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

Complex Fractions with Order of Operations

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:05 Rewrite the fraction as a division expression
00:14 Use long addition in order to calculate
00:20 This is the calculation for the numerator
00:23 Use long addition again and calculate the denominator
00:27 This is the calculation for the first operation denominator
00:35 This is the calculation for the denominator
00:40 Let's continue to solve the problem
00:43 Dividing by 100 means moving the decimal point twice to the left
00:46 Here is the solution

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}}=\text{ ?}

2

Step-by-step solution

First let's work out the numerator of the fraction:

0.18+0.37=0.55 0.18+0.37=0.55

Now we can work out the denominator of the fraction, starting with the division exercise below:

21=2 \frac{2}{1}=2

This gives us the following:

89+132= 89+13-2=

Then we can solve from left to right:

89+13=102 89+13=102

1022=100 102-2=100

This gives us the following:

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

We will then move the decimal point two places to the left—due to the two zeros of 100—to get the answer:

0.0055 0.0055

3

Final Answer

0.0055

Key Points to Remember

Essential concepts to master this topic
  • Order: Calculate numerator and denominator separately first before dividing
  • Technique: Denominator: 89 + 13 - 2/1 = 102 - 2 = 100
  • Check: Final division 0.55 ÷ 100 = 0.0055 when decimal moves left ✓

Common Mistakes

Avoid these frequent errors
  • Dividing before simplifying numerator and denominator
    Don't divide 0.18 by 89 first = confusing mess! This ignores proper order of operations and makes the problem much harder. Always simplify the top and bottom completely before dividing the entire fraction.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I need to calculate 2/1 separately first?

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Even though 21=2 \frac{2}{1} = 2 seems obvious, you must follow order of operations! Division happens before addition/subtraction, so calculate this fraction first.

How do I divide a decimal by 100 quickly?

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Move the decimal point two places to the left! Since 100 has two zeros, 0.55 ÷ 100 becomes 0.0055. This is much faster than long division.

What if I get a different answer for the denominator?

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Double-check your order of operations! Remember: first calculate 21=2 \frac{2}{1} = 2 , then do 89+13=102 89 + 13 = 102 , finally 1022=100 102 - 2 = 100 .

Can I use a calculator for this problem?

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Yes, but be careful with parentheses! Enter it as (0.18 + 0.37) ÷ (89 + 13 - 2) to ensure the calculator follows proper grouping.

Why is my answer 0.55 instead of 0.0055?

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You forgot to divide! 0.55 0.55 is just the numerator. You still need to divide by the denominator: 0.55100=0.0055 \frac{0.55}{100} = 0.0055 .

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