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

What is the result of the following equation?

\( 36-4\div2 \)

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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