UNIT 1 FRACTIONS PARTSANDWHOLE FOR EACH OF THE FOLLOWING
4 DIVIDING FRACTIONS NOTES YOU DO NOT1BENCHMARKS 2DECIMALS 3DENOMINATOR 4EQUIVALENT FRACTIONS 5 FRACTIONS 6 IMPROPER
489 SERUM PROTEIN FRACTIONS IN OBESITY PAKISTAN J ZOOL
ASKING QUESTIONS THAT CHALLENGE THINKING FRACTIONS TIAIE TIAIE TEACHER
CAKE FRACTIONS PURPOSE THE PURPOSE OF THIS ACTIVITY IS
CONVERT THESE IMPROPER FRACTIONS INTO MIXED NUMBERS FOR EXAMPLE
Unit 1: FRACTIONS
Unit 1: FRACTIONS
Parts-and-Whole
For each of the following, be accurate by measuring with a ruler
If this rectangle is one whole, find one-fourth
If this rectangle is one whole, find two-thirds
If this rectangle is one whole, find
five-thirds
If this rectangle is one whole, find three-eighths
If this rectangle is one whole, find
three-halves
If this rectangle is one-third, what could the whole look like?
If this square is three-fourths, what could the whole look like?
What fraction of the big square does the small square represent? (In other
words, how many times can the small square fit into the larger one?)
Whole
What fraction is the large rectangle if the smaller one is the whole?
Whole
If the rectangle for each below is one whole,
a) find one-sixth b) find two-fifths
c) find seven-thirds
If the following rectangle represents two-third, what could the whole look like?
If the following rectangle is one-sixths, what does the whole look like?
If the following rectangle is four-thirds, what does the whole look like?
If the following triangle represents
one-half,
what does the whole look like?
Compare the following fractions. Which fraction in each pair is GREATER?
Use size of the parts, closer to 0, 1/2, 1, and drawings or models.
DO NOT USE MULTIPLICATION OR COMMON DENOMINATORS
and
and
and
and
and
and
and
and
and
and
and
and
and
Improper and Mixed Numbers
Improper Fractions:
,
,
,
more than a whole (the numerator is larger than the denominator)
can always be written as mixed number ( a whole number and a fraction)
Method Make wholes
What makes a whole
with this fraction?
How many
can be made out of
?
=
1 whole
= 1 whole
= 1 whole
(
total
so far) and
is left.
So,
= 3
M
Note:
A fraction line is a
division
line.
ethod
Divide the numerator by the denominator
3
= 7 22 = 3
- 21
1
Practice: Choose a method to write each improper fraction as a mixed number.
=
Making a mixed number from an improper fraction:
Method
3
The 3 means there are 3 wholes:
,
,
then there’s
=
Method
6 3 Denominator (bottom) x whole number + Numerator (top), over the same denominator
4
4
x 6 + 3 =
4
Practice: Choose a method to write each mixed number as an improper fraction.
3
7
4
1
2
6
Equivalent Fractions
Fractions that mean the same amount of the whole
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2
4
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1
2
REMEMBER: the wholes we are comparing are the same size
Practice
Write two (2) equivalent fractions for the following situations.
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Writing Equivalent Fractions
To write equivalent fractions, multiply or divide the numerator and denominator by the same factor:
x
2
÷
7
E
x
2
÷
7
=
=
REMEMBER
the “Golden Rule”: “What you do to the top, you do
to the bottom”
How to tell if fractions are equivalent:
Is the numerator and denominator multiplied or divided by the same
factor?
Cross-multiply; if the products (answers) are the same,
the fractions are equivalent.
Example:
and
Practice: Which of the following situations show equivalent fractions? Show how
you know (multiply or divide by the same factor, or cross multiply).
A. Stephanie ate
of Kit Kat bar; Sam ate
of his Kit Kat bar.
B. Kathy drove
km, Ken walked
km
and Kim ran
km.
C.
of
Tim’s money was loonies and
of
Jim’s were loonies.
D. Jack got
on his test. Jake got
.
There are
boys in Ms. Mckinnon’s class. There are
girls
in Ms. Macleod`s class.
F. Scott shot
baskets, Paul shot
and Steve shot
.
G. Sue ate
of her pizza. Steve ate
of his pizza.
H. Stan read
pages of his book; Jan read
pages and Frank read
pages.
