Division with four digit numbers.

Standard: 4.NBT.B.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Learning Outcomes

Students will be able to understand division as the process of splitting a number into equal parts.
Students will be able to understand that division “undoes” multiplication (e.g., if $18 \div 3 = 6$ ).
Students will use multiplication facts to solve and check division problems accurately.
Students will solve division problems involving simple numbers, especially dividing by 4.
Students will use division to solve practical, real-world problems, such as distributing items among groups or people.

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Division concept:

The division is one of the four basic arithmetic operations. It involves splitting a number (called the dividend) into equal parts, each containing a specified quantity (divisor). The result is called the quotient.

In simple terms, division answers the question,

How many times can one number fit into another?

For example, if you have 12 candies and want to split them equally among 3 friends, each friend would get 4 because .

Division Facts:

Division as the Opposite of Multiplication: Division "undoes" multiplication. For instance, since , it follows that .
Division by 1: Any number divided by 1 remains the same (e.g., ).
Division by Itself: Any number divided by itself is 1 (e.g., ), as long as the number is not zero.
Division by 0: Division by 0 is undefined, as it doesn’t result in a meaningful answer.

Example 1:

Divide: $4,824\div8$

Solution:

8 cannot fit into 4, so take the first two digits (48).
- Divide the first digit ( $4$ ) by $8$ :
- 48÷8=6 Write $6$ in the quotient.
Multiply $6\times8=48$ and subtract: 48−48=0
Bring down the next digit (2):
- $2\div8=0 Write$ $0$ in the quotient.
Bring down the last digit (4):
- $4\div8=0$ with a remainder of $4$ .

Answer: $4,824\div8=603$

Example 2:

Divide .

Solution:

Divide the first digit ( $7$ ) by $6$ : Write 1 in the quotient.
Bring down the next digit ( $5$ ) to make 15: Write in the quotient.
Bring down the next digit ( $3$ ) to make 33: $.$ Write in the quotient.
Bring down the last digit ( $6$ ) to make $6$ : Write in the quotient.

Answer:

Example 3:

Divide

Solution:

Divide the first digit ( $9$ ) by 4: $.$ Write in the quotient.
Bring down the next digit ( $6$ ) to make $6$ : Write in the quotient.
Bring down the next digit ( $4$ ): Write in the quotient.
Bring down the last digit (): Write in the quotient.

Answer:

Dividing by 4 helps students understand equal sharing and grouping, which is essential for everyday problem-solving. These skills are crucial for understanding fractions, ratios, and more complex math concepts. Mastering division enhances logical reasoning and builds a foundation for advanced arithmetic operations.

By practicing division, you can solve real-world problems quickly! Let’s practice and evaluate your work together by division.