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أدلة الدراسة > Prealgebra

Dividing Whole Numbers in Applications

Learning Outcomes

  • Translate word phrases that represent division into mathematical expressions
  • Use division to solve word applications
  • Use both division and multiplication

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 the table below.
Operation Word Phrase Example Expression
Division divided by quotient of divided into 1212 divided by 44 the quotient of 1212 and 44 44 divided into 1212 12÷412\div 4 124\frac{12}{4} 12/412\text{/}4 4)12‾4\overline{)12}

example

Translate and simplify: the quotient of 5151 and 1717. Solution:

the quotient of 51 and 17   -   The word quotient tells us to divide

translate   -   51÷1751\div 17

divide   -   33

We could just as correctly have translated the quotient of 5151 and  1717 using the notation 17)51‾17\overline{)51}   or  5117\frac{51}{17}.

   

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.

example

Cecelia bought a 160-ounce\text{160-ounce} box of oatmeal at the big box store. She wants to divide the 160160 ounces of oatmeal into 8-ounce\text{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. 160160 ounces divided by 88 ounces
Translate to math notation. 160÷8160\div 8
Simplify by dividing. 2020
Write a sentence to answer the question. Cecelia will get 2020 servings from the big box.
  In the following video we show another example of how to translate a situation into an algebraic expression. https://youtu.be/y2K-S3tscz0 Now that we have practiced using both multiplication and division to solve application problems, let's combine both skills to answer the next question.

Example

To save money and reduce waste, Frances bought a giant box of crackers with the plan to divide them up into small bags to take to school with her every day. The box contains 4848 oz. of crackers. Answer the following questions about Frances and her crackers: 1) How many 22 oz. bags of crackers can Frances make from the big bag? 2) If there are 150150 calories in a 11 oz serving of crackers, how many calories are each 2 oz. bag?

Answer: 1. We are asked to find how many 22 oz. bags can be made from 4848 oz.

Write a phrase. 4848 ounces divided by22 ounces
Translate to math notation. 48÷248\div 2
Simplify by dividing. 2424
Write a sentence to answer the question. Frances will get2424 servings from the big box.
2. We are asked how many calories are in each 22 oz. bag of crackers.
Write a phrase. 150150  times 22
Translate to math notation. 150⋅2150\cdot 2
Simplify by multiplying. 300300 calories
Write a sentence to answer the question. There are 300300 calories in each 22 oz. bag of crackers.

In the following video we show another example of how to translate a situation that contains both multiplication and division into an algebraic expression. https://youtu.be/DneLJVZDL7k

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