My
Fractions Handbook
_____________________________________________
By Mrs. Tiffany Howard
www.teacherspayteachers.com
Graphics from the pond: http://frompond.blogspot.com
What fraction of Ms. Lady’s
spots are yellow?
What Is a Fraction?
Table of Contents:
What is a fraction?.........................................1
A fraction is a part out of a whole object or set of objects.
How can I find a fraction of an object?..........2
We write the part on top, then draw a line underneath it to
represent out of. Lastly, we write the total on the bottom.
How can I find a fraction of a set of objects?....4
Example:
There are 4 purple parts out of a total
of 6 parts.
4
How can I make equivalent fractions?............5
What are mixed numbers and improper fractions?...6
6
How can I change between mixed numbers and
improper fractions?........................................7
How can I compare and order fractions?...............8
the part
How can I simplify fractions?......................11
the whole-------------- Denominator
How can I add and subtract fractions and
decimals?...................12
Practice:
How can I change a fraction into a decimal?.......13
How can I change a decimal into a
fraction?.................14
How can I multiply fractions?..........14
------------- Numerator
1. What fraction of these hearts is green? Blue?
Green______
Blue_______
2. Write your own fraction representation below.
How can I divide fractions?...............15
1
How Can I Find a Fraction of an Object?
Practice finding a fraction of an object:
Let’s use this bar of chocolate as an example: How many pieces is 1/5
of this whole bar of chocolate?
1. How many squares are 2/3 of this figure?_____
Remember, 1/5 is read as 1 piece out of 5 total. Does this bar of
chocolate have a total of 5 pieces right now? No, we have too many
pieces! We can fix that by breaking the chocolate into groups so that
each group has a total of 5.
There are now 5 total pieces in each of my groups. It matches the
total in the fraction I am looking for: 1/5.
Now shade in the pieces (1) out of the total (5) for each group:1/5
2. How many pieces of pizza is 1/2 of the pizza?_____
3. Challenge: How many pepperonis are 1/3 of the
pepperonis on the pizza?____4. Double Challenge: You had a birthday party yesterday.
Your birthday cake was cut into 24 total pieces before the
party started. Your mom said 1/8 of your cake was leftover.
How many pieces of cake are left? (hint: you can draw a
picture of the cake)
There are 2 pieces shaded in of my object; so 1/5 of my bar
of chocolate is 2 pieces.
2
3
How Can I Find the Fraction of a Set of
Objects?
How can I make an equivalent fraction?
*Link to Comparing Fractions: Remember you can use a
picture when comparing 2 fractions to see if the fractions
are equal to each other. You can also cross multiply to see if
they are equal.
How many clouds are 1/3 of this set of clouds?____
An equivalent fraction is a fraction that is equal to the
original fraction.
When making an equivalent fraction you can chose to
either multiply or divide the numerator and the
denominator by the same number.
1. Group your objects (by circling them) into what the
fraction has as the total (the denominator). 1/3
Examples:
2.
2. Shade in or place an X over the amount in the numerator
for each group of objects you have. 1/3
3
x 11 = 33
6
÷ 2 = 3
5
x 11 = 55
10 ÷ 2 = 5
Remember whatever you do to the top, you do to the
bottom also!
Practice:
1.
3
9
2.
________
1
12
__________
3. 1/3 of the clouds equals 2 clouds
Practice: Draw 10 coins. How much is 4/5 of the coins?____
4
5
What are mixed numbers and improper
fractions?
How Can I Change Between Mixed Numbers
and Improper Fractions?
A mixed number is a number that is in between two whole
numbers. It is represented by a whole number and a
fraction or a whole number and a decimal.
Mixed Number to Improper Fraction:
3
1.5
1
1½
2
3
An improper fraction is a fraction whose numerator is equal
to or larger than its denominator. It is improper because
the bottom number should be the biggest number.
+1
7
=
x2
2
Multiply the denominator by the whole number. Then add the numerator to
your answer. This number is the numerator of your improper fraction. Then
you get to “steal” the same bottom of the original fraction (Remember the
only time you can steal is with fractions!).
