Download Fractions - MoreMaths

Fractions
4
1. Revision
Description
Recall basics of
fractions
Reflect and Review

Teasers
1) Convert
To convert
into
mixed fraction:
Answers
to improper
1)
fraction.
2)
2) Rocky answered only 9
questions out of 15 in the
English exam. What
fraction of questions did
So, on dividing 23 by 6,
he not answer?
we get Quotient = 3
and Remainder = 5.
Here
is an
improper fraction.
Thus, the mixed
fraction form is
∴

.
.
To evaluate
of 150
Here, on dividing 150
by 15 we get 10, and
on multiplying this
with 4, we get 40.
∴
of 150
=
= 40
2. Equivalent fractions
Description
Reflect and Review
Finding Equivalent
Fractions
Equivalent fractions for

, ,
are
Teasers
Answers
1) Find two equivalent 1)
fractions of .
2) 1; 128
2) Fill in the boxes to
1
a given fraction can be
found either by
multiplying both the
numerator and
denominator by the
same number or by
dividing both the
numerator and
denominator by the
same number.
equivalent fractions,
since
and
form equivalent
fractions:
.
Checking for
Equivalent Fractions
To check whether two
fractions are equivalent
or not, we can use
cross multiplication,
i.e., multiply the
numerator of the first
fraction by the
denominator of the
second and the
denominator of the
first fraction by the
numerator of the
second. If both the
products are equal,
then the given fractions
are equivalent
otherwise they are not
equivalent.
1) Check whether

