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  • Division Properties of One
    • Any number (except 0) divided by itself is one. a ÷ a = 1
    • Any number divided by one is the same number. a ÷ 1 = a
  • Division Properties of Zero
    • Zero divided by any number is 0. 0 ÷ a = 0
    • Dividing a number by zero is undefined. a ÷ 0 undefined
  • Divide whole numbers.
    1. Divide the first digit of the dividend by the divisor.
      If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.
    2. Write the quotient above the dividend.
    3. Multiply the quotient by the divisor and write the product under the dividend.
    4. Subtract that product from the dividend.
    5. Bring down the next digit of the dividend.
    6. Repeat from Step 1 until there are no more digits in the dividend to bring down.
    7. Check by multiplying the quotient times the divisor.

Practice makes perfect

Use Division Notation

In the following exercises, translate from math notation to words.

54 ÷ 9

fifty-four divided by nine; the quotient of fifty-four and nine

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32 8

thirty-two divided by eight; the quotient of thirty-two and eight

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48 ÷ 6

forty-eight divided by six; the quotient of forty-eight and six

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7 63

sixty-three divided by seven; the quotient of sixty-three and seven

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Model Division of Whole Numbers

In the following exercises, model the division.

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.

Mixed Practice

In the following exercises, simplify.

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

the quotient of 45 and 15

45 ÷ 15; 3

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the quotient of 64 and 16

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the quotient of 288 and 24

288 ÷ 24; 12

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the quotient of 256 and 32

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Divide Whole Numbers in Applications

In the following exercises, solve.

Trail mix Ric bought 64 ounces of trail mix. He wants to divide it into small bags, with 2 ounces of trail mix in each bag. How many bags can Ric fill?

Ric can fill 32 bags.

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Crackers Evie bought a 42 ounce box of crackers. She wants to divide it into bags with 3 ounces of crackers in each bag. How many bags can Evie fill?

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Astronomy class There are 125 students in an astronomy class. The professor assigns them into groups of 5 . How many groups of students are there?

There are 25 groups.

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Flower shop Melissa’s flower shop got a shipment of 152 roses. She wants to make bouquets of 8 roses each. How many bouquets can Melissa make?

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Baking One roll of plastic wrap is 48 feet long. Marta uses 3 feet of plastic wrap to wrap each cake she bakes. How many cakes can she wrap from one roll?

Marta can wrap 16 cakes from 1 roll.

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Practice Key Terms 3

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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