Improper Fraction to Mixed Number:
7
Pie Example:
2
3r1
2
7
3
1
2
11 pieces left over
6 total pieces per whole
Or
1 whole and
5
6
Practice: Draw your own pies, pizzas, or bars of chocolate with some
pieces already eaten on a half sheet of paper (split with your neighbor).
Write your name on the paper and ball it up. When the teacher says “go,”
begin a 10 second snowball fight. Remember the rules: 1. You can’t move
your feet, and 2. You can’t aim at someone in close range. When 10 seconds
are up, grab a snowball and write the improper fraction and mixed number
for the picture on the paper. Return it to the owner to check and discuss.
6
Divide the big number (numerator) by the small number
(denominator). Your whole number answer is your whole number in
front of the fraction. Your remainder is the top of the fraction, and
you “steal” the same bottom for the fraction as in the original
fraction.
Practice: Create 1 mixed number problem and 1 improper fraction
problem. Write them on a sheet of paper. Switch papers with the person
next to you. Solve the problems, return the paper, and check each other’s
work. Discuss and help each other when checking.
7
How Can I Compare and Order Fractions?
How Can I Compare and Order Fractions?
3 Options: Cross Multiply Battle Logic, rewrite each fraction
with a common denominator, or draw a visual
representation of each
Rewrite each fraction with a common (same)
denominator:
Cross Multiply Battle Logic: For ordering 3 fractions battle
the first 2 fractions against each other and order them on a
number line.
Example: 1/2, 1/3, and 3/4
3
1
12
2
3
1/3
1/2
Example: Order 2/7, 3/5, and 1/2
Then, cross multiply the third fraction with the first fraction
on the number line. If the third fraction is smaller it will be
the smallest number (the first number) on the number line.
If the third fraction won the battle and was bigger, battle it
against the next fraction on the number line. If it is smaller
it will go in the middle; if it is larger it goes on the end. The
third fraction has 3 possible places it can go (orange
arrows); you must use your logic!
Example: 3/4 is bigger than 1/3 and bigger than 1/2
39
14
4
3
You can change the bottoms around by either multiplying the
bottoms all by each other or finding a number that they all have in
common by being able to either multiply or divide by to get to it.
Remember, whatever you do to the bottom of each individual
fraction, you have to do to the top of that fraction (they are like a
jealous brother and sister). What you may do to one fraction may be
different than what you do to the other fractions when you are trying
to “fix” them to all have the same bottoms. Once the bottoms are the
same, you can look at the tops to order the fractions.
1/3
least
1/2
3/4
greatest
2
3
1
7 x 5
x
2
= 70 this will be the common
denominator for all of the fractions….now let’s fix the tops!
I multiplied my first denominator, 7, by 5 and 2 so I must also multiply
my numerator, 2, by 5 and 2. 2x5x2=20. That turns 2/7 into 20/70
(equivalent fractions)!
I multiplied my 5 by 7 and 2; so I must multiply my 3 by 7 and 2
also…3x7x2=42. 3/5 turns into 42/70!
I multiplied my 2 by 5 and 7; so I must multiply my 1 by 5 and 7
also….1x5x7=35. 1/2 turns into 35/70!
Least to Greatest: 20/70, 35/70, 42/70 or 2/7, 1/2, 3/5
9
8
How Can I Compare and Order Fractions?
How Can I Simplify Fractions?
Drawing a Visual Representation to compare 2 or more
fractions:
A simplified (or reduced) fraction is a fraction in its lowest
term. Think of how much more “simple” it is to draw a
visual representation of 1/2 versus 25/50!
Remember the 2 rules when you draw the representations
of each fraction:
1. The rectangle or circle must be the same size for each
fraction:
NOT:
2. The parts inside the representation must be the same
size within the shape:
Step 1: Write out all the multiples next to each number.
10 - (1x10, 2x5)
15 - (1x15, 3x5)
Step 2: Circle all the numbers that are in both sets.
10 – (1x10, 2x5)
NOT
15 – (1x15, 3x5)
Example: Which is greater, 2/4 or 1/2? They’re equal!
