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The Book of Math
Original Book of Math
AREEBIBRAHIM.M;drfaraz@gmail.com 10/17/21 Math Book
www.studieswithareeb.com
L-1 Fractions.
Original Book of Math
First let's learn Fractions
A fraction shows part of a hole can be a region or a collection,
When read or written fractions you need to know something like Numerator &
Denominator But what is Numerator & Denominator?
E.g.: 2/3 Numerator – 2
Denominator – 3
So now the Numerator is first and the Denominator is second
Now, as you know what is Numerator & Denominator let's start with learning
some more types of fractions.
Types of Fractions
Like Fractions: Fractions with the same Denominator are called Like fractions.
Unlike Fractions: Fractions with different denominators are called as Unlike
fractions.
Proper Fractions: Proper fractions means when the Numerator is smaller than
the Denominator.
Improper Fractions: Improper fractions means when the Numerator is greater
than the Denominator.
Unit Fractions: Unit fraction means when the Numerator is 1 and the
Denominator is any number.
Mixed Fractions: A mixed fraction combines a whole number and a proper
fraction.
Now let me explain what is fractions.
Fraction means part of a hole. Ranbu took a half piece of cake and he left it to
see more go down. See the chart
below
In the previous we have saw he took half now what is the fraction?
Ans: He took ½ (other meaning: HALF) Now see this picture Ranbu took 2 pieces
now what's the answer?
Ans: 2/3
Now what if he takes all the three pieces?
Ans: 3/3 (Called a HOLE) as we have learned before.
They are 7 circles. Ranbu took 5 circles out of 7 now what's the answer?
Ans: 5/7
They are 6 circles. Ranbu took all the circles. Now what's the answer? (Write in 2
names)
Ans: 6/6 or (A HOLE)
FIND OUT PROPER FRACTIONS, IMPROPER FRACTIONS, UNIT FRACTIONS
AND
2/5 - 7/8 -
8/9 - 8/7 -
9/5 - 9/8 -
7/7 - 7/6 -
1/3 - 5/5 -
8/7 - 9/10 -
Changing Mixed Numbers to Improper Fractions.
Steps
1. Multiply the whole number by the denominator
2. Add the number to the product
3. The denominator of the improper fraction will be same as that of the
mixed number
i.e. (Whole Number x Denominator + Numerator)
Convert 2- ¾ into improper fraction
(2x4) +3 = 11
Therefore, 2- ¾ = 11/4
___________________________________________________
Convert 2-3/7
(2x7=14+3=17)
Ans. 17/7
1) 5- 8/9
(5X9=45+8=53)
Ans. 53/9
6- 2/5
6x5=30+2=32
Ans. 32/5
2-3/16
(2x16=32+3=35)
Ans. 35/16
Home work (H.W)
4-3/8 and 7- 4/6
Changing Improper Fraction into mixed numbers.
Steps
1) Divide Numerator by Denominator
2) The Quotient will be the whole number
3) The remainder will be the numerator
4) The denominator of the fractional part will be the same as that of the
improper fraction
Hint: Q, R, D Queen Ran Down.
___________________________________________________
Convert 17/5 into mixed number
17÷5 =3
3- Q
2- R
5- d
Answer- 3-2/5
Home Work (H.W) 3/2
____________________________________________________
EQUILIANT FRACTIONS
The shaded region in each
figure is the same. Therefore,
the shaded region represents
equivalent fractions. Fractions
that show the same parts of
the whole are called equivalent
fractions. Equivalent fractions
represent the value.
Example: ½ = 2/4 = 4/8
Finding Equivalent Fractions in Higher Terms
To find equivalent fractions in higher terms, multiply both the
numerator and denominator by the same number.
½ = 1x3 = 3/ 2x3=6
1 = 1x3 = 3
2 = 2x3=6
Exercise:
Multiply the numerator and denominator by 4 in each of the following to get an
equivalent fraction:
1) ¼ = 1x4=4
4x4=16 Answer- 4/16
___________________________________________________
2) 3/5 = 3x4=12
5x4=20 Answer- 12/20
___________________________________________________
3) 2/5 = 2x4=8
5x4=20 Answer- 8/20
4) 4/5 = 4x4=16
5x4=20 Answer- 16/20
Home Work (H. W)
Multiply the numerator and denominator by 2 in each of the following to get an
equivalent fraction:
1/5
2/3
Equalnet Fractions in LOWEST TERMS
To find equivalent fractions in lower terms, divide both the
numerator and denominator by one of their common factors.
