JUNIOR HIGH SCHOOL
MATHEMATICS
MODULE 7
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The Set of Fractions
This module is all about set of fractions. Fractions are one of the most important
topics students need to understand in order to be successful in algebra and beyond.
Understanding fractions means understanding all the possible concepts that
fractions can represent. One of the commonly used meanings of fraction is part‐
whole. But many who research fraction understanding believe students would
understand fractions better with more emphasis across other meanings of fractions.
(Lamon,2012)
In this lesson, the students will learn to express rational numbers from
fraction form to decimal form and vice versa and perform operations on rational
numbers
Learning Information
Elements of a fraction
a
The fraction is composed of a numerator aand a denominator b.
b
Equivalent fractions
A fraction remains equivalent if the numerator and the denominator
are multiplied or divided by the same number.
Example:
2
2 2× 2 4 ∧4
= = 3 are equivalent fractions
3 3×2 6
6
10
10 10 ÷ 5 2 ∧2
= = 15 are equivalent fractions
15 15 ÷ 5 3
3
Simplification of a fraction
A fraction is written in its simplified form if the numerator and
the denominator have no common factor.
Example:
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25
The fraction is not written in its simplified form since there are numbers that
30
divide both 25 and 30. The largest common divisor (factor) of 25 and 30 is 5,
where
25 25 ÷ 5 5
= =
30 30 ÷ 5 6
Since we divided the numerator and the denominator by the same number (5),
5 25 5 25
the fraction is equivalent to . In addition, is the simplified form of since
6 30 6 30
no other common factor exists for 5 and 6.
Changing Fractions into Decimals
Changing fractions into decimals is even easier than changing decimals into
fractions. It is just a matter of remembering the line in a fraction actually means.
1
2 1
This line means DIVIDE. So, =1÷ 2=0.5
2
Examples:
9
1. Change to a decimal
13
9 ÷ 13 = 0.692 (or 0.7)
2
2. Change 3 to a decimal 2 ÷ 8 = 0.25.
8
So the answer is 3.25. 3 is a whole number, so we leave it unchanged.
6
3. Change 4 to a decimal
7
4 is a whole number, so we 6 ÷ 7 = 0.857 (or 0.9).
So the answer is 4.857 or 4.9, leave it unchanged.
Self-Check Activity No. 1
Change fractions to decimal.
7 5 2
a. b. c. 3
5 6 3
Check your answer on page 88
Changing Decimals into Fraction
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Example 1: Change 7.95 into a fraction
To change this decimal into a fraction, write down the whole number first:
7 is a whole number. Now look at the numbers after the decimal point (.95).
This is a fraction of a whole number: 95’ To work out, look at how many
decimal places are being used: The number 9 is in the tenths column, and the 5
is in the hundredths column. This means that we have 95 hundredths or
𝟗𝟓 /𝟏𝟎𝟎 So, 7.95 = 7 and 95/100 (you can simplify this to make
95/100 = 19/20 )
Examples:
1. Change 2.30 to a fraction 30 3
2.30¿ 2 =2
Notice that 2.30 is the same as 2.3 100 10
In fact, 2.30 = 2.300 = 2.3000 etc.
2. Change 0.791 to a fraction 791
0.791¿
Notice that 0.791 = .791 1000
The zero in front of the decimal place
is not needed.
´ fraction
4. Change 3. 36
Solution: The repeating digit is 36.
100n= 336.36
´
100n=336.36 (Eq.1)
−¿ ´
n=−3. 36 (Eq.2)
______________
99n = 333
333
n=
99
333 3
n= ÷
99 3
111
n=
33
Self-Check Activity No. 2
Change decimals to fraction.
a. 0.123 b. 1. 40 ´
c. 2. 23
Check your answer on page 88
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For more concepts and examples, scan
your book in Next Century Mathematics 7 on
pages 84-101.
Learning Activity
Answer Me!
Learning Activity No. 9: Changing fractions to decimal and
vice versa
A. Completing the Table: Complete the following table by changing fractions to
decimals and vice versa.
Fractions to Decimals (Show your solution)
1 3 7 11
= = = =
3 8 25 15
2 9 1 9
= = = =
5 20 5 10
Solutions here!
Decimals to fractions (Show your solution)
0.1= 0.86= 0.250= 0.12=
0.75= 0.356= ´
0.35=¿ ´ =
1.21
Solutions here!
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Lesson 5.2: Operations on Fractions
Rules for adding and subtracting fractions
a c a±c
± =
b b b
The symbol ±, which is read "plus or minus", indicates that this rule applies
both to sums and subtractions.
