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Division - Division of 4-digit numbers by 1 and 2-digit numbers

Grade 4ICSE

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

🔑Concepts

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Terms of Division: In the long division layout, the Dividend is the 4-digit number placed inside the division bracket. The Divisor is the number outside to the left that we are dividing by. The Quotient is the answer written on top of the bracket, and the Remainder is the leftover value found at the very bottom after all subtractions.

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Order of Operations: Division always begins from the highest place value. For a 4-digit number, we start at the thousands place and move towards the right (hundreds, tens, and then ones). Visually, this is like moving a spotlight across the number from left to right.

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Dividing by 2-Digit Numbers: When the divisor has two digits, we first look at the first two digits of the dividend. If the first two digits are smaller than the divisor, we must look at the first three digits to begin our division. Estimation helps here; for example, if dividing by 2121, you can think of it as dividing by 2020 to guess the quotient digit.

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The Place-Holder Zero: If a digit brought down from the dividend makes a number that is still smaller than the divisor, a 00 must be placed in the quotient at that specific place value. Visually, this ensures every digit in the dividend has a corresponding partner in the quotient 'roof' above it.

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The Remainder Rule: The Remainder must always be strictly less than the Divisor (R<DR < D). If your subtraction results in a number equal to or larger than the divisor, it indicates that the digit chosen for the quotient was too small and needs to be increased.

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Division by 10: When a 4-digit number is divided by 1010, the digit in the ones place automatically becomes the Remainder, while the digits in the thousands, hundreds, and tens places form the Quotient. For example, in 5678÷105678 \div 10, the quotient is 567567 and the remainder is 88.

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Verification Strategy: To check if a division is correct, we can use the inverse operation of multiplication. By multiplying the divisor and quotient and adding the remainder, we should arrive back at the original dividend. Visually, this creates a 'circle' of operations that confirms the math is sound.

📐Formulae

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

Remainder<Divisor\text{Remainder} < \text{Divisor}

Quotient≈Dividend÷Divisor\text{Quotient} \approx \text{Dividend} \div \text{Divisor}

💡Examples

Problem 1:

Divide 48524852 by 44 and verify the result.

Solution:

  1. Divide the thousands: 4÷4=14 \div 4 = 1. Write 11 in the thousands place of the quotient.
  2. Divide the hundreds: 8÷4=28 \div 4 = 2. Write 22 in the hundreds place of the quotient.
  3. Divide the tens: 5÷4=15 \div 4 = 1 with a remainder of 11. Write 11 in the tens place.
  4. Bring down the 22 to the remainder 11 to make 1212. Divide the ones: 12÷4=312 \div 4 = 3. Write 33 in the ones place.
  5. Quotient = 12131213, Remainder = 00.
  6. Verification: (4×1213)+0=4852(4 \times 1213) + 0 = 4852.

Explanation:

This is a simple division by a 1-digit number where we process each place value one by one from left to right.

Problem 2:

Divide 25852585 by 1212.

Solution:

  1. Look at the first two digits: 2525. 25÷12=225 \div 12 = 2 (since 12×2=2412 \times 2 = 24).
  2. Subtract: 25−24=125 - 24 = 1. Bring down the 88 to make 1818.
  3. 18÷12=118 \div 12 = 1 (since 12×1=1212 \times 1 = 12).
  4. Subtract: 18−12=618 - 12 = 6. Bring down the 55 to make 6565.
  5. 65÷12=565 \div 12 = 5 (since 12×5=6012 \times 5 = 60).
  6. Subtract: 65−60=565 - 60 = 5.
  7. Quotient = 215215, Remainder = 55.

Explanation:

When dividing by a 2-digit number, we group the dividend digits and use multiplication tables of the divisor (12) to find the closest multiples.