Example: 12/16 = 6 ÷ 2 = 3
8 ÷ 2 = 4 Answer – ¾
____________________________________________________ Divide by a common factor
to get an equivalent fraction
Find the missing Numerator or Denominator in a given pair of
equivalent fractions
2/5 = __/15
Here the numerator of one of the equivalent fractions is missing. From the
denominators, we know 5x3 = 15. Therefore, in the numerator also we will
multiply by 3
____________________________________________________ Checking equivalent
fractions
To check whether two fractions are equivalent or not, cross multiply it. If the
cross products are equal, the fractions are equivalent. If the cross products are
not equal, then the fractions are not equivalent.
1) Are 2/3 and 10/15 are Equilient fractions?
Are 6/9 and 3/2 Equilient Fractions?
They are not because 6x2=12 and 9x3=27
Addition
Addition of like fractions
3/7 + 2/7 = 5/7
3/19 + 9/19 = 12/19
5/13 + 3/13 + 2/13 = 10/13
You are going to ADD the numerators and leave the denominators itself
Compare Fractions
To do compare of unlike fractions take the 1st
fraction and multiply with the
denominator do the same to the 2nd
fraction also multiply with 1st
denominator
and recheck by checking the denominators LCM meaning LOWEST COMMON
MULTIPLES. If correct compare the bot fractions and it will be your answer. In
case the denominators are even you will change the denominators to the Lowest
Terms and compare also with the lowest terms then compare and write the
greater fraction by the original fraction do this only when the denominators are
even.
Take an example
3
7
and
8
4
Go below for Solution
There is one even and one odd
3
7
x
4
4
=
12
28
Now, you have got the answer
12
28
8
4
x
7
7
=
21
28
Now, you have got the answer
21
28
You have got the denominators same now compare them
12
28
<
21
28
3
7
<
8
4
Answer -
8
4
Mixing Both Improper Fraction and Mixed Fraction
10
5
= 10÷5=2
Q-2 2
0
5
Change to Improper Fraction:
R-0
D-5
5x2=10+0=10
Answer:
10
5
Do has H. W
8
5
10
2
3
3
9
Subtracting Like Fractions
With same denominators
To subtract like denominators, you have only 1 step to do. Just add the
numerators of both the fractions but the denominator will be same and Wala!
There is your answer.
Example:
2
5
8
5
= 2+8 = 10 answer is
10
5
Subtracting Unlike Fractions.
Subtracting fractions with unlike denominators means the subtraction of
fractions with the different denominator values. Go through the below steps to
subtract the unlike fractions.
Step 1: Determine the LCM of the denominator values.
Step 2: Convert the denominator to the LCM value by multiplying the
numerator and denominator using the same number.
Step 3: Subtract the numerators, once the fractions have the same
denominator values.
Step 4: Simplify the fraction, if required. Or change to LT Lowest Term
Subtract
2
3
from
3
5
The LCM of the denominators 3 and 5 is 15
Cross multiply
3
5
and
2
3
and change the denominators to the LCM value i.e. you
will actually change the denominators as 15 (the LCM value) you get:
3
15
and
2
15
now as the denominators are like fractions you could subtract this fraction
because you have converted to Like fractions.
3
15
-
2
15
=
1
15
Question: Do you have to change this to Lowest term?
Answer: No because the Numerator is 1.
Practice Questions
Fill in the blanks:
(a) 25 paise is ……………. part of one rupee.
(b) 50 paise is ……………. part of one rupee.
(c) How many 10 paise will make one rupee? …………….
(d) How many 20 paise will make one rupee? …………….
(e) …………………. 25 paise will make one rupee.
(f) How many 50 paise will make one rupee? …………….
(g) How many 5 paise will make one rupee? ………………
(h) 75 paise is ………………. part of one rupee?
I Fill in the blanks / boxes
a) A fraction that has 1 as the numerator is called a ________ fraction.
b) We can multiply and divide the numerator and denominator by the same non-zero
number to get its ______________________.
c) A fraction is said to be in the___________________ if its numerator and
denominator do not have any common factor other than 1.
d) A fraction with value less than one whole is called a __________ fraction.
e) A fraction with value more than or equal to one whole is called a __________
fraction.
f) Mixed fraction is a combination of whole number and ___________ fraction.
g) If you multiply fractions in any _________________, product remains the same.
h) When we multiply a fraction by __________, we get the same fraction.
I) Fractions with ___________ denominators are called unlike fractions.
j) The mixed number for 23 6 is __________.
k) The improper fraction for 2 3 5 is ____________
l) 5 9 X 0 = _______
m) 1 7 X 8 17 = _______ X 1 7
n) 1 X 5 16 = ________
o) 20 paise is ___________ part of one rupee.
p) _________ paise is 1 10 of two rupees.
II Find the missing numerator or denominator in a given pair of equivalent fractions
III Choose Yes / No
a) Are 3/7 and 12/9 equivalent fractions? Yes / No
b) Are 15/10 and 6/4 equivalent fractions? Yes / No
c) Is 50 paise half of one Rupee? Yes / No
d) Is 25 paise 1/9 of two Rupees? Yes / No
Parts and wholes notes new book  1

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Parts and wholes notes new book 1

  • 1. The Book of Math Original Book of Math AREEBIBRAHIM.M;drfaraz@gmail.com 10/17/21 Math Book
  • 2.