Example:
Similar Fractions
3 2
Addition: a. 7 + 7 =¿
3 2 3+2 5
+ = =
7 7 7 7
Since the denominator is the same, add the numerators 3 and 2 then copy
the denominator 7. Answer is already in simplified form.
3 7
b. + =¿
8 8
3 7 3+7 10 5
+ = = =
8 8 8 8 4
Since the denominator is the same, add the numerators 3 and 7 then copy the
denominator 7. Answer is not in simplified form. The largest common
divisor (factor) of 10 and 8 is 4, where 10 and 8 will be divided by 4. The
5
fraction is now in simplified form.
4
Self-Check Activity No. 3
Add similar fractions:
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a. + b. +
3 3 9 9
Check your answer on page 88
5 2
Subtraction: a. − =¿
10 10
5 2 5−2 3
− = =
10 10 10 10
Since the denominator is the same, subtract the numerators 5 and 2 then
Copy the denominator 10. Answer is already in simplified form.
10 6
b. − =¿
12 12
10 6 10−6 4 4 1
− = = ÷ =
12 12 12 12 4 3
Since the denominator is the same, subtract the numerators 10 and 6 then
copy the denominator 12. Answer is not in simplified form. The largest
common divisor (factor) of 4 and 12 is 4, where 4 and 12 will be divided
1
by 4. The fraction is now in simplified form.
3
Self-Check Activity No. 4
Subtract similar fractions:
3 1 5 2
b. − b. −
4 4 9 9
Check your answer on page 88
Adding and subtracting directly for fractions is applicable only if
both fractions have the same denominator or fractions are similar.
However, this will generally not be the case. If fractions don’t have the
same denominator or fractions are dissimilar, we will need to rewrite the
fractions into equivalent fractions with a common denominator.
Dissimilar Fractions
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1 2
Addition: a. + =¿
2 3
1 2 3(1)+2(2) 3+4 7
+ = = =
2 3 6 6 6
Since the denominators are not the same, we will get the LCM
(least common Multiple) of 2 and 3 which is 6. Divide the new
denominator 6 to each original denominators 2 and 3 then multiply to their
corresponding numerators 1 and 2. So, 6 divided by 2 is 3 then multiply to
1 and 6 divided by 3 is 2 then multiply to 2, then add the numerators. The
7
resulted fraction is in simplified form.
6
4 5
b. +
5 6
4 4 6(4 )+ 5(4 ) 24+ 20 44 2 22
+ = = = ÷ =
5 6 30 30 30 2 15
Since the denominators are not the same, we will get the LCM (least
common Multiple) of 5 and 6 which is 30. Divide the new denominator
30 to each original denominators 5 and 6 then multiply to their
corresponding numerators 4 and 4. So, 30 divided by 5 is 6 then multiply
to 4 and 30 divided by 6 is 5 then multiply to 4, then add the numerators.
44
The resulted fraction is not in simplified form. The largest common
30
divisor (factor) of 44 and 30 is 2, where 44 and 30 will be divided by 2.
22
The fraction is now in simplified form.
15
Self-Check Activity No. 5
Add dissimilar fractions:
3 1 4 3
c. + b. +
4 3 5 2
Check your answer on page 88
1 2
Subtraction: a. − =¿
2 3
1 2 3 ( 1 )−2 ( 2 ) 3−4 −1
− = = =
2 3 6 6 6
Since the denominators are not the same, we will get the LCM
(least common Multiple) of 2 and 3 which is 6. Divide the new denominator
6 to each original denominators 2 and 3 then multiply to their corresponding
numerators 1 and 2. So, 6 divided by 2 is 3 then multiply to 1 and 6 divided
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by 3 is 2 then multiply to 2, then subtract the numerators. The resulted
−1
fraction is in simplified form.
6
3 2
b. −
4 5
3 2 5 ( 3 )−4( 2) 15−8 7
− = = =
4 5 20 20 20
Since the denominators are not the same, we will get the LCM
(least common Multiple) of 4 and 5 which is 20. Divide the new denominator
20 to each original denominators 4 and 5 then multiply to their corresponding
numerators 3 and 2. So, 20 divided by 4 is 5 then multiply to 3 and 20 divided
by 5 is 2 then multiply to 2, then subtract the numerators. The resulted
7
fraction is in simplified form.
