Mixed Operations: Whole Numbers

Grade 5 Math – Notes & Formulae for All Operations

Addition

• Add digits from right (ones) to left, carrying over when sum ≥ 10.
• Formula: \( \text{Sum} = a + b \)
• Word clue: Total, sum, in all.
• Example: \( 482 + 379 = 861 \)

Subtraction

• Subtract digits right to left, borrow (regroup) if needed.
• Formula: \( \text{Difference} = a - b \)
• Word clue: Difference, less, minus, left.
• Example: \( 726 - 438 = 288 \)

Multiplication

• Multiply digits, regroup as needed. Sum partial products.
• Formula: \( \text{Product} = a \times b \)
• Word clue: Times, product, area, double/triple.
• Example: \( 36 \times 42 = 1,512 \)

Division

• Divide, multiply, subtract, bring down digits (long division). Remainders if any.
• Formula: \( \text{Quotient} = a \div b \)
• Word clue: Divide, split, share, each, per, quotient, remainder.
• Example: \( 1,368 \div 24 = 57 \)

Mixed Operations Word Problems

• Read and underline keywords for operations (see above clues).
• Follow the order: Parentheses → Multiplication/Division → Addition/Subtraction (PEMDAS/BODMAS).
• Estimate to check reasonableness.
• Show working steps; label your answer.
• Example: A school has 125 students in each class, and there are 8 classes. How many students?
  \( 125 \times 8 = 1,000 \)
• Multi-step: Arun buys 3 packs of 12 pencils each, then gives away 7. How many left?
  \(3 \times 12 = 36,\, 36 - 7 = 29\) pencils.

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