Solve Complex Expression: 1-(4·13·7÷(2/26)-13·13·7·4)

Q: Why do I flip the fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: dividing by $ \frac{2}{26} $ asks "how many $ \frac{2}{26} $ fit into 7?" This equals $ 7 \times \frac{26}{2} $.

Q: How do I handle the colon (:) symbol in math?

The colon (:) is another way to write division. So $ 7 : \frac{2}{26} $ means exactly the same as $ 7 ÷ \frac{2}{26} $. Use whichever symbol you prefer!

Q: Why do both parts of the expression equal 4732?

This isn't a coincidence! The expression is designed so that $ 4 \cdot 13 \cdot 7 : \frac{2}{26} $ and $ 13 \cdot 13 \cdot 7 \cdot 4 $ give the same result, making their difference zero.

Q: What's the correct order of operations here?

Follow PEMDAS/BODMAS: First handle the division by fraction inside parentheses, then multiply from left to right, subtract the products, and finally subtract from 1.

Q: How can I check if 52 × 91 really equals 4732?

$ 52 \times 91 = 52 \times (90 + 1) = 52 \times 90 + 52 \times 1 $$ = 4680 + 52 = 4732 $ ✓

Order of Operations with Division by Fractions

$1-(4\cdot13\cdot7:\frac{2}{26}-13\cdot13\cdot7\cdot4)=?$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:07 Let's break down 26 into factors 13 and 2

00:25 Let's reduce what we can

00:31 Division is also multiplication by the reciprocal

00:50 Let's reduce what we can

00:53 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1-(4\cdot13\cdot7:\frac{2}{26}-13\cdot13\cdot7\cdot4)=?$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Solve the division inside the parentheses: $7 : \frac{2}{26}$ is equivalent to $7 \times \frac{26}{2}$ .
Step 2: Calculate $\frac{26}{2} = 13$ .
Step 3: Thus, $7 \times 13 = 91$ .
Step 4: Determine the full product expression: $4 \cdot 13 \cdot 91$ .
Step 5: $4 \cdot 13 = 52$ .
Step 6: Therefore, $52 \cdot 91 = 4732$ .
Step 7: Compute the second product: $13 \cdot 13 \cdot 7 \cdot 4$ .
Step 8: Begin with $13 \cdot 13 = 169$ .
Step 9: Continue with $169 \cdot 7 = 1183$ .
Step 10: Finally, $1183 \cdot 4 = 4732$ .
Step 11: Subtract the two calculated products: $4732 - 4732 = 0$ .
Step 12: Subtract this result from 1, yielding $1 - 0 = 1$ .

Therefore, the solution to the problem is $1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Division by fraction equals multiplication by its reciprocal
Technique: Convert $7 : \frac{2}{26}$ to $7 \times \frac{26}{2} = 91$
Check: Both products equal 4732, so 4732 - 4732 = 0, then 1 - 0 = 1 ✓

Common Mistakes

Avoid these frequent errors

Treating division by fraction as regular division
Don't divide 7 by 2/26 using regular division = wrong result of 0.27! Division by a fraction means multiply by its reciprocal. Always flip the fraction and multiply: 7 ÷ (2/26) = 7 × (26/2) = 91.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I flip the fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: dividing by $\frac{2}{26}$ asks "how many $\frac{2}{26}$ fit into 7?" This equals $7 \times \frac{26}{2}$ .

How do I handle the colon (:) symbol in math?

The colon (:) is another way to write division. So $7 : \frac{2}{26}$ means exactly the same as $7 ÷ \frac{2}{26}$ . Use whichever symbol you prefer!

Why do both parts of the expression equal 4732?

This isn't a coincidence! The expression is designed so that $4 \cdot 13 \cdot 7 : \frac{2}{26}$ and $13 \cdot 13 \cdot 7 \cdot 4$ give the same result, making their difference zero.

What's the correct order of operations here?

Follow PEMDAS/BODMAS: First handle the division by fraction inside parentheses, then multiply from left to right, subtract the products, and finally subtract from 1.

How can I check if 52 × 91 really equals 4732?

$52 \times 91 = 52 \times (90 + 1) = 52 \times 90 + 52 \times 1$
$= 4680 + 52 = 4732$ ✓

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