Transcript Understanding Fractions

Understanding
Fractions
By Bob Snyder
2007
Writing Fractions
Fractions can be written two ways:
1. With a flat line - ⅝
2. With a slanted line – 5/8
Definition of a Fraction
A fraction shows
parts of a whole. In
this group of puzzle
pieces ¼ of the
puzzle is green. One
piece is green, and
the puzzle has four
pieces in all.
Parts of a Fraction
The top
number in a
fraction is
called the
numerator. It
tells how many
you have.
¼
The bottom
number in a
fraction is
called the
denominator.
It tells how
many parts
there are in all.
The Three Types of
Fractions
There are three types of fractions,
which are:
1. Proper fraction: the numerator is smaller than
the denominator – ½
2. Improper fraction: the numerator is larger than
the denominator – 7/3 (we’ll talk more about this later)
3. Mixed number: a combination of a whole number
and a fraction - 1⅝ (we’ll talk more about this later, too)
Parts of a Whole
Fractions show
parts of a whole.
You might eat
one slice of this
pizza, which has
six equal parts.
Parts of a Set
Fractions can also show
parts of a set. For
example, in this set of
crayons one of the six
crayons is purple, and
the other five are not.
We would say therefore
that 1/6 of the set of
crayons is purple.
Ordering Fractions
Just like with whole numbers, we can order fractions
from least to greatest or greatest to least.
¼
½
¾
These fractions are ordered from least to
greatest: ¼ is smaller than ½, which is smaller
than ¾.
Comparing Fractions
We can also compare fractions to see if one is less
than the other, one is greater than the other, or if
they’re equal.
Here we can say that 2/8 is equal to 1/4. We
would write that like this 2/8 = 1/4.
Here we can see that ¼ is less than ½. We
would write that like this: ¼ ‹ ½.
We can also say that 5/6 is greater than 2/3.
We would write that like this: 5/6 › 2/3.
Equivalent Fractions
3/ , 1/ ,
9
3
and 2/6 are all equal, so we call
them equivalent fractions.
Definition of equivalent
fractions: fractions that are
equal.
Fractions on the Number
Line
Numbers like 0, 1, and 2 are whole numbers. Fractions
represent parts of a whole and they always fit between
whole numbers on a number line.
½
0
1½
1
2½
2
Fraction Rules
1. If two fractions have the same
numerator, the fraction with the
smaller denominator is larger.
1/
1/
>
3
9
>
2. If two fractions have the same
denominator, the fraction with the
larger numerator is larger.
4/
2/
>
5
5
>
3. The larger the denominator, the
smaller the fraction.
1/
36
1/
2
Would you rather have 1/36 of a
cake or 1/2?
4. If the numerator and denominator
are equal, then the fraction is equal
to one whole.
6/
6
1
If Drew ate 6/6 of a pie, he ate
the whole thing!
5. A fraction with a numerator of zero
is equal to zero.
If someone offered you 0/4 of a
pie, you would get nothing!
Mixed Numbers & Improper
Fractions
Let’s start with mixed numbers. All of
you have used mixed numbers before but
you just never realized it! You may have
said, “I spent a day and a half at camp”.
A day and a half is a mixed number! It’s
one whole day plus part of another day.
Let’s represent a day and a half like this:
1 day
½ day
We could also use an improper fraction to represent the
same thing. Instead of a day and a half, let’s think of it as
three half days. Let’s represent it like this instead:
½ day
½ day
½ day
½ day
½ day
½ day
Since each day is split into halves, we
could say we have three halves and write
it like this: 3/2. The denominator tells us
how many parts each day is cut into; the
numerator tells us how many parts we
have in all.
Now we know that a day and a half is the
same thing as three half days. We would
write it like this:
1 ½ = 3/ 2
1 day
½ day
=
½ day
½ day
½ day
Fractional Parts of a
Whole Number
It is very important to know both
multiplication and division when working with
fractions! What if you need to find ¼ of 16??
Sometimes it’s easy, and you can just visualize
what the answer would be, but…
other times it’s not so easy! What if
you need to find 2/7 of 28? We use
multiplication and division to help us!
Here’s how it works:
2
Step 2: multiply the
answer to step 1 (in
this case 4) by the
numerator. 4 x 2 = 8
7
28
Step 1: divide 28 by the
denominator (in this case 7).
28 ÷ 7 = 4.
Step 3: Since 4 x 2 = 8, the answer is 8.
2/
7
of 28 = 8
Let’s look at that one
more time!
To find 2/7 of 28, we first divide 28 by the denominator then multiply
the quotient by the numerator. It is very important to remember the
order of operations and do what is in the parentheses first!
(28 ÷ 7) x 2 = 8
Order of Operations*:
1. Please (parentheses)
2. My - multiply
3. Dear - divide
4. Aunt - add
5. Sally – subtract
*Always work left to right!