I. Ann made
serves during the volleyball game; Nathalie made
serves.
J. Dan ate
pieces of skittles; Harry ate
pieces.
K. Nancy read
pages of her book and Beth read
pages.
L. Roxanne drank
ml of her juice. Rick drank
ml.
Simplifying Fractions: writing equivalent fractions in lowest terms.
Example:
can
be simplified to
by
dividing both the denominator and numerator by the same factor, 2.
Practice: Express in the simplest form.
=
=
=
=
=
Adding and Subtracting Fractions
The denominators have to be the same before we add or subtract the numerators
We add or subtract the numerators only
DO NOT ADD OR SUBTRACT THE DENOMINATORS!
If the denominators are not the same, we must find a common denominator.
Rewrite the fractions with the common denominator.
Simplify if possible and rewrite as a mixed number if needed.
E
x
4
x
4
+
=
=
1
Example :
-
=
-
=
-
=
=
x
9
E
x
9
7
x
7
x
+
=
+
=
+
=
= 1
Practice: Find the sum.
+
=
+
=
+
=
+
=
+
=
+
=
+
=
+
=
+
=
Practice: Find the difference.
-
=
-
=
-
=
-
=
-
=
-
=
-
=
-
=
-
=
Practice: Add or subtract.
-
=
+
=
-
=
+
=
-
=
+
=
+
+
=
+
+
=
-
+
=
+
-
=
Adding Mixed Numbers
Method
Add the whole numbers
Add the fractions; DO NOT FORGET TO HAVE A COMMON DENOMINATOR
Add the whole number to the fraction
Simplify to the lowest terms if possible
E
x
3
4
x
+ 2
=
Step
4 + 2 = 6
x
3
4
x
+
=
+
=
+
=
=
1
Step
6 + 1
=
7
Method
Write the mixed numbers improper fractions
Add the fractions; DO NOT FORGET TO HAVE A COMMON DENOMINATOR
Simplify if possible and rewrite as a mixed number if needed
E
3
4
+ 2
=
3 x
4 + 1
+ 4 x
2 + 3
=
+
=
+
=
= 7
Practice: Choose a method to find the sum.
3
+
1
=
4
+
6
=
2
+
2
=
1
+ 2
+ 3
=
Subtracting Mixed Numbers
Method Borrowing
Subtract the fractions first; DO NOT FORGET TO HAVE A COMMON DENOMINATOR
If the subtraction cannot be performed, borrow 1 from the first whole number
Make a whole in fractional form using the common denominator
Subtract the whole numbers
Subtract the fractions; simplify if possible
Add the whole number(s) and the fraction
x
6
x
5
E
x
6
x
5
xample:
7
- 2
=
Step
7
- 2
= 7
-
2
Step
6
+
- 2
=
6
-
2
=
Step 6 – 2 = 4
Step
-
=
=
4
Method
Write the mixed numbers as improper fractions
Subtract the fractions; DO NOT FORGET TO HAVE A COMMON DENOMINATOR
Simplify if possible and rewrite as a mixed number if needed
E
3
4
- 2
=
3 x
4 + 1
- 4
x 2 + 3
=
-
=
-
=
= 1
Practice: Choose a method and find the difference.
3
- 1
=
6
- 4
=
2
-
2
=
8
- 2
=
Solve the following problems.
Beth ate
of
cheese pizza and Scott ate
of the same pizza. How much
pizza was eaten? How much was left?
Harvey gas tank showed
full
at the beginning of the week. On Friday, the
gas gauge read
full.
How much gas did he use in a week?
Anne worked 2
hours
on Monday, 3
hours
on Wednesday and 4
on
Friday. How many hours did she work in total?
The Nadeau family drove from Ottawa to Cambridge to see relatives. They
drove for 3
hours,
stopped for
hour
for lunch and continued to Cambridge
for another 2
hours.
How long were they driving?
How long did the total trip take?
Anne bought 7 meters of rope
for a school project. She used 5
of
it. How
much rope was not used?
Beth planted 2
rows
of beans, 3
rows
of peppers and 4 rows carrots.
How many rows of vegetables did she plant?
b) How much more carrots than peppers did she plant?
STOP and Review…
Fill in the blank
6
1
3
Fill in the blanks
-
# parts
Fraction
Word
2
Half
Quarters
Place the following fractions
on the number line below: 2
,
, , 1
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Place the following fractions in the proper column in the table below.
