Calculate the following without the use of a calculator 1.1-3-(-2)(5)-(-4)raised by 3 1.2 50mutiple by 33 plus 25mutiple 50 out of 10 multiple 50 plus50 multiple 19 1.3 3raised by 3-(-square root 4)raised by 2 plus-(4) out of-4 multiple 4 plus 1 plus 17

4.1.1

Interpret as $-3 - (-2)(5) - (-4)^3$

Step 1: Exponents first.
$(-4)^3 = (-4) \times (-4) \times (-4)$
$= 16 \times (-4) = -64$

Step 2: Multiplications next.
$(-2)(5) = -10$

Step 3: Substitute values.
$-3 - (-10) - (-64)$

Step 4: Left to right.
$-3 - (-10) = -3 + 10 = 7$
$7 - (-64) = 7 + 64$
$7 + 64 = 71$

71

4.1.2

Interpret as $50 \times 33 + 25 \times \frac{50}{10} \times 50 + 50 \times 19$

Step 1: First term.
$50 \times 33 = 50 \times (30 + 3)$
$50 \times 30 = 1500$
$50 \times 3 = 150$
$1500 + 150 = 1650$

Step 2: Second term, inside parentheses first.
$\frac{50}{10} = 5$
$25 \times 5 = 125$
$125 \times 50 = 125 \times (5 \times 10)$
$125 \times 5 = 625$
$625 \times 10 = 6250$

Step 3: Third term.
$50 \times 19 = 50 \times (20 - 1)$
$50 \times 20 = 1000$
$50 \times 1 = 50$
$1000 - 50 = 950$

Step 4: Add them up.
$1650 + 6250 = 7900$
$7900 + 950 = 8850$

8850

4.1.3

Interpret as $3^3 - (-\sqrt{4})^2 + \left[ -\frac{4}{-4} \times 4 \right] + 1 + 17$

Step 1: Exponents and roots first.
$\sqrt{4} = 2$
$-\sqrt{4} = -2$
$( -2 )^2 = (-2) \times (-2) = 4$
$3^3 = 3 \times 3 \times 3 = 9 \times 3 = 27$

Step 2: Division inside brackets.
$\frac{4}{-4} = -1$
$-\frac{4}{-4} = -(-1) = 1$
$1 \times 4 = 4$

Step 3: Substitute values.
$27 - 4 + 4 + 1 + 17$

Step 4: Left to right.
$27 - 4 = 23$
$23 + 4 = 27$
$27 + 1 = 28$
$28 + 17 = 45$

45