Calculations - Division of 4-digit numbers by 1-digit numbers (including remainders)

Grade 4IGCSE

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

🔑Concepts

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Place Value: Understanding that a 4-digit number consists of Thousands, Hundreds, Tens, and Ones.

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The 'Bus Stop' Method: The formal written method for short division where the divisor sits outside the 'bus stop' and the dividend sits inside.

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Dividend, Divisor, and Quotient: Knowing that the Dividend is the number being divided, the Divisor is the number you divide by, and the Quotient is the result.

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Remainders: Understanding that a remainder (R) is the amount left over when a number cannot be divided equally.

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Interpreting Zero: Learning how to place a zero in the quotient when the divisor cannot go into a specific digit of the dividend.

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Inverse Operations: Using multiplication to check the answer (Divisor \times Quotient + Remainder = Dividend).

📐Formulae

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

\text{Short Division Structure: } \text{Divisor} \overline{) \text{Dividend}}

💡Examples

Problem 1:

4,852 \div 4

Solution:

1,213

Explanation:

Divide each place value: 4 into 4 is 1. 4 into 8 is 2. 4 into 5 is 1 with a remainder of 1. Carry the 1 to the next digit to make 12. 4 into 12 is 3. Result: 1,213.

Problem 2:

7,341

Solution:

1,223 \text{ R } 3

Explanation:

6 goes into 7 once (R1). Carry 1 to make 13. 6 goes into 13 twice (R1). Carry 1 to make 14. 6 goes into 14 twice (R2). Carry 2 to make 21. 6 goes into 21 three times (18), leaving a remainder of 3.

Problem 3:

5,029 \div 5

Solution:

1,005 \text{ R } 4

Explanation:

5 into 5 is 1. 5 into 0 is 0. 5 into 2 is 0 (carry the 2). 5 into 29 is 5 with a remainder of 4. It is important to place the zeros in the quotient to maintain correct place value.