Fractions
Contents
Intro to Fractions…………………………………….. page 2
Reducing Fractions………………………………….. page 13
Ordering Fractions…………………………………… page 16
Multiplication and Division of Fractions………… page 18
Addition and Subtraction of Fractions………….. page 26
Answer Keys………………………………………….. page 39
, Intro to Fractions
Reading Fractions
Fractions are parts. We use them to write and work with amounts that are less
than a whole number (one) but more than zero. The form of a fraction is one
number over another, separated by a fraction (divide) line.
1 3 5
i.e. , , and
2 4 9
These are fractions. Each of the two numbers tells certain information about
the fraction (partial number). The bottom number (denominator) tells how many
parts the whole (one) was divided into. The top number (numerator) tells how
many of the parts to count.
1
says, “Count one of two equal ports.”
2
3
says, “Count three of four equal parts.”
4
5
says, “Count five of nine equal parts.”
9
Fractions can be used to stand for information about wholes and their parts:
EX. A class of 20 students had 6 people absent one day. 6 absentees are
6
part of a whole class of 20 people. represents the fraction of people
20
absent.
EX. A “Goodbar” candy breaks up into 16 small sections. If someone ate 5
5
of those sections, that person ate of the “Goodbar”.
16
,Exercise 1 Write fractions that tell the following information:
(answers on page 39)
1. Count two of five equal parts
2. Count one of four equal parts
3. Count eleven of twelve equal parts
4. Count three of five equal parts
5. Count twenty of fifty equal parts
6. It’s 25 miles to Gramma’s. We have already driven 11 miles. What
fraction of the way have we driven?
7. A pizza was cut into twelve slices. Seven were eaten. What fraction of
the pizza was eaten?
8. There are 24 students in a class. 8 have passed the fractions test.
What fraction of the students have passed fractions?
The Fraction Form of One
Because fractions show how many parts the whole has been divided into and
how many of the parts to count, the form also hints at the number of parts
needed to make up the whole thing. If the bottom number (denominator) is
5
five, we need 5 parts to make a whole: 1 . If the denominator is 18, we
5
18
need 18 parts to make a whole of 18 parts: 1 . Any fraction whose top
18
and bottom numbers are the same is equal to 1.
2 4 100 11 6
Example: 1, 1, 1, 1, 1
2 4 100 11 6
, Complementary Fractions
Fractions tell us how many parts are in a whole and how many parts to count.
The form also tells us how many parts have not been counted (the complement).
The complement completes the whole and gives opposite information that can
be very useful.
3
says, “Count 3 of 4 equal parts.” That means 1 of the 4 was not counted and
4
is somehow different from the original 3.
3 1 4
implies another 1 (its complement). Together, 3 and make , the whole
4 4 4 4 4
thing.
5
says, “Count 5 of 8 equal parts.” That means 3 of the 8 parts have not been
8
3 5 3 8
counted, which implies another , the complement. Together, and make ,
8 8 8 8
which is equal to one.
Complementary Situations
5
It’s 8 miles to town, We have driven 5 miles. That’s of the way, but we still
8
3
have 3 miles to go to get there or of the way.
8
5 3 8
+ = = 1 (1 is all the way to town).
8 8 8
7
A pizza was cut into 12 pieces. 7 were eaten . That means there are 5 slices
12
5 7 5 12
left or of the pizza. + = = 1 (the whole pizza).
12 12 12 12
Mary had 10 dollars. She spent 5 dollars on gas, 1 dollar on parking, and 3
dollars on lunch. In fraction form, how much money does she have left?
5
Gas = , parking = 1 , lunch = 3
10 10 10
5 1 3 9 1
+ + = ; is the complement (the leftover money)
10 10 10 10 10
10
Altogether it totals or all of the money.
10
Contents
Intro to Fractions…………………………………….. page 2
Reducing Fractions………………………………….. page 13
Ordering Fractions…………………………………… page 16
Multiplication and Division of Fractions………… page 18
Addition and Subtraction of Fractions………….. page 26
Answer Keys………………………………………….. page 39
, Intro to Fractions
Reading Fractions
Fractions are parts. We use them to write and work with amounts that are less
than a whole number (one) but more than zero. The form of a fraction is one
number over another, separated by a fraction (divide) line.
1 3 5
i.e. , , and
2 4 9
These are fractions. Each of the two numbers tells certain information about
the fraction (partial number). The bottom number (denominator) tells how many
parts the whole (one) was divided into. The top number (numerator) tells how
many of the parts to count.
1
says, “Count one of two equal ports.”
2
3
says, “Count three of four equal parts.”
4
5
says, “Count five of nine equal parts.”
9
Fractions can be used to stand for information about wholes and their parts:
EX. A class of 20 students had 6 people absent one day. 6 absentees are
6
part of a whole class of 20 people. represents the fraction of people
20
absent.
EX. A “Goodbar” candy breaks up into 16 small sections. If someone ate 5
5
of those sections, that person ate of the “Goodbar”.
16
,Exercise 1 Write fractions that tell the following information:
(answers on page 39)
1. Count two of five equal parts
2. Count one of four equal parts
3. Count eleven of twelve equal parts
4. Count three of five equal parts
5. Count twenty of fifty equal parts
6. It’s 25 miles to Gramma’s. We have already driven 11 miles. What
fraction of the way have we driven?
7. A pizza was cut into twelve slices. Seven were eaten. What fraction of
the pizza was eaten?
8. There are 24 students in a class. 8 have passed the fractions test.
What fraction of the students have passed fractions?
The Fraction Form of One
Because fractions show how many parts the whole has been divided into and
how many of the parts to count, the form also hints at the number of parts
needed to make up the whole thing. If the bottom number (denominator) is
5
five, we need 5 parts to make a whole: 1 . If the denominator is 18, we
5
18
need 18 parts to make a whole of 18 parts: 1 . Any fraction whose top
18
and bottom numbers are the same is equal to 1.
2 4 100 11 6
Example: 1, 1, 1, 1, 1
2 4 100 11 6
, Complementary Fractions
Fractions tell us how many parts are in a whole and how many parts to count.
The form also tells us how many parts have not been counted (the complement).
The complement completes the whole and gives opposite information that can
be very useful.
3
says, “Count 3 of 4 equal parts.” That means 1 of the 4 was not counted and
4
is somehow different from the original 3.
3 1 4
implies another 1 (its complement). Together, 3 and make , the whole
4 4 4 4 4
thing.
5
says, “Count 5 of 8 equal parts.” That means 3 of the 8 parts have not been
8
3 5 3 8
counted, which implies another , the complement. Together, and make ,
8 8 8 8
which is equal to one.
Complementary Situations
5
It’s 8 miles to town, We have driven 5 miles. That’s of the way, but we still
8
3
have 3 miles to go to get there or of the way.
8
5 3 8
+ = = 1 (1 is all the way to town).
8 8 8
7
A pizza was cut into 12 pieces. 7 were eaten . That means there are 5 slices
12
5 7 5 12
left or of the pizza. + = = 1 (the whole pizza).
12 12 12 12
Mary had 10 dollars. She spent 5 dollars on gas, 1 dollar on parking, and 3
dollars on lunch. In fraction form, how much money does she have left?
5
Gas = , parking = 1 , lunch = 3
10 10 10
5 1 3 9 1
+ + = ; is the complement (the leftover money)
10 10 10 10 10
10
Altogether it totals or all of the money.
10