A fraction is said to be in its lowest form if
the only common factor of the numerator
and the denominator is 1.
Reducing a given fraction to its lowest
2
and are
equivalent or not.
and are not
equivalent fractions
since 7 × 8 = 56 and
12 × 5 = 60, and 56 ≠
60.
3. Lowest Form of a Fraction
Description
1) Yes
Reflect
and
Review
,
since HCF of
48 and 108 is
12.
Teasers
Reduce the
following to its
lowest form:
1)
Answers
1)
2)
form can be done using either the two
given methods:
2)
Method 1: A fraction can be reduced to its
lowest form by dividing both the
numerator and the denominator by a
common factor. Repeat the process till the
numerator and the denominator have no
common factor except 1.
Method 2: Find the HCF of the numerator
and the denominator and divide both of
them by their HCF. The fraction will get
reduced to the lowest form in one step.
4. Comparison of Fractions
Description
Reflect and
Review
Comparison of Like
Fractions
Like fractions have
same denominator.
So, we can easily
compare them by
comparing the
numerators.
Between
, the
smallest is .
When the denominators
are same, the fraction
with the smallest
numerator is the
smallest.
Teasers
1) Arrange
Answers
1)
in
ascending order
3
1) Arrange
Comparison of
Unlike Fractions
Case 1: Fractions with 
the same numerator.
Case 2: Fractions with
different numerators. 
- Convert these
type of unlike
fractions into
like fractions by
making the
denominators
same.
Between
in
ascending order.
,
the smallest is .
When the
numerators are
same, the fraction
with the largest
denominator is the
smallest.
1)
2)
2) Arrange
in
descending
order.
are in
ascending order.
Since they are all
unlike fractions, the
LCM of
denominators 8, 3
and 4 is 24.
So,
,
and
.
5. Addition of Fractions
Description
Reflect and
Review
Addition of Like
Fractions
To add two or more
like fractions, add the
numerators and put
the answer over the
same denominator.
4
The sum of
,
Teasers
Answers
Find the sum of the following:
1)
1)
,
and
2)
,
and
since
2)
Addition of Unlike
Fractions
To add two or more
unlike fractions, first
change them into like
fractions and then add.
,
1) Solve
Since the LCM of 5
and 7 is 35.
So,
,
the tank, Neel filled
1) Solve:
,
Since 2 + 3 = 5 and
.
Method 2:
Convert the mixed
fractions into improper
fractions and then add.
1) 16
.
2) Anupam bought 1 ½ kg of
sugar and 3 ¼ kg of flour and
kg of butter to bake her
cake. Find the total weight of
ingredients used by her to
bake the cake.
6. Subtraction of Fractions
Description
Reflect and
Review
Teasers
Subtraction of Like
Fractions
1) Solve:
,
from
2) 6
kg
Answers
.
2) Subtract
The difference of
since
th of
the tank and Monti filled th
of the tank. Could three of
them together fill the tank
completely, or not?
Addition of Mixed
Fractions
To subtract two or more
like fractions, subtract
the numerators in order,
and put the answer over
the same denominator.
2) Yes.
2) Raghu, Neel and Monti
decided to fill the tank with
water. Raghu filled
th of
And,
Method 1:
First add the whole
numbers and then add
the fractions.
1)
.
1)
2)
.
.
5
Subtraction of Unlike
Fractions
To subtract two or more
unlike fractions, first
convert the fractions
into like fractions by
finding the LCM of their
denominators, and then
subtract.
1) Solve:
2) Neetu completed
reading ½ of the book
last week and she
Since the LCM of 5 and 9
completed reading
is 45.
of the remaining in the
first two days of this
So,
,
week. Find what
fraction of the book is
,
left for her to finish.
and
.
1) Solve:
Subtraction of Mixed
Fractions
First convert the mixed
fractions into improper
fractions with the same
denominator, and then
subtract.
Since
6
2)
1)
2) Meenakshi bought 15 L
of oil in her monthly
grocery and by the end
of the month she was
left with 8 ¾ L of oil.
.
How much did she
consume in the whole
month?
Teasers
Simplify the following:
1)
Multiplication of a
Fraction by a Whole
Number
Step 2: Cancel out the
common factors in the
numerator and the
denominator.
1)
.
7. Multiplication of Fractions
Description
Reflect and
Review
Step 1: Write the whole
number as a fraction
with 1 as the
denominator.
.
2)
,
since 135 can be
written as
and be
simplified as
.
2) 6 L
Answers
1) 216
2)
Step 3: Multiply the
numerators and multiply
the denominators to
obtain the final product.
Multiplication of a
Fraction by Another
Fraction
Step 1: Multiply the
numerators and the
denominators
respectively.
Step 2: Simplify to
reduce it to the lowest
form.
1) Solve:
.
Here, on cancelling
the common factors,
we get
which
gives the product as
.
Multiplication of a
Fraction by a Mixed
Fraction
Step 1: Change the
mixed fraction into
improper fraction and
cancel out the common
factors in the numerator
and the denominator.
Step 2: Multiply the
numerators and the
denominators
respectively.
.
1) 3
2) Subhash’s mother
packed him with th
of the cake made by
her for his lunch.
Subash shared ¼ of it
with his friend. What
part of the cake did
Subhash’s friend get?
2)
th of the
cake.
1) The cost of 1 kg of
rice is ₹45 ½. What is
the cost of 5 ½ kg of
rice?
1) ₹250 ¼
2)
,
2) Solve:
.
Since improper
fraction form of
is , and cancelling
the common factors,
we get
.
Step 3: Simplify to get a
mixed fraction.
7
8. Multiplicative Inverse
Description
Reflect and Review
Two numbers are The multiplicative inverse
said
to
be of 4 is ¼, since 4 × ¼ = 1.
multiplicative
inverse of each
other if their
product is 1.
9. Division of Fractions
Description
Teasers
Answers
Write the multiplicative inverse
of the following:
1) 1
2)
Reflect and
Review
Teasers
Division of a Whole
Number by a Fraction
Step 1: First we find the
multiplicative inverse of the
divisor.
Step 2: Then we multiply the
dividend with the
multiplicative inverse of the
divisor, and write the answer
in the lowest form.
1) Solve:
,
Since
and
its multiplicative
inverse is .
Division of a Fraction by a
Whole Number
While dividing a fraction by a
whole number, we need to
write the whole number as a
fraction with denominator 1
and follow the same steps as
above.
Since
and multiplicative
inverse of 187 is
.
Division of a Fraction by
Another Fraction
Same as the division of whole
number by a fraction.
8
2)
1)
2) The weight of 25
bags of rice is 175
kg 500 g. Find the
weight of each bag
of rice.
1) 72
2)
kg
Divide the following:
1) ¾
1)
2)
2)
.
.
2) 15
2) Amrit ordered 8
pizzas for his
birthday party and
he distributed them
equally among his
friends and himself,
such that each of
them could get ½ of
a pizza. Find how
many friends had
pizza.
1) Solve:
27.
1)
.
Since, the
multiplicative
inverse of is
Answers