Dividing Multi-Digit Numbers (No Remainder)
Dividing Multi-Digit Numbers (No Remainder) is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 1: Numerical Expressions and Factors. Students apply the long division algorithm to divide multi-digit numbers cleanly, using the repeating cycle of divide-multiply-subtract-bring down until the remainder is zero. The relationship: Dividend ÷ Divisor = Quotient. Examples: 168 ÷ 7 = 24; 2184 ÷ 42 = 52. Fluency with long division is foundational for fraction simplification, polynomial division, and all higher-level arithmetic.
Key Concepts
Property Division is the process of finding how many times a number (the divisor) is contained within another number (the dividend). The result is called the quotient. $$ \text{Dividend} \div \text{Divisor} = \text{Quotient} $$.
Examples To calculate $168 \div 7$: $$\begin{array}{r} 24 \\ 7 \overline{) 168} \\ 14\phantom{0} \\ \hline 28 \\ 28 \\ \hline 0 \end{array}$$ The quotient is $24$. To calculate $2184 \div 42$: $$\begin{array}{r} 52 \\ 42 \overline{) 2184} \\ 210\phantom{0} \\ \hline 84 \\ 84 \\ \hline 0 \end{array}$$ The quotient is $52$.
Explanation Division is the inverse operation of multiplication and is used to split a whole into equal parts. Long division is a standard algorithm used to solve division problems with multi digit numbers. The process involves a repeating cycle of steps: divide, multiply, subtract, and bring down the next digit from the dividend. In these examples, the final subtraction results in zero, indicating there is no remainder.
Common Questions
How do you do long division step by step?
Step 1: Divide — how many times does the divisor go into the current group of digits? Step 2: Multiply — multiply that estimate by the divisor. Step 3: Subtract — subtract from the current group. Step 4: Bring down — bring down the next digit. Repeat until done.
How do you divide 168 by 7?
168 ÷ 7: 7 goes into 16 twice (14), subtract: 16-14=2, bring down 8 to get 28. 7 goes into 28 four times exactly. Quotient = 24. Check: 24 × 7 = 168.
What is the relationship between dividend, divisor, and quotient?
Dividend ÷ Divisor = Quotient. The dividend is the number being divided, the divisor is what you divide by, and the quotient is the result. When there is no remainder: Divisor × Quotient = Dividend.
How do you check your long division answer?
Multiply the quotient by the divisor. If the result equals the dividend (with no remainder), the answer is correct. Example: 2184 ÷ 42 = 52; check: 52 × 42 = 2184. Correct.
When do Grade 6 students practice long division?
Long division is reviewed in Big Ideas Math, Course 1, Chapter 1: Numerical Expressions and Factors, as foundational arithmetic for Grade 6 work with factors, multiples, and rational numbers.
Why is long division important?
Long division is a foundational algorithm used in fraction simplification, converting fractions to decimals, polynomial division in algebra, and any situation requiring exact division. It also builds number sense about the relationship between multiplication and division.