Simplify the following expressions: a) 6 - 4 + 3, b) 15 - 4 imes 2, c) 10 + 16 / 8, d) 7 x 2 + (8 - 3). And a) (-45 / (3 - 12)) + 6, b) 20 - 5 x 2 + (-21) / 3.

Here are the solutions to the practice problems:

1. Simplify.

• a) $6 - 4 + 3$

  Step 1: Perform subtraction from left to right.

  $$6 - 4 = 2$$

  Step 2: Perform addition.

  $$2 + 3 = 5$$

  The simplified expression is $\boxed{\text{5}}$.

• b) $15 - 4 \times 2$

  Step 1: Perform multiplication.

  $$4 \times 2 = 8$$

  Step 2: Perform subtraction.

  $$15 - 8 = 7$$

  The simplified expression is $\boxed{\text{7}}$.

• c) $10 + 16 \div 8$

  Step 1: Perform division.

  $$16 \div 8 = 2$$

  Step 2: Perform addition.

  $$10 + 2 = 12$$

  The simplified expression is $\boxed{\text{12}}$.

• d) $7 \times 2 + (8 - 3)$

  Step 1: Perform the operation inside the parentheses.

  $$8 - 3 = 5$$

  Step 2: Perform multiplication.

  $$7 \times 2 = 14$$

  Step 3: Perform addition.

  $$14 + 5 = 19$$

  The simplified expression is $\boxed{\text{19}}$.

2. Simplify.

• a) $(-45 \div (3 - 12)) + 6$

  Step 1: Perform the operation inside the innermost parentheses.

  $$3 - 12 = -9$$

  Step 2: Perform division.

  $$-45 \div (-9) = 5$$

  Step 3: Perform addition.

  $$5 + 6 = 11$$

  The simplified expression is $\boxed{\text{11}}$.

• b) $20 - 5 \times 2 + (-21) \div 3$

  Step 1: Perform multiplication.

  $$5 \times 2 = 10$$

  Step 2: Perform division.

  $$(-21) \div 3 = -7$$

  Step 3: Rewrite the expression with the results.

  $$20 - 10 + (-7)$$

  Step 4: Perform subtraction from left to right.

  $$20 - 10 = 10$$

  Step 5: Perform addition.

  $$10 + (-7) = 3$$

  The simplified expression is $\boxed{\text{3}}$.

• c) $-4 \times [1 - (10 - 13)]$

  Step 1: Perform the operation inside the innermost parentheses.

  $$10 - 13 = -3$$

  Step 2: Substitute the result back into the brackets.

  $$-4 \times [1 - (-3)]$$

  Step 3: Simplify inside the brackets.

  $$1 - (-3) = 1 + 3 = 4$$

  Step 4: Perform multiplication.

  $$-4 \times 4 = -16$$

  The simplified expression is $\boxed{\text{-16}}$.

• d) $20 - \{32 \div (16 \div 1 + 3)\} \div 2 + (-10)$

  Step 1: Perform the innermost division.

  $$16 \div 1 = 16$$

  Step 2: Perform the addition inside the parentheses.

  $$16 + 3 = 19$$

  Step 3: Perform the division inside the curly braces.

  $$32 \div 19 = \frac{32}{19}$$

  Step 4: Rewrite the expression.

  $$20 - \frac{32}{19} \div 2 + (-10)$$

  Step 5: Perform the division.

  $$\frac{32}{19} \div 2 = \frac{32}{19} \times \frac{1}{2} = \frac{16}{19}$$

  Step 6: Rewrite the expression.

  $$20 - \frac{16}{19} - 10$$

  Step 7: Perform subtraction from left to right.

  $$20 - \frac{16}{19} = \frac{380}{19} - \frac{16}{19} = \frac{364}{19}$$

  Step 8: Perform the final subtraction.

  $$\frac{364}{19} - 10 = \frac{364}{19} - \frac{190}{19} = \frac{174}{19}$$

  The simplified expression is $\boxed{\frac{174}{19}}$.

• e) $(80 + 16) \div 8 \times 9 + (-10)$

  Step 1: Perform the operation inside the parentheses.

  $$80 + 16 = 96$$

  Step 2: Rewrite the expression.

  $$96 \div 8 \times 9 + (-10)$$

  Step 3: Perform division from left to right.

  $$96 \div 8 = 12$$

  Step 4: Perform multiplication.

  $$12 \times 9 = 108$$

  Step 5: Perform addition.

  $$$$