Learn on PengiReveal Math, Course 1Module 3: Compute with Multi-Digit Numbers and Fractions

3-1 Divide Multi-Digit Whole Numbers

In Lesson 3-1 of Module 3 in Reveal Math Course 1, Grade 6 students learn to divide multi-digit whole numbers using the standard long division algorithm, including key vocabulary such as dividend, divisor, and quotient. The lesson covers dividing with and without remainders, annexing zeros to express quotients as decimals, and converting remainders to fractions or decimals. Students apply these skills to real-world problems involving multi-digit division.

Section 1

Divisor, dividend, and quotient

divisor)dividend‾ \text{divisor}\overline{)\text{dividend}}
The dividend is the total amount you are dividing. The divisor is the number you are dividing by. The quotient is the answer to the division problem. Understanding these roles is the first step to becoming a division master, helping you set up any problem correctly, whether it is for homework or sharing snacks with friends.

In the problem 81÷9=981 \div 9 = 9, the dividend is 81, the divisor is 9, and the quotient is 9. For 6)42‾6 \overline{)42}, the number 6 is the divisor and 42 is the dividend. In the fraction 5010=5\frac{50}{10} = 5, the number 5 is the quotient.

Think of it like sharing a pizza! The dividend is the whole pizza. The divisor is the number of friends you are sharing it with. The quotient is the number of slices each friend gets. It is a delicious way to remember the parts of division!

Section 2

Standard Algorithm for Division: No Remainder

Property

When a dividend is perfectly divisible by a divisor, the result is a whole number quotient with a remainder of zero. This relationship can be expressed as:

Dividend÷Divisor=QuotientDividend \div Divisor = Quotient

or

Dividend=Divisor×QuotientDividend = Divisor \times Quotient

Examples

  • 378÷14=27378 \div 14 = 27
      2714)378‾   28‾        98     98‾        0\begin{array}{r} \ \ \ \ \ \ 27 \\ 14 \overline{)378} \\ \ \ \ \underline{28}\ \ \\ \ \ \ \ \ \ 98 \\ \ \ \ \ \ \underline{98} \\ \ \ \ \ \ \ \ \ 0 \\ \end{array}
  • 2,125÷25=852,125 \div 25 = 85
      8525)2125‾   200‾       125     125‾        0\begin{array}{r} \ \ \ \ \ \ 85 \\ 25 \overline{)2125} \\ \ \ \ \underline{200}\ \ \\ \ \ \ \ \ 125 \\ \ \ \ \ \ \underline{125} \\ \ \ \ \ \ \ \ \ 0 \\ \end{array}

Explanation

The standard algorithm for division is a systematic method for dividing multi-digit numbers. The process involves a repeating cycle of steps: divide, multiply, subtract, and bring down the next digit from the dividend. You repeat these steps until all digits of the dividend have been used and the final remainder is zero. This algorithm is an efficient way to solve division problems with large numbers.

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Module 3: Compute with Multi-Digit Numbers and Fractions

  1. Lesson 1Current

    3-1 Divide Multi-Digit Whole Numbers

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  2. Lesson 2

    3-2 Compute With Multi-Digit Decimals

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  3. Lesson 3

    3-3 Divide Whole Numbers by Fractions

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  4. Lesson 4

    3-4 Divide Fractions by Fractions

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  5. Lesson 5

    3-5 Divide with Whole and Mixed Numbers

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Section 1

Divisor, dividend, and quotient

divisor)dividend‾ \text{divisor}\overline{)\text{dividend}}
The dividend is the total amount you are dividing. The divisor is the number you are dividing by. The quotient is the answer to the division problem. Understanding these roles is the first step to becoming a division master, helping you set up any problem correctly, whether it is for homework or sharing snacks with friends.

In the problem 81÷9=981 \div 9 = 9, the dividend is 81, the divisor is 9, and the quotient is 9. For 6)42‾6 \overline{)42}, the number 6 is the divisor and 42 is the dividend. In the fraction 5010=5\frac{50}{10} = 5, the number 5 is the quotient.

Think of it like sharing a pizza! The dividend is the whole pizza. The divisor is the number of friends you are sharing it with. The quotient is the number of slices each friend gets. It is a delicious way to remember the parts of division!

Section 2

Standard Algorithm for Division: No Remainder

Property

When a dividend is perfectly divisible by a divisor, the result is a whole number quotient with a remainder of zero. This relationship can be expressed as:

Dividend÷Divisor=QuotientDividend \div Divisor = Quotient

or

Dividend=Divisor×QuotientDividend = Divisor \times Quotient

Examples

  • 378÷14=27378 \div 14 = 27
      2714)378‾   28‾        98     98‾        0\begin{array}{r} \ \ \ \ \ \ 27 \\ 14 \overline{)378} \\ \ \ \ \underline{28}\ \ \\ \ \ \ \ \ \ 98 \\ \ \ \ \ \ \underline{98} \\ \ \ \ \ \ \ \ \ 0 \\ \end{array}
  • 2,125÷25=852,125 \div 25 = 85
      8525)2125‾   200‾       125     125‾        0\begin{array}{r} \ \ \ \ \ \ 85 \\ 25 \overline{)2125} \\ \ \ \ \underline{200}\ \ \\ \ \ \ \ \ 125 \\ \ \ \ \ \ \underline{125} \\ \ \ \ \ \ \ \ \ 0 \\ \end{array}

Explanation

The standard algorithm for division is a systematic method for dividing multi-digit numbers. The process involves a repeating cycle of steps: divide, multiply, subtract, and bring down the next digit from the dividend. You repeat these steps until all digits of the dividend have been used and the final remainder is zero. This algorithm is an efficient way to solve division problems with large numbers.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 3: Compute with Multi-Digit Numbers and Fractions

  1. Lesson 1Current

    3-1 Divide Multi-Digit Whole Numbers

    LearnPractice
  2. Lesson 2

    3-2 Compute With Multi-Digit Decimals

    LearnPractice
  3. Lesson 3

    3-3 Divide Whole Numbers by Fractions

    LearnPractice
  4. Lesson 4

    3-4 Divide Fractions by Fractions

    LearnPractice
  5. Lesson 5

    3-5 Divide with Whole and Mixed Numbers

    LearnPractice