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Curriculum
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learn about
fractions!
FRACTIONS
What are
fractions?
Basic
Fractions
Comparing
Fractions
Adding
Fractions
Subtracting
Fractions
Fraction
Fun!
What are fractions?
•
Fractions are for counting PART of something
• The denominator
tells us how many
pieces something
is cut into.
• The numerator
tells how many
fractional pieces
there are
Basic Fractions
A fraction is part of an entire object.
1/4 is
pink
1/2 is
pink
3/4 is
pink
4/4 or
one whole
is pink
Comparing Fractions
If the denominators of two fractions are the same, the
fraction with the largest numerator is the larger fraction.
For example:
5/8 is larger than 3/8
all of the pieces are the same and
five pieces are more than three pieces.
Comparing,
cont.
Comparing Fractions, cont.
If the numerators of two fractions are the same, the fraction
with the smaller denominator is the larger fraction.
For example:
5/8 is larger than 5/16
Each fraction says there are five pieces. If an
object is divided into 8 pieces, each piece will be
larger than if the object were split into 16 pieces.
Therefore five larger pieces are more than five
smaller pieces.
Adding Fractions
Adding fractions with COMMON
denominators is simple.
Just add the numerators together, and place the
resulting answer in the top of a fraction and use the
existing denominator for the bottom number. Then
reduce the fraction, if possible
For example:
3/8 + 2/8 = 5/8
Adding,
cont.
Adding Fractions
You can only add together fractions that have the same
denominator, so you must first change one or both of
the fractions so that you end up with two fractions
having a common denominator.
The easiest way to do this, is to simply select the
opposite fraction's denominator to use as a top and
bottom multiplier.
Please look at the example on the next page…
Adding,
cont.
Adding Fractions
Example:
You have the fractions 2/3 and 1/4
Select the denominator of the second fraction (4) and multiply
the top and bottom of the first fraction (2/3) by that number:
4/4 x 2/3 = 8/12
Select the denominator of the first fraction (3) and multiply the
top and bottom of the second fraction (1/4) by that number:
3/3 x 1/4 = 3/12
These two fractions (8/12 and 3/12) have common denominators the number 12 on the bottom of the fraction.
Add these two new fractions together:
8/12 + 3/12 = 11/12
Subtracting Fractions
To subtract two fractions with the same denominator, subtract
the numerators and place that difference over the common
denominator.
Look at a pizza cut into 8 pieces.
Each piece is 1/8 of the pizza.
Here we have 7 pieces or 7/8 of
the pizza.
Now take away 3/8 or 3 pieces.
We’re left with 4 pieces!
We just subtracted the numerators!
Subtracting
, cont.
Subtracting Fractions
To Subtract Fractions with different denominators:
• Find the Lowest Common Denominator (LCD) of the
fractions Click here to learn more about the LCD
• Rename the fractions to have the LCD
• Subtract the numerators of the fractions
• The difference will be the numerator and the LCD will be
the denominator of the answer.
• Simplify the Fraction
LCD
To find the least common denominator, list the multiples of each
denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that
appears in each list.
Example: Suppose we wanted to add 1/5 + 1/6. We would find the least
common denominator as follows...
•First list the multiples of each denominator.
Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...
Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...
LCD, cont.
•Now, when you look at the list of multiples, you can see that 30 is the
smallest number that appears in each list.
•Therefore, the least common denominator of 1/5 and 1/6 is 30.
LCD
For more
LCD help
click here!
Fraction Fun!
If you eat 1/4 of this
pizza how much will
be left?
If you eat 2 pieces of this
pizza and your friend eats
1 how many 10ths did you
eat altogether?
Answer
Fraction Fun!
All the children are going
to share the pizza. We
will cut enough pieces
so each child can have
one, and the pieces
should all be the same
size.
If 7 children shared the
pizza equally, what
fraction of the pizza did
each child get?
Answer
Fraction Fun!
1. What fraction
of the circle is
shaded green?
2. What fraction
of the circle is
shaded red?
3. What fraction
would you write
for the color
RED?
4. What fraction
would you write
for the color
green?
Answers
3/4 left
3/10 eaten
More
Fun!
Back to
Question
1/7
More
Fun!
Back to
Question
1. 4/6 or 2/3
2. 2/3
3. 3/8
4. 1/8
Back to
Question
Concept Map
2005 Connecticut Mathematics
Curriculum Framework
Numerical and Proportional Reasoning –
Quantitative relationships can be expressed
numerically in multiple ways in order to make
connections and simplify calculations using a variety
of strategies, tools and technologies.
How are quantitative relationships
represented by numbers?
Standards 2.1 and 2.2
Grade 3
2.1
Students should understand that a variety of numerical representations can
be used to describe quantitative relationships.
a. Represent numbers in expanded and regrouped forms in the base ten
place value system.
b. Recognize that a fraction with the same numerator and denominator
represents the whole object or an entire set.
c. Use fractions to measure and to represent points on a ruler or number
line.
2.2
Students should use numbers and their properties to compute flexibly and
fluently, and to reasonably estimate measures and quantities
a. Use strategies that involve place value patterns and algebraic properties
to estimate, add and subtract.
b. Approximate solutions to problems involving computation through the
use of efficient methods.
c. Solve multiplication and division problems using rectangular arrays,
number patterns, skip counting and repeated addends.
d. Compare fractions, identify equivalent fractions, add and subtract
fractions with like and unlike denominators using models and pictures.