  • 3. www.studieswithareeb.com L-1 Fractions. Original Book of Math First let's learn Fractions A fraction shows part of a hole can be a region or a collection, When read or written fractions you need to know something like Numerator & Denominator But what is Numerator & Denominator? E.g.: 2/3 Numerator – 2 Denominator – 3 So now the Numerator is first and the Denominator is second Now, as you know what is Numerator & Denominator let's start with learning some more types of fractions. Types of Fractions Like Fractions: Fractions with the same Denominator are called Like fractions. Unlike Fractions: Fractions with different denominators are called as Unlike fractions. Proper Fractions: Proper fractions means when the Numerator is smaller than the Denominator. Improper Fractions: Improper fractions means when the Numerator is greater than the Denominator. Unit Fractions: Unit fraction means when the Numerator is 1 and the Denominator is any number. Mixed Fractions: A mixed fraction combines a whole number and a proper fraction. Now let me explain what is fractions. Fraction means part of a hole. Ranbu took a half piece of cake and he left it to see more go down. See the chart
  • 4. below In the previous we have saw he took half now what is the fraction? Ans: He took ½ (other meaning: HALF) Now see this picture Ranbu took 2 pieces now what's the answer? Ans: 2/3 Now what if he takes all the three pieces? Ans: 3/3 (Called a HOLE) as we have learned before.
  • 5. They are 7 circles. Ranbu took 5 circles out of 7 now what's the answer? Ans: 5/7 They are 6 circles. Ranbu took all the circles. Now what's the answer? (Write in 2 names)
  • 6. Ans: 6/6 or (A HOLE) FIND OUT PROPER FRACTIONS, IMPROPER FRACTIONS, UNIT FRACTIONS AND 2/5 - 7/8 - 8/9 - 8/7 - 9/5 - 9/8 - 7/7 - 7/6 - 1/3 - 5/5 - 8/7 - 9/10 - Changing Mixed Numbers to Improper Fractions. Steps 1. Multiply the whole number by the denominator 2. Add the number to the product 3. The denominator of the improper fraction will be same as that of the mixed number i.e. (Whole Number x Denominator + Numerator) Convert 2- ¾ into improper fraction (2x4) +3 = 11 Therefore, 2- ¾ = 11/4 ___________________________________________________ Convert 2-3/7 (2x7=14+3=17) Ans. 17/7 1) 5- 8/9 (5X9=45+8=53) Ans. 53/9 6- 2/5 6x5=30+2=32 Ans. 32/5 2-3/16 (2x16=32+3=35) Ans. 35/16 Home work (H.W) 4-3/8 and 7- 4/6
  • 7. Changing Improper Fraction into mixed numbers. Steps 1) Divide Numerator by Denominator 2) The Quotient will be the whole number 3) The remainder will be the numerator 4) The denominator of the fractional part will be the same as that of the improper fraction Hint: Q, R, D Queen Ran Down. ___________________________________________________ Convert 17/5 into mixed number 17÷5 =3 3- Q 2- R 5- d Answer- 3-2/5 Home Work (H.W) 3/2 ____________________________________________________ EQUILIANT FRACTIONS The shaded region in each figure is the same. Therefore, the shaded region represents equivalent fractions. Fractions that show the same parts of the whole are called equivalent fractions. Equivalent fractions represent the value. Example: ½ = 2/4 = 4/8
  • 8. Finding Equivalent Fractions in Higher Terms To find equivalent fractions in higher terms, multiply both the numerator and denominator by the same number. ½ = 1x3 = 3/ 2x3=6 1 = 1x3 = 3 2 = 2x3=6 Exercise: Multiply the numerator and denominator by 4 in each of the following to get an equivalent fraction: 1) ¼ = 1x4=4 4x4=16 Answer- 4/16 ___________________________________________________ 2) 3/5 = 3x4=12 5x4=20 Answer- 12/20 ___________________________________________________ 3) 2/5 = 2x4=8 5x4=20 Answer- 8/20 4) 4/5 = 4x4=16 5x4=20 Answer- 16/20 Home Work (H. W) Multiply the numerator and denominator by 2 in each of the following to get an equivalent fraction: 1/5 2/3 Equalnet Fractions in LOWEST TERMS To find equivalent fractions in lower terms, divide both the numerator and denominator by one of their common factors. Example: 12/16 = 6 ÷ 2 = 3 8 ÷ 2 = 4 Answer – ¾ ____________________________________________________ Divide by a common factor to get an equivalent fraction
  • 9. Find the missing Numerator or Denominator in a given pair of equivalent fractions 2/5 = __/15 Here the numerator of one of the equivalent fractions is missing. From the denominators, we know 5x3 = 15. Therefore, in the numerator also we will multiply by 3 ____________________________________________________ Checking equivalent fractions To check whether two fractions are equivalent or not, cross multiply it. If the cross products are equal, the fractions are equivalent. If the cross products are not equal, then the fractions are not equivalent. 1) Are 2/3 and 10/15 are Equilient fractions?
