Solve (0.18 + 0.37)/(89 + 13 - 2/1): Complex Fraction Challenge

Complex Fractions with Mixed Operations

0.18+0.3789+1321= \frac{0.18+0.37}{89+13-\frac{2}{1}}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:11 Any number divided by 1 equals the number itself
00:20 Count each operation one time
00:53 When dividing, for each 0 move the decimal point 1 place to the left
01:05 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

0.18+0.3789+1321= \frac{0.18+0.37}{89+13-\frac{2}{1}}=

2

Step-by-step solution

To solve the expression 0.18+0.3789+1321= \frac{0.18+0.37}{89+13-\frac{2}{1}}= , we need to follow the order of operations carefully.


  • Step 1: Simplify the expression in the numerator: 0.18+0.37 0.18 + 0.37 .


0.18+0.37=0.55 0.18 + 0.37 = 0.55

  • Step 2: Simplify the expression in the denominator. Start by simplifying 21 \frac{2}{1} which is simply 2 2 .

  • Step 3: Continue with the expression: 89+132 89 + 13 - 2 .


89+13=102 89 + 13 = 102
1022=100 102 - 2 = 100

  • Step 4: Substitute the simplified expressions back into the main fraction: 0.55100 \frac{0.55}{100} .


0.55100=0.0055 \frac{0.55}{100} = 0.0055

Thus, the solution to the expression is 0.0055 0.0055 .

3

Final Answer

0.0055

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Simplify numerator and denominator separately first
  • Technique: Calculate 89 + 13 - 2/1 = 102 - 2 = 100
  • Check: Verify 0.55 ÷ 100 = 0.0055 by multiplying back ✓

Common Mistakes

Avoid these frequent errors
  • Adding before simplifying the fraction 2/1
    Don't calculate 89 + 13 - 2/1 as (89 + 13 - 2)/1 = 100/1! This changes the expression structure and gives 0.55/100 = 0.0055 instead of the wrong 0.55/1 = 0.55. Always simplify 2/1 = 2 first, then perform 89 + 13 - 2 = 100.

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FAQ

Everything you need to know about this question

Why do I simplify 2/1 to 2 first?

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Any number divided by 1 equals itself! So 21=2 \frac{2}{1} = 2 . This simplification must happen before doing addition and subtraction in the denominator.

Do I add the decimals in the numerator first?

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Yes! Always simplify the numerator and denominator separately before dividing. So calculate 0.18 + 0.37 = 0.55, then work on the denominator: 89 + 13 - 2 = 100.

How do I divide 0.55 by 100?

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When dividing a decimal by 100, move the decimal point two places to the left. So 0.55 ÷ 100 = 0.0055.

Can I use a calculator for this problem?

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Absolutely! Just make sure to follow the order of operations. Calculate the top (0.18 + 0.37), then the bottom (89 + 13 - 2), then divide the results.

What if I get a different decimal answer?

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Double-check your arithmetic! The most common errors are: forgetting that 21=2 \frac{2}{1} = 2 , or making calculation mistakes in 89 + 13 - 2 = 100.

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