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Divide. Then check by multiplying: 78,641 ÷ 256 .

307 R49

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Divide. Then check by multiplying: 76,461 ÷ 248 .

308 R77

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Translate word phrases to math notation

Earlier in this section, we translated math notation for division into words. Now we’ll translate word phrases into math notation. Some of the words that indicate division are given in [link] .

Operation Word Phrase Example Expression
Division divided by
quotient of
divided into
12 divided by 4
the quotient of 12 and 4
4 divided into 12
12 ÷ 4
12 4
12 / 4
4 12

Translate and simplify: the quotient of 51 and 17 .

Solution

The word quotient tells us to divide.

the quotient of 51 and 17 Translate. 51 ÷ 17 Divide. 3

We could just as correctly have translated the quotient of 51 and 17 using the notation

17 51 or 51 17 .

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Translate and simplify: the quotient of 91 and 13 .

91 ÷ 13; 7

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Translate and simplify: the quotient of 52 and 13 .

52 ÷ 13; 4

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Divide whole numbers in applications

We will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question.

Cecelia bought a 160-ounce box of oatmeal at the big box store. She wants to divide the 160 ounces of oatmeal into 8-ounce servings. She will put each serving into a plastic bag so she can take one bag to work each day. How many servings will she get from the big box?

Solution

We are asked to find the how many servings she will get from the big box.

Write a phrase. 160 ounces divided by 8 ounces
Translate to math notation. 160 ÷ 8
Simplify by dividing. 20
Write a sentence to answer the question. Cecelia will get 20 servings from the big box.
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Marcus is setting out animal crackers for snacks at the preschool. He wants to put 9 crackers in each cup. One box of animal crackers contains 135 crackers. How many cups can he fill from one box of crackers?

Marcus can fill 15 cups.

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Andrea is making bows for the girls in her dance class to wear at the recital. Each bow takes 4 feet of ribbon, and 36 feet of ribbon are on one spool. How many bows can Andrea make from one spool of ribbon?

Andrea can make 9 bows.

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Key concepts

Operation Notation Expression Read as Result
Division ÷
a b
b a
12 ÷ 4
12 4
4 12
Twelve divided by four the quotient of 12 and 4
  • Multiplication Property of Zero
    • The product of any number and 0 is 0.
      a 0 = 0
      0 a = 0
  • Identity Property of Multiplication
    • The product of any number and 1 is the number.
      1 a = a
      a 1 = a
  • Commutative Property of Multiplication
    • Changing the order of the factors does not change their product.
      a b = b a
  • Multiply two whole numbers to find the product.
    1. Write the numbers so each place value lines up vertically.
    2. Multiply the digits in each place value.
    3. Work from right to left, starting with the ones place in the bottom number.
    4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
    5. If a product in a place value is more than 9, carry to the next place value.
    6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
    7. Insert a zero as a placeholder with each additional partial product.
    8. Add the partial products.
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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