-
3 3
Proper fractions
Improper Fractions
Mixed Number
Write a
single fraction for 3
.
How do you know you are right?
Rewrite as a mixed number or as an improper fraction as necessary.
-
9
6
3
4
3
Which is greater? Briefly explain why.
-
4 or 3
5 4
11 or 10
10 11
7 or 3
8 8
22 or 4
50 8
2 or 2
3 5
13 or 7
25 16
Place in order from least to greatest.
5, 6, 7¸ 3, 11
8 11 8 2 22
M
ultiplying
Fractions (Do
not need common denominators)
Multiply the numerators together (the two top numbers)
Multiply the denominators together (the two bottom numbers)
Simplify if possible and rewrite as a mixed number if needed
Example:
x
=
=
Whole number multiplied by a fraction
The whole number can be written as a fraction with a denominator of 1
Follow the multiplication rule
Example:
9
x
=
x
=
=
6
Mixed Number multiplied by a Mixed Number
Write the mixed numbers as improper fractions
Follow the multiplication rule
Simplify if possible and rewrite as a mixed number if needed
Example:
2
x
1
=
x
=
=
3
=
3
Practice: Find the product.
x
=
11 x
=
x
=
of 8 =
x
=
of
=
x
=
of
=
x
=
Practice: Solve.
x
x
=
2 x 1
=
of 2
=
3
x 4
=
1
x 1
=
5
of 4 =
During the summer Scott work
4
hours
for 8 weeks. How many hours did he
work in total?
What is
of 60?
Harvey takes 1
weeks to paint a house. How many weeks will it take to paint
15 houses on the block?
How many minutes are there in
5
hours?
Dividing Fractions (Do not need common denominators)
Keep the first fraction the same
Change the division to multiplication
Write the reciprocal of the second fraction (switch the numerator and the denominator of around)
Follow the multiplication rule (multiply the numerators together and the denominators together)
Simplify if possible and rewrite as a mixed number if needed
Mixed Numbers: write the mixed numbers as improper fractions, then follow the above steps
Example:
=
x
=
= 1
=
1
Example:
2
2
=
=
x
=
=
1
Practice: Find the quotient.
=
=
=
3 =
6
=
2
=
3
1
=
4
3
=
Practice: Solve.
2
=
4
4 =
1
4
2
=
Sally is getting ready to cut
a 20 meter ribbon into smaller pieces of
meters
each. How many
meter
pieces of ribbon will she have?
Scott and Vitto are have
of
a pizza to share. How much will each boy get?
How
many boards 1
meters
long can be cut from a board that is
11
meters
long?
You are going to a birthday party and bring 10 litres of ice-cream. You
estimate that each guest will eat
1
cup (there are 4 cups in one
litre).
How many guests can be served ice-cream?
1
÷
1
÷
3 =
O
Whatever
comes first from left to right
S
A
B = brackets
E
M
Whatever
comes first from left to right
D
D
M
= multiplication
A = addition
S
E
B
START
2
Example:
÷
2 +
-
Do
the exponent first
÷
2 +
x
-
Do
the division next
÷
2 +
-
x
=
Get
a common denominator for
the
addition
+
-
+
=
Get
a common denominator for
the
subtraction
Simplified
answer: dividing the numerator and denominator by the factor 2
-
=
-
=
=
Practice: Solve following the order of operations
-
+
=
+
x
=
2
x
+
=
÷
+
x
=
+
x
+
1
=
÷
+
÷
1
=
5
-
3
+
3
=
÷
x
1
-
=
Extra Practice
A.
+ G.
-
B.
+ H.
+
C. - I. + -
D. - J. -
E. + K. +
F. + L. -
M. During four days the Gatineau River went up of a metre, down of a metre, down
of a metre and finally up of a metre. What was the net change? Don’t forget to
state up (+) or down (-) in your answer.
COURSE 2 UNIT 2 FRACTIONS STUDY GUIDE DATE TOPIC
DETAILED HELP FOR ADDING FRACTIONS WITH DIFFERENT DENOMINATORS
EQUIVALENT FRACTIONS FRACTIONS COME IN ALL DIFFERENT SHAPES AND
Tags: following rectangle, solve following, fractions, following, partsandwhole
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