20
Self-Check Activity No. 6
Subtract dissimilar fractions:
6 2 4 2
d. − b. −
5 3 7 5
Check you answer on page 88
Multiplication rule for two fractions
a c a ×c ac
× = =
b d b × d bd
It is important to note that contrary to sums, the multiplication rule does not
impose constraints to the denominator values. This means they do not need to be
common.
Example:
2 1
a. × =¿
3 4
2 1 2 ×1 2 2 1
= × = = ÷ =
3 4 3× 4 12 2 6
Note : It may be useful to simplify fractions before multiplying. In addition to simplifying
each fraction individually, simplifying the denominator of one fraction with the numerator
of the other fraction is permitted, provided that both have common factors.
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Self-Check Activity No. 7
Multiply the following fractions:
1 4 7 5
a. × b. ×
5 3 8 2
Check your answer on page 88
Division rule of two fractions
a c a× d ad
÷ = =
b d b × c bc
The rule allows us to transform a division into a multiplication.
Example:
2 1
a. ÷ =¿
3 4
2 1 2 ×4 6 3
= ÷ = = ÷ =2
3 4 3×1 3 3
1 3
b. ÷ =¿
2 4
1 3 1× 4 4 2 2
= ÷ = = ÷ =
2 4 2 ×3 6 2 3
Self-Check Activity No. 8
Divide the following fractions:
7 5 4 2
a. ÷ b. ÷
6 6 7 9
Check you answer on page 88
For more concepts and examples, scan
your book in Next Century Mathematics 7 on
pages 84-94.
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Self-Assessment
Consider the following skills/concepts. Rate your comfort level with each
skill/concept by checking the box that best describes your progress in mastering each
skill/concept.
Skill/Concept Beginning Developing Practical Skill Skill Mastery,
Understanding Skill and and Deep
Understanding Understanding Understanding
Find the sum I struggle to add Most of the time I always get the I always get the
of fractions fractions when I add right answer right answer
accurately fractions I get when I add when I add
the right fractions fractions. I can
answer. explain how I
got my answer.
Find the I struggle to Most of the time I always get the I always get the
difference of subtract fractions when I subtract right answer right answer
fractions fractions I get when I subtract when I subtract
accurately the right fractions fractions. I can
answer. explain how I
got my answer.
Find the I struggle to Most of the time I always get the I always get the
product of multiply integers when I multiply right answer right answer
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fractions fractions I get when I multiply when I multiply
accurately the right fractions fractions. I can
answer. explain how I
got my answer.
Find the I struggle to Most of the time I always get the I always get the
quotient of divide fractions when I divide right answer right answer
fractions fractions I get when I divide when I divide
accurately the right fractions fractions. I can
answer. explain how I
got my answer.
Learning Activities:
Answer Me!
Learning Activity No. 10: Operations of fractions
A. Solving: Perform the indicated operations of fractions.
2 5
1. + =¿
4 4
7 6
2. + =¿
10 10
6 2
3. − =¿
9 3
6 3
4. − =¿
8 4
5 2
5. − =¿
10 10
3 2
6. × =¿
6 5
7 2
7. × =¿
15 5
5 2
8. ÷ =¿
10 7
3 6
9. ÷ =¿
7 8
8 5
10. ÷ =¿
9 7
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ANSWER KEY: Self-Check Activities: The Set of
Fractions
Activity No.1
Change fractions to decimal.
7 5 2
b. b. c. 3
5 6 3
Answer:
a. 1.4 b. 0.83 c. 3.67
Activity No.2
Change decimals to fraction.
b. 0.123 b. 1. 40 ´
c. 2. 23
Answer:
123 4 221
a. b. 1 c.
1000 10 99
Activity No.3
Add similar fractions:
2 5 7 4 7 11
e. + = b. + =
3 3 3 9 9 9
Activity No.4
Subtract similar fractions:
3 1 2 1 5 2 7
a. − = = b. − =
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Activity No.5
Add dissimilar fractions:
REFERENCES
Yeo, J. et.al. (2015). New Syllabus Mathematics Singapore Math Worktext 7. Manila.
Rex Bookstore Publishing.
Oronce, F., et.al (2018). E-Math Worktext in Mathematics 7. Manila. Rex Bookstore
Publishing.
Orines, F., et.al. (2012). Next Century Mathematics 7. Manila. Phoenix Publishing
House.
Crisostomo, R., et.al. (2013). Our World of Math 7. Manila. Vibal Publishing House.
Retrieved July 10, 2020 from
https://www.researchgate.net/publication/285819281_Rational
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