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Multiplying and Dividing Decimals

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We usually add numbers when we have different and varied data but when we are given with a set of repeated data, we multiply.

Here are some of the decimal multiplications.

How do you multiply with decimals?

  • Multiplying a decimal and a whole number.
  • Multiplying decimals with decimals.
  • Multiplication of decimals by 10s and 100s.
multiplying and dividing decimals
multiplying and dividing decimals

How do you multiply decimals by 10, 100, and 1000?

When we multiply a decimal by 10, 100 or 1000, the decimal point moves to the right as many zeroes are there in the factor.

multiplying and dividing decimals

Let’s see the example below –

multiplying and dividing decimals

Example: The Baker’s oven sells the best croissants in the town. Each croissant costs $1.75. If Charlene needs to buy 45 croissants for her day picnic with her friends, how much will it cost her?

 

Step 1. Understanding the problem

We do that by eliminating unnecessary information:

The Baker’s oven sells the best croissants in the town. Each croissant costs $1.75. If Charlene needs to buy 45 croissants for her day picnic with her friends, how much will it cost her?

Step 2. Translation and Evaluation

Translating the word problem into mathematical formula

Cost of one croissant = $1.75

Number of croissants needed to buy = 45

Total cost of croissants = 1.75 × 45

Step 3. Solving it correctly and being specific about the unit.

Total Cost of croissants = 1.75 × 45                                                 1.75

                                                                                                         x    45

                                                                                                       ————

                         = $ 78.75                                                                       875

                                                                                                            700 x

                                                                                                       ————–

                                                                                                           78.75

                                                                                                       —————

multiplying and dividing decimals

How do you divide with decimals?

Division is an efficient way to subtract repeated data. It’s again same with decimal numbers. Let’s discuss stepwise how to divide decimals.

  • Dividing decimals with decimals.
  • Dividing decimals by 10s, 100s and 1000s.
multiplying and dividing decimals

How do you divide by the powers of 10?

multiplying and dividing decimals
multiplying and dividing decimals

  

 Example: There are 21 sixth grade Math books on the shelf of the school library. If the total width is 79.38 cm thick, what is the width of one book?

Step 1. Understanding the problem

We do that by eliminating unnecessary information. (In this problem, we have question to the point).

There are 21 sixth grade Math books on the shelf of the school library. If the total width is 79.38 cm thick, what is the width of one book?

 Step 2. Translation and Evaluation

Translating the word problem into mathematical formula

Total width of the books in the book shelf = 79.38 cm

No. of books in the shelf = 21

Width of one book = \frac{79.38}{21}

Step 3. Solving it correctly and being specific about the unit

 

So, width of one book = = 3.78 cm    

 

 

Solve the following:

  1. \frac{0.867}{100}
  2. \frac{234}{10}
  3. Amanda made 8 trips to her parent’s home. She drove 323.2 miles in all. How far did Amanda drive for each trip?
  4. 125 × 0.2
  5. 5 × 0.87
  6. What is the total cost of 7 shirts produced in a textile industry if one shirt costs $9.78?
  7. 10 students participated in a science club which charges $4.75 participation fee for each student. What will be the total fees paid by 10 students?

 

Answer key
  1. 0.00867
  2. 23.4
  3. 40.4 miles
  4. 25
  5. 4.35
  6. $68.46
  7. $47.5

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