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Multiplying fractions by whole numbers
Free lesson with a video

In the video below (also available at my Youtube channel), I teach multiplying fractions by whole numbers, which is a fairly easy concept. Students just need to remember that 4 x (2/3) is not calculated as (4 x 2) / (4 x 3). In the visual model, you can color two thirds, four times, to get the answer. Doubling or tripling recipes is a nice application of this concept.

I also show an interesting connection between (1/3) x 5 or one-third of five pies, and 5 x (1/3), or five copies of 1/3.


1. a. Color first 

3

8

.  Color another 

3

8

.  Continue
        till you have colored five times 

3

8

 .
 
      5 ×  

3

8

 =
[available in the book]
    c. Color five times 

7

12

 .
 
       5 ×  

7

12

 =
 
    e. [available in the book]

 

Multiplication of whole numbers can be solved by repeated addition:

  5 × 4  =  4 + 4 + 4 + 4 + 4  = 20              3 × 120  =  120 + 120 + 120  = 360

Multiplying a fraction by a whole number can be solved the same way:

3 ×

1

4

  =  

1

4

 + 

1

4

 + 

1

4

  =  3

4

5 ×

2

9

  =  

2

9

 + 

2

9

 + 

2

9

 + 

2

9

 + 

2

9

  = 

10

9

  =  1

1

9

2. Write the multiplication problems as addition problems and solve. Remember to give your answer as a mixed number and simplify the fractional parts to lowest terms whenever possible.

 a.  5 ×

1

4

=
 
   
  f. [available in the book]


3. Solve. Can you find a SHORTCUT where you don't have to solve these by actually adding?

 a.   3 ×

2

9

     
     
h.   3 ×

3

10

 The shortcut is (explain) __________________________________________________________

____________________________________________________________
 

We know multiplication can be done in any order.
In other words, multiplication is commutative.
So, 5 ×

3

8

 is the same as 

3

8

× 5.  Both equal 

15

8

or 1

7

8

.

4. Multiply.

  a.   5 ×

7

9

[available in the book]    
     
h.  

12

17

  × 10

 

A fraction of a number is the same as that fraction TIMES the number. 
In other words, the word 'of ' translates into multiplication. For example:

3

7

of 14  is

3

7

× 14. You can solve this by multiplying 14 ×

3

7

  = 

42

7

 = 6.

 

5. a.  Marlene wants to cut down on sugar - so she decided to
         only use 2/3 of the amount of sugar mentioned in the
         recipe. How much sugar will she need?
 

    b.  [available in the book]

 
Brownies

1/2 C butter
2 C brown sugar
4 eggs
12 tbsp cocoa powder
2 cups flour
1 tsp vanilla




The ideas in this fraction lesson are taken from the Math Mammoth Fractions 2 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Math Mammoth Fractions 2
A self-teaching worktext that teaches fractions using visual models, a sequel to Math Mammoth Fractions 1. The book covers simplifying fractions, multiplication and division of fractions and mixed numbers, converting fractions to decimals, and ratios.

Available as an affordable download ($5.00), and also as a printed copy.

=> Learn more and see the free samples!

See more topical Math Mammoth books


Next lesson: Multiplying fractions by fractions




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