MATH
ONLINE
KUMUSTAHAN
DECEMBER 13, 2021
10:00am
WEEK 4
LESSON 1: CHANGING
IMPROPER FRACTION
TO MIXED NUMBERS
AND VICE VERSA
CARMELA M. MAZO
LOMA ES
In this lesson, you will
observe that improper
and mixed fractions
are related and can be
changed
to
each
other.
After going through
this lesson, you are
expected to change
improper and mixed
fraction or number and
vice versa.
1
2
Numerator
Fraction Bar
Denominator
IMPROPER FRACTION - are fractions
that the numerators are greater than
the denominators
Each whole is divided
into 4 parts
There are 10 shaded parts
10
4
It is read as 10
4
It is an IMPROPER FRACTION
Mixed fraction - is a number always
expressed in a whole number and a
fraction
4
4
and another
One whole is
4
4
2
parts are shaded
and
2
4
4
=1 4
4
2
1
=1 4
It is read 2 or 2
4
4
2
From the illustration, it can be said that
1
10
= 2
4
2
STEPS ON HOW TO CHANGE
IMPROPER FRACTION TO MIXED
NUMBER
1. Divide the numerator by
the denominator
10 = 10 ÷ 4
4
2
2. Express the remainder
4
10
as a fraction
8
3. Write the whole number
2
and the fraction together
2
2
4
STEPS ON HOW TO CHANGE MIXED
NUMBER TO IMPROPER FRACTION
1. Multiply the
denominator by
whole number
2. Add the numerator
3. Affix or copy
the denominator
4x2=8 +2=
+2
2x
4
10
4
To change improper fraction
to mixed number of fraction,
divide the numerator by the
denominator, express the
remainder as a fraction and
write the whole number and
fraction together
Mixed fraction to improper
fraction,
multiply
the
denominator and the whole
number, add the product to
the numerator and express
the sum as fraction, using the
original denominator.
LEARNING
TASK
Changing Improper Fraction to Mixed Number and Vice Versa
Example:
Learning Task 1: Change the following to
improper fraction or mixed number.
Example 1:
3
83
= 10
8
8
10
8 - 83
8
-3
0
3
Example 2:
+3
83
10x
=
8
8
8 x 10 = 80 + 3 = 83
Learning Task 2: Fill in with the
correct numerator or denominator.
Example 1:
Example 2:
46
+1
=
9x
5
5
9 x 5 = 45 + 1= 46
27
= 3
8
3
8 27
-24
3
3
8
WEEK 4
LESSON 2:
CHANGING
FRACTION TO
LOWEST TERM
In the previous lesson, you have
learned how to get the greatest
common factor (GCF) of two
numbers
using
the
prime
factorization.
In this lesson you will use the GCF
to get the lowest form or lowest
terms of the fractions
After going through this
lesson, you are expected
to change fraction to
lowest forms or lowest term.
Study the illustration of two fractions.
Observe if two fractions are equal or
equivalent fraction.
4
This shows 8 of the figure
This shows 1 of the figure
2
The above illustrations of fractions are equal.
You may also noticed that 1 is the lowest
2
term of 4
8
STEPS IN CHANGING FRACTION TO
LOWEST TERM
8
Example: Change
to lowest term
12
Step 1. Find the prime factors of 8 and 12 or
both numerator and denominator to get the
GCF
8 =2x2x2
8
12
12 = 2 x 2 x 3
2x6
2x4
GCF = 2 x 2 = 4
2
2x2 2
2x3
Step 2. Divide both 8 and 12 or both
numerator and denominator with
the same number or GCF.
8÷ 4 = 2
12 ÷ 4 = 3
8 is 2
Therefore the lowest term of 12
3
12
Example: Change
to lowest term
15
Step 2
Step 1
12 = 2 x 2 x 3
12 ÷ 3 = 4
3x5
15 =
15 ÷ 3 = 5
GCF = 3
12
15
2x6 3x5
2 2x3
4
The lowest term is
5
To simplify fractions or
change fractions into lowest
forms divide both numerator
and denominator by their
greatest common factor or
GCF.
When the GCF of
both numerator and
denominator is 1,
the fraction is in
lowest term.
WEEK 4
LEARNING
TASK
Changing Fraction to Lowest Term
Learning Task 1: Change the following
fractions into its lowest term.
Example: Solution: Prime factors and GCF
6. 28 ÷ 4 = 7
36 ÷ 4 = 9
28
36
2 x 14
2
2 x 18
2x7
2
2
2x9
2 3x3
28 = 2 x 2 x 7
36 = 2 x 2 x 3 x 3
GCF = 4
Learning Task 3: Express the given fractions
in its simplest form or lowest term
Example:
6. 9 ÷ 9 = 1
54 ÷ 9 = 6
9
54
3x3
2 x 27
2
2
3x9
3 3x3
28 = 3 x 3
36 = 3 x 3 x 3 x 2
GCF = 9
Example:
Learning Task 2: Put check if the fraction is
already in the simplest form and put an x if
not.
