Learn on PengienVision, Mathematics, Grade 4Chapter 5: Use Strategies and Properties to Divide by 1-Digit Numbers

Lesson 5: Use Partial Quotients to Divide

In this Grade 4 enVision Mathematics lesson from Chapter 5, students learn how to divide by finding partial quotients, breaking a division problem into smaller, more manageable steps using estimation, multiplication, and place value. Students practice subtracting partial quotients repeatedly until no remainder is left, then adding those partial quotients to find the full quotient. The lesson also connects partial quotients to the Distributive Property, showing how dividing a number broken into parts yields the same result.

Section 1

Finding the Number of Groups

Property

Division can be used to find the number of groups when you know the total amount and the size of each group. The equation is:

Total÷Size per Group=Number of GroupsTotal \div \text{Size per Group} = \text{Number of Groups}

Examples

Section 2

Decomposing the Dividend with the Distributive Property

Property

To solve a division problem, you can decompose the dividend into two addends that are both evenly divisible by the divisor.

(a+b)÷c=(a÷c)+(b÷c)(a + b) \div c = (a \div c) + (b \div c)

Examples

Section 3

Finding Quotients and Remainders

Property

When a whole number (the dividend) cannot be evenly divided by another whole number (the divisor), the result is a quotient and a remainder.
The remainder is the amount left over and must be less than the divisor.
The relationship is:

Dividend=(Divisor×Quotient)+RemainderDividend = (Divisor \times Quotient) + Remainder

Examples

  • Find 125÷4125 \div 4:
314)125120541\begin{array}{r} 31 \\ 4 \overline{) 125} \\ -12 \downarrow \\ \hline 05 \\ -4 \\ \hline 1 \end{array}

The quotient is 3131 with a remainder of 11, written as 31 R131 \text{ R}1.

  • Find 347÷8347 \div 8:
438)3473227243\begin{array}{r} 43 \\ 8 \overline{) 347} \\ -32 \downarrow \\ \hline 27 \\ -24 \\ \hline 3 \end{array}

The quotient is 4343 with a remainder of 33, written as 43 R343 \text{ R}3.

Explanation

To divide whole numbers using long division, follow the divide, multiply, subtract, and bring down steps. If you have a non-zero number left after the final subtraction step and no more digits to bring down, that number is the remainder. The remainder represents the part of the dividend that is left over after creating as many equal groups as possible. Always make sure the remainder is smaller than the divisor.

Book overview

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Chapter 5: Use Strategies and Properties to Divide by 1-Digit Numbers

  1. Lesson 1

    Lesson 1: Mental Math: Find Quotients

  2. Lesson 2

    Lesson 2: Mental Math: Estimate Quotients

  3. Lesson 3

    Lesson 3: Mental Math: Estimate Quotients for Greater Dividends

  4. Lesson 4

    Lesson 4: Interpret Remainders

  5. Lesson 5Current

    Lesson 5: Use Partial Quotients to Divide

  6. Lesson 6

    Lesson 6: Use Partial Quotients to Divide: Greater Dividends

  7. Lesson 7

    Lesson 7: Use Sharing to Divide

  8. Lesson 8

    Lesson 8: Continue Sharing to Divide

  9. Lesson 9

    Lesson 9: Choose a Strategy to Divide

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Finding the Number of Groups

Property

Division can be used to find the number of groups when you know the total amount and the size of each group. The equation is:

Total÷Size per Group=Number of GroupsTotal \div \text{Size per Group} = \text{Number of Groups}

Examples

Section 2

Decomposing the Dividend with the Distributive Property

Property

To solve a division problem, you can decompose the dividend into two addends that are both evenly divisible by the divisor.

(a+b)÷c=(a÷c)+(b÷c)(a + b) \div c = (a \div c) + (b \div c)

Examples

Section 3

Finding Quotients and Remainders

Property

When a whole number (the dividend) cannot be evenly divided by another whole number (the divisor), the result is a quotient and a remainder.
The remainder is the amount left over and must be less than the divisor.
The relationship is:

Dividend=(Divisor×Quotient)+RemainderDividend = (Divisor \times Quotient) + Remainder

Examples

  • Find 125÷4125 \div 4:
314)125120541\begin{array}{r} 31 \\ 4 \overline{) 125} \\ -12 \downarrow \\ \hline 05 \\ -4 \\ \hline 1 \end{array}

The quotient is 3131 with a remainder of 11, written as 31 R131 \text{ R}1.

  • Find 347÷8347 \div 8:
438)3473227243\begin{array}{r} 43 \\ 8 \overline{) 347} \\ -32 \downarrow \\ \hline 27 \\ -24 \\ \hline 3 \end{array}

The quotient is 4343 with a remainder of 33, written as 43 R343 \text{ R}3.

Explanation

To divide whole numbers using long division, follow the divide, multiply, subtract, and bring down steps. If you have a non-zero number left after the final subtraction step and no more digits to bring down, that number is the remainder. The remainder represents the part of the dividend that is left over after creating as many equal groups as possible. Always make sure the remainder is smaller than the divisor.

Book overview

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

Continue this chapter

Chapter 5: Use Strategies and Properties to Divide by 1-Digit Numbers

  1. Lesson 1

    Lesson 1: Mental Math: Find Quotients

  2. Lesson 2

    Lesson 2: Mental Math: Estimate Quotients

  3. Lesson 3

    Lesson 3: Mental Math: Estimate Quotients for Greater Dividends

  4. Lesson 4

    Lesson 4: Interpret Remainders

  5. Lesson 5Current

    Lesson 5: Use Partial Quotients to Divide

  6. Lesson 6

    Lesson 6: Use Partial Quotients to Divide: Greater Dividends

  7. Lesson 7

    Lesson 7: Use Sharing to Divide

  8. Lesson 8

    Lesson 8: Continue Sharing to Divide

  9. Lesson 9

    Lesson 9: Choose a Strategy to Divide