Question

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

Answer 1

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:
\[
\boxed{-1}
\]