Numerical Expressions

Grade 5 Math – Short Notes & Formulae

Write Numerical Expressions

• Numerical expression: Numbers, operators, and grouping symbols (no equals sign).
• Example: "The sum of 5 and 8" → \( 5 + 8 \).
• With two operations: "Twice the sum of 7 and 3" → \( 2 \times (7 + 3) \).

Evaluate Numerical Expressions & Order of Operations

• Order of operations (PEMDAS/BODMAS):
  Parentheses
  Exponents
  Multiplication Division (left-to-right)
  Addition Subtraction (left-to-right)
• Example: \( 6 + 3 \times 4 = 6 + 12 = 18 \) (multiply before add)
• With parentheses: \( (6 + 3) \times 4 = 9 \times 4 = 36 \)
• Brackets [ ] and { } used for extra grouping.

Parentheses and Brackets

• Always solve the innermost parentheses/brackets first.
• Example: \( [8 + (3 \times 2)]^2 \)
  First: \( 3 \times 2 = 6 \), so \( 8 + 6 = 14 \), then \( 14^2 = 196 \)
• Grouping affects answer! Check location of each grouping symbol.

Check for Mistakes (Order of Operations)

• Did you multiply/divide before add/subtract?
• Did you solve inside parentheses first?
• Did you move left-to-right within the same rank (e.g., multiplication and division)?
• Double-check your steps!

Evaluate with Fractions

• Follow the same PEMDAS/BODMAS rules.
• Solve all operations inside numerators and denominators first.
• Example: \( \frac{6+2}{4} = \frac{8}{4} = 2 \)

Missing Operators & Largest Possible Quotient

• Insert +, –, ×, ÷ to match a target value!
• Use mathematical reasoning and estimation to find the best operator(s).
• To maximize a quotient: Make the numerator as large, or denominator as small as possible (but not 0).

Comparison Statements

• Use >, <, = to compare results of two expressions.
• Example: Is \( 4 \times 9 \) > \( 6 \times 5 \)? Yes, 36 > 30.
• Always compute both sides before comparing.