Hint: a fraction is in lowest term if:
1. The numerator is 1
2. The numerator and denominator are
consecutive number
3. The numerator and denominator are
both prime numbers
4. There is no common factor except 1
Learning Task 2: Put check if the
fraction is already in the simplest
form and put an x if not.
25 ÷ 5 = 5
60 ÷ 5 = 12
25 x
60
WEEK 4
LESSON 3: VISUALIZING
ADDITION AND
SUBTRACTION OF
SIMILAR
You already know how to add
similar
fractions
in
your
previous grade. When the
fractions to be added have
common denominators, you
just add the numerators and
copy the original denominator
After going through this
lesson, you are expected
to visualize the addition
and subtraction of similar
and fractions
1
2
Similar fraction
The same
denominator
Numerator
Denominator
Dissimilar fraction
Different
denominator
Identify similar (S) and dissimilar (D)
fraction
2
and
S
____1.
3
3 and
S
____2.
4
1
3
1
4
D
____3. 4 and 7
7
8
2 and 5
D
____4.
5
9
Study the illustration and try to analyze
how to visualize the subtraction and
addition of fraction.
Example 1: Addition of Similar Fraction
1 1 1
5 5 5
3
5
1
5
+
1
4
=
5
5
Example 2: Subtraction of Similar Fraction
-
=
4
6
8
8
6- 4
2
2
1
= ÷ =
8 8
8 2 4
2
8
2=2
8=2x2x2
8
2x4
2x2
Example 3: Subtraction of Fraction
from Whole Number
May divided the whole pizza into
eight equal parts. She ate 3/8 of
pizza. What part of the pizza was
left?
May divided the whole pizza into eight equal parts. She
ate 3/8 of pizza. What part of the pizza was left?
When subtracting fraction
from a whole number,
rename first the whole
number into fraction then
proceed to subtraction.
1=8
8
3
8
8- 3
8 8
=
5
8
WEEK 4
LEARNING
TASK
Visualizing Addition and Subtraction of Similar Fraction
4
8
+
3
8
7
=
8
WEEK
WEEK45
LESSON 3: VISUALIZING
ADDITION AND
SUBTRACTION OF
DISSIMILAR
Example 4: Subtraction of Dissimilar Fraction
Subtract 1 from 5
3
Find the LCD
3 3 6
1 2
LCD = 3 x 1 x 2
LCD = 6
6
Subtract the
renamed fractions
Rename the fraction
to equivalent fraction
using LCD
5
6
1 1x 2 2
=
=
3 3x2 6
5 5
=
6 6
1= 2
3 6
= 3
6
1
3
5
6
1
3
5
6
3
6
11 11 1
66 66 6
1=2
3 6
5 - 2 = 3 ÷ 3 = 1
6 ÷ 3 = 2
6 6
Lowest term
GCF
3=3x1
6= 3 x 2
GCF = 3
Example 5: Addition of Dissimilar Fraction
Add 4 to
6
Find the LCD
3
12
Rename the fraction
to equivalent fraction
using LCD
Subtract the
renamed fractions
8
4
=
12
6
2 6 12
+
4
4
x
2
8
6
3 3
3= 3
=
=
6 6 x 2 12
1 2
12 12
LCD = 2 x 3 x 1 x 2
3
=
11
=
LCD = 12
12
12
8
3
11
+
=
12 12
12
To add dissimilar fractions, you
first express them as similar
fractions by finding their least
common denominator (LCD)
To get the LCD, get the prime
factors of the denominators
using the listing method or
continuous division.
WEEK 4
LEARNING
TASK
Visualizing Addition and Subtraction of Dissimilar Fraction
Example 1:
10 - 2 = 10 - 8 = 2 ÷ 2 =
12 12 12 ÷ 2
12 3
3 12 3 2 x 4 = 8
2 4 1 3 x 4 = 12
2 1
2 2 12
LCD = 3 x 2 x 2 x 1
LCD = 12
GCF = 2
Improper
Fraction
Example 2:
5 + 1
8
2 8 2
2 4 1
2 1
2
5 + 4
9
=
=
8 8
8
1 x4= 4
2x4= 8
LCD = 2 x 2 x 2 x 1
LCD = 8
Mixed
Number
1
or 1
8
1
8 9
-8
1
1
18
+3
+
5
x4
+5
3
=
x6
23 + 23 69 46
=
+
4
6
12 12
LCD = 2 x 2 x 3 x 1 x 1
LCD = 12
2 4
6
23 x 3 =
4 x 3
23 x 2
=
6 x2
=
=
-