  • 10. Are 6/9 and 3/2 Equilient Fractions? They are not because 6x2=12 and 9x3=27 Addition Addition of like fractions 3/7 + 2/7 = 5/7 3/19 + 9/19 = 12/19 5/13 + 3/13 + 2/13 = 10/13 You are going to ADD the numerators and leave the denominators itself Compare Fractions To do compare of unlike fractions take the 1st fraction and multiply with the denominator do the same to the 2nd fraction also multiply with 1st denominator and recheck by checking the denominators LCM meaning LOWEST COMMON MULTIPLES. If correct compare the bot fractions and it will be your answer. In case the denominators are even you will change the denominators to the Lowest Terms and compare also with the lowest terms then compare and write the greater fraction by the original fraction do this only when the denominators are even. Take an example 3 7 and 8 4
  • 11. Go below for Solution There is one even and one odd 3 7 x 4 4 = 12 28 Now, you have got the answer 12 28 8 4 x 7 7 = 21 28 Now, you have got the answer 21 28 You have got the denominators same now compare them 12 28 < 21 28 3 7 < 8 4 Answer - 8 4 Mixing Both Improper Fraction and Mixed Fraction 10 5 = 10÷5=2 Q-2 2 0 5 Change to Improper Fraction: R-0 D-5 5x2=10+0=10 Answer: 10 5 Do has H. W 8 5 10 2 3 3 9 Subtracting Like Fractions With same denominators To subtract like denominators, you have only 1 step to do. Just add the numerators of both the fractions but the denominator will be same and Wala! There is your answer. Example: 2 5 8 5 = 2+8 = 10 answer is 10 5 Subtracting Unlike Fractions. Subtracting fractions with unlike denominators means the subtraction of fractions with the different denominator values. Go through the below steps to subtract the unlike fractions. Step 1: Determine the LCM of the denominator values. Step 2: Convert the denominator to the LCM value by multiplying the numerator and denominator using the same number.
  • 12. Step 3: Subtract the numerators, once the fractions have the same denominator values. Step 4: Simplify the fraction, if required. Or change to LT Lowest Term Subtract 2 3 from 3 5 The LCM of the denominators 3 and 5 is 15 Cross multiply 3 5 and 2 3 and change the denominators to the LCM value i.e. you will actually change the denominators as 15 (the LCM value) you get: 3 15 and 2 15 now as the denominators are like fractions you could subtract this fraction because you have converted to Like fractions. 3 15 - 2 15 = 1 15 Question: Do you have to change this to Lowest term? Answer: No because the Numerator is 1.
  • 13. Practice Questions Fill in the blanks: (a) 25 paise is ……………. part of one rupee. (b) 50 paise is ……………. part of one rupee. (c) How many 10 paise will make one rupee? ……………. (d) How many 20 paise will make one rupee? ……………. (e) …………………. 25 paise will make one rupee. (f) How many 50 paise will make one rupee? ……………. (g) How many 5 paise will make one rupee? ……………… (h) 75 paise is ………………. part of one rupee? I Fill in the blanks / boxes a) A fraction that has 1 as the numerator is called a ________ fraction. b) We can multiply and divide the numerator and denominator by the same non-zero number to get its ______________________. c) A fraction is said to be in the___________________ if its numerator and denominator do not have any common factor other than 1. d) A fraction with value less than one whole is called a __________ fraction. e) A fraction with value more than or equal to one whole is called a __________ fraction. f) Mixed fraction is a combination of whole number and ___________ fraction. g) If you multiply fractions in any _________________, product remains the same. h) When we multiply a fraction by __________, we get the same fraction. I) Fractions with ___________ denominators are called unlike fractions. j) The mixed number for 23 6 is __________. k) The improper fraction for 2 3 5 is ____________ l) 5 9 X 0 = _______ m) 1 7 X 8 17 = _______ X 1 7 n) 1 X 5 16 = ________
  • 14. o) 20 paise is ___________ part of one rupee. p) _________ paise is 1 10 of two rupees. II Find the missing numerator or denominator in a given pair of equivalent fractions III Choose Yes / No a) Are 3/7 and 12/9 equivalent fractions? Yes / No b) Are 15/10 and 6/4 equivalent fractions? Yes / No c) Is 50 paise half of one Rupee? Yes / No d) Is 25 paise 1/9 of two Rupees? Yes / No