Evaluate the Fraction Expression: (20-5)/(7+3)

Order of Operations with Mixed Numbers

20−57+3= \frac{20-5}{7+3}=

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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

Let's write the exercise in a different form:

(20−5):(7+3)= (20-5):(7+3)=

According to the order of operations in arithmetic, we'll first solve the expressions in parentheses:

20−5=15 20-5=15

7+3=10 7+3=10

Now we'll get the exercise:

15:10= 15:10=

Let's write the exercise as a fraction:

1510 \frac{15}{10}

Let's reduce the numerator and denominator by 10:

1.51=1.5=112 \frac{1.5}{1}=1.5=1\frac{1}{2}

3

Final Answer

112 1\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Always solve parentheses first before dividing
  • Technique: Calculate 20-5=15 and 7+3=10, then divide 15÷10
  • Check: Convert 1510 \frac{15}{10} to 112 1\frac{1}{2} by reducing ✓

Common Mistakes

Avoid these frequent errors
  • Solving the division before parentheses
    Don't calculate 5÷7 first = 0.714... and then subtract from 20! This ignores order of operations and gives a completely wrong answer. Always solve expressions in parentheses before doing any other operations.

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 work left to right?

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Mathematical expressions must follow the order of operations (PEMDAS). Parentheses come first, so you must calculate what's inside them before doing division or any other operation.

How do I convert the improper fraction to a mixed number?

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Divide the numerator by the denominator: 15÷10=1 15 ÷ 10 = 1 remainder 5 5 . Write as 1510 1\frac{5}{10} , then simplify to 112 1\frac{1}{2} .

What does the colon (:) mean in math?

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The colon (:) means division, just like the division sign (÷) or fraction bar. So 15:10 15:10 is the same as 15÷10 15 ÷ 10 or 1510 \frac{15}{10} .

Do I need to reduce fractions to lowest terms?

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Yes! Always simplify fractions by dividing both numerator and denominator by their greatest common factor. Here, 1510=32=112 \frac{15}{10} = \frac{3}{2} = 1\frac{1}{2} .

Can I use a calculator for this problem?

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While calculators help verify answers, practice doing these by hand first. Understanding the steps builds your math foundation and helps you catch calculation errors!

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