Solved Examples: Evaluating Algebraic Expressions with Integers and Decimals

📚 Quick Study Guide

• 🔢 Order of Operations (PEMDAS/BODMAS): Remember the order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
• ➕ Integer Rules: When adding integers with the same sign, add their absolute values and keep the sign. When adding integers with different signs, subtract their absolute values and use the sign of the larger absolute value.
• ➖ Subtracting Integers: To subtract an integer, add its opposite. For example, $a - b = a + (-b)$.
• ✖️ Multiplying/Dividing Integers: The product or quotient of two integers with the same sign is positive. The product or quotient of two integers with different signs is negative.
• ➗ Decimal Operations: Align decimal points when adding or subtracting decimals. Multiply decimals as usual, then count the total number of decimal places in the factors and place the decimal point in the product accordingly. For division, make the divisor a whole number by moving the decimal point, and move the decimal point in the dividend the same number of places.
• 💡 Substitution: Replace variables in an algebraic expression with their given values. Be careful with signs!
• 📝 Simplifying: After substituting, simplify the expression using the order of operations.

Practice Quiz

1. Evaluate the expression $3x - 2y$ when $x = -2$ and $y = 1.5$.
   1. -9
   2. -3
   3. 3
   4. 9
2. Simplify: $4.2 + a - 7.5$ when $a = -3.3$
   1. -6.6
   2. 6.6
   3. 15
   4. -15
3. Evaluate: $-2(p + q)$ where $p = -4$ and $q = 2$.
   1. -12
   2. 12
   3. 4
   4. -4
4. What is the value of the expression $5m + \frac{n}{2}$ when $m = 3$ and $n = -8$?
   1. 11
   2. 19
   3. -11
   4. -19
5. If $a = -1.5$ and $b = 2$, what is the value of $a^2 + b$?
   1. -0.25
   2. 0.25
   3. 4.25
   4. -4.25
6. Evaluate $x(y - z)$ when $x = -2$, $y = 5$, and $z = -3$.
   1. -16
   2. 16
   3. -4
   4. 4
7. What is the value of $|-3a + 2b|$ when $a = -2$ and $b = -1$?
   1. -8
   2. 8
   3. 4
   4. -4