Transcript Document

Functions: those strange machines
STARTER Session 5
MIXED
NUMBERS
In the roads of UK, United States and
others countries in the
Commonwealth, it’s usual to see
signposts like this:
They usually use miles to measure
distances, speeds…
They usually use miles to measure
distances, speeds…
1Mile = 1,609 Km
But sometimes, the distances are
expressed in this way:
This way to express fractions is
called “mixed numbers”.
This way to express fractions is
called “mixed numbers”.
In the past, they were very common,
and we still use them in several
situations:
Could you give me 3½
dozens of eggs?
Could you give me
7/2 dozen of eggs?
1
When we write 3 1/2 , we mean 3 
2
1
When we write 3 1/2 , we mean 3 
2
In a mixed number, there are always two
parts:
a whole number
1
3
2
a fraction smaller
than one
1
When we write 3 1/2 , we mean 3 
2
In a mixed number, there are always two
parts:
a whole number
1
3
2
a fraction lower
than unit
It’s intuitive, because these parts
correspond to the decimal expression of
the number:
whole part
3'5
decimal part
Can you see the equivalence?
Improper fraction
or “top heavy fraction”
7
1
 3
2
2
Mixed number
or proper fraction
Can you see the equivalence?
Improper fraction
or “top heavy fraction”
Better this way?
7
1
 3
2
2
Mixed number
or proper fraction
1
3   
2 2 2 2
Can you see the equivalence?
Improper fraction
or “top heavy fraction”
Better this way?
7
1
 3
2
2
Mixed number
or proper fraction
1
3   
2 2 2 2
1 6 1
3   
2 2 2 2
Can you see the equivalence?
Improper fraction
or “top heavy fraction”
Better this way?
7
1
 3
2
2
Mixed number
or proper fraction
1
3   
2 2 2 2
1 6 1
3   
2 2 2 2
1 6 1 7
3   
2 2 2 2
Can you change the number form?
Improper fraction form
Proper fraction form
7
1
 3
2
2
?
2
 5
?
3
11
?
 ?
4
?
31
?
 ?
7
?
Can you change the number form?
Improper fraction form
Proper fraction form
7
1
 3
2
2
17
2
 5
3
3
11
?
 ?
4
?
31
?
 ?
7
?
Can you change the number form?
Improper fraction form
Proper fraction form
7
1
 3
2
2
17
2
 5
3
3
11
?
 ?
4
?
31
?
 ?
7
?
Can you change the number form?
Improper fraction form
Proper fraction form
7
1
 3
2
2
17
2
 5
3
3
11
3
 2
4
4
31
?
 ?
7
?
Can you change the number form?
Improper fraction form
Proper fraction form
7
1
 3
2
2
17
2
 5
3
3
11
3
 2
4
4
31
?
 ?
7
?
Can you change the number form?
Improper fraction form
Proper fraction form
7
1
 3
2
2
17
2
 5
3
3
11
3
 2
4
4
31
3
 4
7
7
Adding mixed numbers can be easy:
3  2
?

 5    1    ? 
7  7
?

Adding mixed numbers can be easy:
3  2
?

 5    1    6 
7  7
?

Adding mixed numbers can be easy:
3  2
5

 5    1    6 
7  7
7

Adding mixed numbers can be easy:
3  2
5

 5    1    6 
7  7
7

but sometimes, we must work with
fractions:
2
?
 1 
3     4    7 
3 
5
?

Adding mixed numbers can be easy:
3  2
5

 5    1    6 
7  7
7

but sometimes, we must work with
fractions:
2
11
 1 
3     4    7 
3 
5
15

1 2 5 6 11
   
3 5 15 15 15
And sometimes, we need to arrange the
result, in order obtain a mixed number:
2 
5
?

 5     2    ?
3 
6
?

And sometimes, we need to arrange the
result, in order to have a proper mixed
number:
2 
5
?

 5     2    ?
3 
6
?

2 
5
9

5     2    7 
3 
6
6

The fraction
part is not
lower than unit
And sometimes, we need to arrange the
result, in order to have a proper mixed
number:
2 
5
?

 5     2    ?
3 
6
?

2 
5
9

5     2    7 
3 
6
6

2 
5
3

5     2    7 1
3 
6
6

Express as a
mixed number,
and add again
And sometimes, we need to arrange the
result, in order to have a proper mixed
number:
2 
5
?

 5     2    ?
3 
6
?

2 
5
9

5     2    7 
3 
6
6

2 
5
3

5     2    7 1
3 
6
6

2 
5
1

5     2    8 
3 
6
2

(remember to
simplify the
fraction)
NOW YOU INVESTIGATE (voluntary)
• What about multiplying a mixed number by a
integer?
4

7· 3  
5

• And by other mixed number?
2
4

 5  · 3  
3
5

• What about subtracting and “negative mixed
numbers”?
4

 3  
5