Step 3: If there is any number other than the 1 circled, the
fraction is currently not in its simpliest form. Select the
largest number you circled to divide both the top and
bottom by.
10
÷ 5 =
2
2/3 is the simpliest form of 10/15
Section Practice:
15 ÷ 5 = 3
Don’t forget these are eqivalent
fractions! (Cross Multiply if you don’t believe me!)
Practice all 3 strategies to order fractions 2/5, 4/10, and 1/2
least to greatest.
Practice: Simplify each fraction if needed.
8
10
24
_______
18
3
36 _______
11________
11
How Can I Add and Subtract Fractions and
Decimals?
How Can I Change a Fraction Into a Decimal?
Adding and Subtracting Fractions:
If you have a fraction whose bottom can reach 10, 100, or
1000 by either multiplication or division, rewrite the
fraction with this bottom by making an equivalent fraction.
Then write your top number in the decimal position of the
bottom number (the tenths spot if a 10 is on the bottom,
the hundredths spot if a 100 is on the bottom, etc.)
1. Make sure the bottoms (denominators) of each fraction
are the same. If they are not, rewrite them with a common
denominator. (refer to page 9 for how to do this)
2. Add or subtract just your top numbers (numerators).
“Steal” the denominator from the original fractions.
Option 1: 10, 100, 1000 bottoms
Example:
Examples:
2 x2= 4
2
+
7
1
=
7
3 5
3
This fraction is read as “four tenths”
5 x 2 = 10
7
1
3x2= 6
6 - 1 = 5
10
5 x 2 = 10
10 10
10
Adding and Subtracting Decimals:
Therefore, a 4 is written in the tenths spot of
a decimal: 0.4 (also read as four tenths) –
Remember they are the same amount, just written in
different formats!
Option 2: Divide and Conquer!
2. Remember .1 is the same as .10
Divide the numerator by the denominator. When you first set up the
division problem add a decimal followed by 2 zeros to the numerator.
Also add a “0.” in front of your answer. Ignore the decimal while you
divide.
Practice:
Example:
1. Line up your decimals, and add or subtract like usual.
45.3
- 12.01
12
375.62 + 1.97 = _______
Practice: Change to Decimals
0. 4
2/5 =
5 2.00
1. 16/25 = _______
2. 3/20 = ________
13
How Can I Change a Decimal Into a Fraction?
Write the number without the decimal in your numerator
position. Read your original decimal. If it is a tenths, write a
10 in the denominator. If it is a hundredths, write a 100 in
the denominator. If it is in the thousandths, write a 1000 in
the denominator position.
Examples:
0.69 = 69/100
7.05 = 7 and 5/100
0.3 = 3/10
0.891 = 891/1000
Practice Continued From Page 14: Prank or Real? Fold a clean sheet
of paper into fourths. Number each box on one side 1-4. In each
square write a math problem. You should include 2 problems where
you have to change a decimal into a fraction and 2 problems where
you have to multiply fractions. On the back, number 1-4 for the same
problems to write the answer to each (show your work). Return to
the front side, here you can choose to write the real answer or a
prank answer with each question. Exchange papers with your
neighbor. Your neighbor should solve each of the 4 problems on the
front side and write either “Real” or “Prank” for each square. Once
your neighbor has completed the front side he can check his work
using the answer sheet you created for him on the back. You follow
the same procedures for his paper.
How Can I Divide Fractions?
How Can I Multiply Fractions?
1. Change any mixed numbers to improper fractions.
2. Flip your second fraction (called the reciprocal).
Multiply the tops across. Multiply the bottoms across.
Simplify if needed.
3
10
x
x
8 =
24 ÷ 24 = 1
12 =
120 ÷ 24 = 5
Practice: Prank or Real? Turn to page 15 for directions.
3. Multiply the tops across and the bottoms across.
4. Simplify if needed. Change improper to proper (mixed number).
Example:
4 ÷ 1
4
x 3 =
12
5
5
x 1
5
3
=
Practice:
1. 6/11 ÷ 1/9 = _____
14
2 and 2/5
2. 3 and 4/5 ÷ 1/4 =______
15
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