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starMay 2013

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This is where you'll find the latest happenings, news, & ideas in math teaching

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How to help students with multiplication tables?


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Dividing Fractions 2a: How Many Times Does It Fit?

The video below shows two kinds of examples of fraction division where we do not have to use the "rule", but instead can use "mental math". The first type is dividing fractions by whole numbers. The second is divisions where the answer is a whole number, and we can think "How many times does it (the divisor) fit into the dividend?"



How many times does one thing fit into another? From this situation, you can always write a division, and think: "How many times does the divisor go into the dividend?"
How many times does 

1

4

  go into  2?
How many times does 

 go into  ?
8 times. We write a division:  2 ÷

1

4

  = 8 
How many times does 

1

2

  go into  3?
How many times does 

 go into 
?
6 times. We write a division:  3 ÷

1

2

  = 6 

1. Solve. Write a division.

a. How many times does 

1

3

  go into  2?
    How many times does 

 go into  ?
2 ÷

1

3

  = 
 
 
f. [available in the book]
g. [available in the book]
h. [available in the book]


2. Divide. Think “How many times does (the divisor) go into (the dividend)?” Use pictures to help.

a.   3 ÷

1

6

=
b.   3 ÷

2

6

=
[available in the book]  
g.   3 ÷

1

2

=
  [available in the book]

3. a. How many 1/2-meter pieces can you cut out of
        a roll of string that is 6 meters long?

    b.[available in the book]

    c. [available in the book]
 

Did you notice anything?  There is a shortcut to some of these kind of problems!

5  ÷

1

4

 
  ↓ ↓  
5 × 4  = 20
3  ÷

1

8

 
  ↓ ↓  
3 × 8  = 24
9  ÷

1

7

 
  ↓ ↓  
9 × 7  = 63

To solve the division, multiply by the reciprocal of the divisor.

We call 1/4 and 4 reciprocal numbers. Similarly, 1/5 and 5 are reciprocal numbers.

This also makes sense. For example, in the problem 5 ÷ 1/4, you can think that
1/4 goes into one exactly four times, so it goes into five exactly 5 × 4 = 20 times.

4. Solve. Use the shortcut.

a.   3 ÷

1

6

=
  [available in the book]
e.   7 ÷

1

4

=
 
h.   9 ÷

1

8

=

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: Reciprocal Numbers

Practice makes perfect. Practice math at IXL.com

Free online math games and more - www.mathnook.com

Free math worksheets and practice - Adapted Mind


New! Times Tales is now on DVD!

The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
 
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