Download Fractions

Fractions: The Basics
Ms. Davis’s & Ms. Hillman’s 5th Grade Math Classes
What is a Fraction?



Like a decimal, a fraction is part of a whole
A fraction is less than one whole
A fraction has 2 parts:
numerator


1
3
denominator
The numerator indicates the counted
parts of a fraction
The denominator indicates the
total parts of a fraction
Parts of Wholes & Sets

A fraction can express part of a
whole:
1/4

1 of 4 pieces
of the whole
pizza was
eaten
A fraction can express part of a set
1/4
1 of 4
cookies in
the set was
eaten
Numerators, Denominators,
and Division
A fraction is also simply a
division expression
 The numerator is the dividend
 The denominator is the divisor
 So, the fraction 1/3 is the same as
1 divided by 3

Expressions as Fractions
If we take the expression, 9 ÷ 10, we
can write it as the fraction, 9/10, so
9 ÷ 10 = 9/10
 Can you write each expression as a
fraction?
1÷3
3÷6
2÷7
6 ÷ 13
5÷8

Proper vs. Improper
A fraction is proper when its
numerator is smaller than its
denominator (3/4, 5/8, 6/10).
 A fraction is improper when its
numerator is larger than its
denominator (4/3, 8/5, 10/6).
 Which are improper fractions?
4/7
6/5
2/3
3/5
8/3 7/12
2/1
5/6

Mixed Numbers

A mixed number has a whole
number with a fraction:
2
3
 The mixed number above is read,
“four and two-thirds.”
 Mixed numbers are made by changing
improper fractions.
4
Making Mixed Numbers

To change an improper fraction to a
mixed number:
1. Write the improper fraction as
a division expression:
23
= 23 ÷ 6
6
Making Mixed Numbers
2. Solve the expression:
3R5
6 23
18
5
Making Mixed Numbers
Use the quotient (3) as the whole number.
Use the
3R5
remainder (5) as
6 23
the numerator of
18
the fraction.
5
Use the divisor (6) as the
denominator of the fraction.
Making Mixed Numbers
So, the improper fraction, 23/6 =
the mixed number, 3 and 5/6!
3R5
6 23
18
5
36
5
Let’s Make Mixed Numbers!




Convert the improper fraction, 7/5 to a mixed
number.
What do we do first?
Write 7/5 as a division expression!
Now what?
Solve the expression!
Finally…
Use the quotient as the whole number,
the remainder as the numerator,
and the divisor as the denominator!
Let’s Make Mixed Numbers!
Convert the improper fractions to mixed
numbers.
1. 6/4 1-2/4
2. 12/5 2-2/5
3. 37/9 4-1/9
4. 17/7 2-3/7
Can You Do the Opposite?

To convert a mixed number to an
improper fraction:
1. Multiply the denominator by the
whole number.
2. Add in the numerator.
3. Write the answer as the numerator
of the improper fraction, and the
original denominator as the
improper fraction’s denominator.
Let’s Try One!
Convert 5-2/3 to an improper fraction.
 What should we do first?
2
3
Multiply 3 x 5!
(denominator x whole number)
 Now what?
Add 2 (numerator)!
 Finally?
Use 17 as the numerator and
3 as the denominator!

5
Let’s Try Some More!
Convert to improper fractions.
1.
2.
3.
4.
3-4/5
6-1/3
4-5/6
10-2/7
19/5
19/3
29/6
72/7
Whole Numbers to Fractions


How do we show a whole number
as a fraction?
Think back to what we learned about
fractions being division expressions.
If I want to convert 3 into a fraction, I
think about what I could divide into 3 so
that it will still equal 3.
What do you think?
Whole Numbers to Fractions
Just put the whole number over 1!
3
3=
1
Convert each whole number to a fraction:
6 17 92 435 78
1
1
1
1
1
Fractions Equal to 1
How do we make a fraction equivalent to
the whole number, 1?
 Think back to what we learned about
fractions being division expressions.
 If I want to convert 3 into the whole
number, 1, I think about what I could
divide into 3 so that it will equal 1.
What do you think?
Fractions Equal to 1
Just put the whole number over itself!
3 =1
3
Convert each whole number to 1:
6 17 92 435 78
6
17
92
435
78
Whew!
That was
a lot
of information!
Good job!