}{5} = 5.2 by adding whole and fractional parts ✓

Common Mistakes

Avoid these frequent errors
  • Converting fraction to decimal without simplifying first
    Don't divide 40 ÷ 200 directly = 0.2 but harder calculation! Working with large numbers increases error risk and makes division more difficult. Always find the GCD and simplify the fraction first to make conversion easier and more accurate.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

\( \frac{5}{100}= \)

FAQ

Everything you need to know about this question

Why do I need to simplify the fraction before converting?

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Simplifying makes the conversion much easier! Dividing 1 ÷ 5 is simpler than 40 ÷ 200, and you're less likely to make calculation errors with smaller numbers.

How do I find the GCD of 40 and 200?

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List factors or use division: 40 = 2³ × 5 and 200 = 2³ × 5². The GCD is 2³ × 5 = 40. You can also divide: 200 ÷ 40 = 5 exactly, so 40 is the GCD!

Can I just use a calculator to divide 40 by 200?

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Yes, but understanding the simplification helps you recognize patterns! Plus, 15 \frac{1}{5} is easier to work with in future problems than the decimal 0.2.

What if the fraction doesn't simplify to a nice decimal?

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Some fractions like 13 \frac{1}{3} give repeating decimals (0.333...). In those cases, you can leave the answer as a mixed number or use decimal approximation as needed.

How do I add the whole number and decimal parts?

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Simply add them together: 5 + 0.2 = 5.2. Think of it as 5.0 + 0.2 = 5.2. The whole number becomes the digits before the decimal point.

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