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

Question

1(4137:226131374)=? 1-(4\cdot13\cdot7:\frac{2}{26}-13\cdot13\cdot7\cdot4)=?

Video Solution

Solution Steps

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 Solution

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

  • Step 1: Solve the division inside the parentheses: 7:226 7 : \frac{2}{26} is equivalent to 7×262 7 \times \frac{26}{2} .
  • Step 2: Calculate 262=13 \frac{26}{2} = 13 .
  • Step 3: Thus, 7×13=91 7 \times 13 = 91 .
  • Step 4: Determine the full product expression: 41391 4 \cdot 13 \cdot 91 .
  • Step 5: 413=52 4 \cdot 13 = 52 .
  • Step 6: Therefore, 5291=4732 52 \cdot 91 = 4732 .
  • Step 7: Compute the second product: 131374 13 \cdot 13 \cdot 7 \cdot 4 .
  • Step 8: Begin with 1313=169 13 \cdot 13 = 169 .
  • Step 9: Continue with 1697=1183 169 \cdot 7 = 1183 .
  • Step 10: Finally, 11834=4732 1183 \cdot 4 = 4732 .
  • Step 11: Subtract the two calculated products: 47324732=0 4732 - 4732 = 0 .
  • Step 12: Subtract this result from 1, yielding 10=1 1 - 0 = 1 .

Therefore, the solution to the problem is 1 1 .

Answer

1