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Operations and Calculations - Short and long division with remainders

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Parts of Division: Dividend (number being divided), Divisor (number you divide by), Quotient (the answer), and Remainder (what is left over).

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Short Division (Bus Stop Method): Used when dividing by a single-digit number. You carry the remainder of each step to the next digit.

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Long Division: Used when dividing by numbers with two or more digits. It involves a repeating cycle: Divide, Multiply, Subtract, and Bring Down.

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Interpreting Remainders: Remainders can be written as a whole number (r), a fraction (Remainder/Divisor), or a decimal.

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Checking Answers: Use inverse multiplication to verify the result.

📐Formulae

Dividend=(Divisor×Quotient)+Remainder\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}

Fractional Remainder=RemainderDivisor\text{Fractional Remainder} = \frac{\text{Remainder}}{\text{Divisor}}

💡Examples

Problem 1:

Calculate 458÷3458 \div 3 using short division.

Solution:

152152 r 22

Explanation:

  1. 3 goes into 4 once, remainder 1. 2. Carry the 1 to make 15; 3 goes into 15 exactly 5 times. 3. 3 goes into 8 twice, remainder 2. Result: 152 remainder 2.

Problem 2:

Calculate 765÷15765 \div 15 using long division.

Solution:

5151

Explanation:

  1. 15 goes into 76 five times (15×5=7515 \times 5 = 75). 2. Subtract 75 from 76 to get 1. 3. Bring down the 5 to make 15. 4. 15 goes into 15 exactly once. Final answer is 51.

Problem 3:

Divide 25÷425 \div 4 and express the remainder as a fraction.

Solution:

6146 \frac{1}{4}

Explanation:

4 goes into 25 six times (4×6=244 \times 6 = 24). The remainder is 25−24=125 - 24 = 1. To write as a fraction, place the remainder over the divisor: 1/41/4.