Solve the Fraction Expression: (20-5)/(7+3) Step by Step

Order of Operations with Fraction Simplification

20−57+3= \frac{20-5}{7+3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:04 Calculate the denominator
00:08 Rewrite as a mixed fraction
00:20 Calculate the whole fraction
00:25 Break down 10 into factors 5 and 2
00:31 Reduce wherever possible
00:39 Break down 2 into 1 + 1
00:46 Calculate the subtraction
00:51 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

20−57+3= \frac{20-5}{7+3}=

2

Step-by-step solution

First, let's solve the numerator of the fraction:

20−5=15 20-5=15

Now let's solve the denominator of the fraction:

7+3=10 7+3=10

We get:

1510=1510=112 \frac{15}{10}=1\frac{5}{10}=1\frac{1}{2}

3

Final Answer

112 1\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always solve parentheses first before dividing fractions
  • Technique: Calculate 20-5=15 and 7+3=10, then simplify 15/10
  • Check: Convert to mixed number: 15÷10 = 1 remainder 5 = 1⅕ = 1½ ✓

Common Mistakes

Avoid these frequent errors
  • Trying to subtract and add across the fraction bar
    Don't subtract 20-7 and 5-3 separately = wrong calculation! This ignores the fraction structure and gives incorrect results. Always solve the numerator completely first, then the denominator completely, then divide.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why can't I just work left to right across the fraction?

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The fraction bar acts like parentheses - you must complete all operations above it and below it separately first. Think of it as (20−5)÷(7+3) (20-5) ÷ (7+3) .

How do I know when to convert to a mixed number?

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When your improper fraction (top number bigger than bottom) can be simplified, always convert it. Divide the numerator by denominator: 15÷10=1 15 ÷ 10 = 1 remainder 5 5 , so 1510=1510 \frac{15}{10} = 1\frac{5}{10} .

Do I need to reduce the fractional part too?

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Yes, always simplify! Since 510=12 \frac{5}{10} = \frac{1}{2} (divide both by 5), your final answer is 112 1\frac{1}{2} .

What if I get a decimal instead?

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While 1510=1.5 \frac{15}{10} = 1.5 is correct, the answer choices show mixed numbers and fractions. Always match the format of the given options!

Can I simplify before I divide?

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You could simplify 1510 \frac{15}{10} to 32 \frac{3}{2} first by dividing both by 5, then convert 32=112 \frac{3}{2} = 1\frac{1}{2} . Both methods work!

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