Solve Complex Fraction Expression: [(25+3·2)-6]:5 ÷ (4+1) - 76/19

Q: Why do I need to solve the brackets before the division?

The order of operations (PEMDAS) requires you to solve parentheses and brackets first! If you don't, you'll get the wrong numbers to divide and your final answer will be incorrect.

Q: How do I handle the colon symbol in [25]:5?

The colon : symbol means division, just like ÷. So $ 25:5 = 25 ÷ 5 = 5 $. It's commonly used in some countries instead of the division sign.

Q: Do I need to convert everything to the same denominator?

Not necessarily! Since $ \frac{76}{19} = 4 $ is a whole number, you can simply subtract: $ 1 - 4 = -3 $. Always check if fractions simplify to whole numbers first.

Q: What if I get confused by all the brackets and parentheses?

Work from the innermost grouping symbols outward! Start with regular parentheses ( ), then square brackets [ ], solving each completely before moving to the next level.

Q: How can I check if -3 is really the right answer?

Substitute back into each step: $ [(25+6)-6] = 25 $, then $ 25:5 = 5 $, then $ \frac{5}{5} = 1 $, finally $ 1-4 = -3 $ ✓

Complex Fractions with Nested Operations

Complete the following exercise:
$\frac{[(25+3\cdot2)-6]:5}{4+1}-\frac{76}{19}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:02 Always solve the parentheses first

00:05 Multiplication precedes addition

00:22 The parentheses come first

00:30 Continue to solve the expression according to the proper order of operations

00:40 A number divided by itself will always equal 1

00:45 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:
$\frac{[(25+3\cdot2)-6]:5}{4+1}-\frac{76}{19}=$

Step-by-step solution

Let's solve the given expression step-by-step, applying the order of operations, commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
The given expression is:
$\frac{[(25+3\cdot2)-6]:5}{4+1}-\frac{76}{19}$

Step 1: Solve inside the innermost parentheses
We start by solving the expression inside the square brackets $[\cdot]$ :

Simplify: $3\cdot2 = 6$
Add: $25 + 6 = 31$
Subtract: $31 - 6 = 25$

Thus,

[ (25 + 3 \cdot 2) - 6 ] = 25

Step 2: Solve the division inside the fraction
Next, we calculate:

Divide: $25:5 = 5$

Thus, the fraction becomes:

\frac{5}{4+1}

Step 3: Solve the denominator of the fraction

Add: $4 + 1 = 5$

Now the entire fraction simplifies to:

\frac{5}{5} = 1

Step 4: Solve the subtraction
Finally, perform the subtraction:

Subtract: $1 - \frac{76}{19}$

Since

76 \div 19 = 4

, then:

Subtract: $1 - 4 = -3$

Thus, the solution is

-3

The solution to the question is: -3

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always solve parentheses and brackets first before division
Technique: Calculate 25 ÷ 5 = 5, then 5 ÷ 5 = 1 before subtracting
Check: Verify 76 ÷ 19 = 4, so 1 - 4 = -3 ✓

Common Mistakes

Avoid these frequent errors

Ignoring the order of operations in complex fractions
Don't solve from left to right ignoring brackets = wrong answer like -1! This violates PEMDAS and creates calculation errors. Always solve brackets first, then division, then subtraction in the correct sequence.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why do I need to solve the brackets before the division?

The order of operations (PEMDAS) requires you to solve parentheses and brackets first! If you don't, you'll get the wrong numbers to divide and your final answer will be incorrect.

How do I handle the colon symbol in [25]:5?

The colon : symbol means division, just like ÷. So $25:5 = 25 ÷ 5 = 5$ . It's commonly used in some countries instead of the division sign.

Do I need to convert everything to the same denominator?

Not necessarily! Since $\frac{76}{19} = 4$ is a whole number, you can simply subtract: $1 - 4 = -3$ . Always check if fractions simplify to whole numbers first.

What if I get confused by all the brackets and parentheses?

Work from the innermost grouping symbols outward! Start with regular parentheses ( ), then square brackets [ ], solving each completely before moving to the next level.

How can I check if -3 is really the right answer?

Substitute back into each step: $[(25+6)-6] = 25$ , then $25:5 = 5$ , then $\frac{5}{5} = 1$ , finally $1-4 = -3$ ✓

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Solve Complex Fraction Expression: [(25+3·2)-6]:5 ÷ (4+1) - 76/19

Complex Fractions with Nested Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to solve the brackets before the division?

How do I handle the colon symbol in [25]:5?

Do I need to convert everything to the same denominator?

What if I get confused by all the brackets and parentheses?

How can I check if -3 is really the right answer?

🌟 Unlock Your Math Potential

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