Calculate each of the following without using a calculator.show all calculations.

1.1.1.(69273-6398)+(1701÷63)
1.1.2.256+27³
1.1.3.2×3+2-3×5+1+1×4+1

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
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Let's go through each of the calculations step by step.

1.1.1. Calculate \( (69273 - 6398) + (1701 \div 63) \)

Step 1: Calculate \( 69273 - 6398 \)

\[ 69273 - 6398 = 62875 \]

Step 2: Calculate \( 1701 \div 63 \)

To perform this division, we can break it down:

  • \( 63 \times 10 = 630 \) (which is close to \( 1701 \))
  • \( 63 \times 25 = 1575 \) (to determine how many times 63 fits into 1701)

Continuing: \[ 1701 - 1575 = 126 \] \[ 63 \times 2 = 126 \] So, \( 1701 \div 63 = 27 \).

Step 3: Add the results from Step 1 and Step 2 \[ 62875 + 27 = 62898 \]

Final Result for 1.1.1:

\[ \boxed{62898} \]


1.1.2. Calculate \( 256 + 27^3 \)

Step 1: Calculate \( 27^3 \)

We can calculate \( 27^3 \) as follows: \[ 27^3 = 27 \times 27 \times 27 \] First calculate \( 27 \times 27 \): \[ 27 \times 27 = 729 \] Now calculate: \[ 27 \times 729 \] We can break this down as: \[ 27 \times 700 + 27 \times 29 = 18900 + 783 = 19683 \]

Step 2: Add \( 256 + 19683 \) \[ 256 + 19683 = 19939 \]

Final Result for 1.1.2:

\[ \boxed{19939} \]


1.1.3. Calculate \( 2 \times 3 + 2 - 3 \times 5 + 1 + 1 \times 4 + 1 \)

Step 1: Perform multiplication first according to the order of operations (PEMDAS/BODMAS)

Calculating each part: \[ 2 \times 3 = 6 \] \[ 3 \times 5 = 15 \] \[ 1 \times 4 = 4 \]

Now substitute back into the equation: \[ 6 + 2 - 15 + 1 + 4 + 1 \]

Step 2: Carry out the addition and subtraction from left to right: \[ 6 + 2 = 8 \] \[ 8 - 15 = -7 \] \[ -7 + 1 = -6 \] \[ -6 + 4 = -2 \] \[ -2 + 1 = -1 \]

Final Result for 1.1.3:

\[ \boxed{-1} \]