UNIVERSIDAD DE STA.

ISABEL PILI CAMPUS

San Agustin, Pili, Camarines Sur
SY 2020 - 2021

MODULE 5
Real Numbers
OVERVIEW…
Real numbers are one of the foundations in mathematics and extremely useful in everyday life. That is
probably one of the main reasons we all learn how to count compute and use the four fundamental operations
from very young age. It also helps us to measure out quantities of different items. Even when relaxing at the
end of the day in front of the television flicking form one channel to the next you are using real numbers.
When ringing your friend for a catch up you will also be inputting real numbers into your phone to give them
call.
Learning Standards and Outcome

 Content Standards: The learner demonstrates understanding of the sets and the real number
system.
 Performance Standards: The learner is able to formulate challenging situations involving sets
and real numbers and solve these in a variety of strategies.
 Learning Targets: After accomplishing all the learning activities in the module, I can;
1. illustrates the different subsets of real numbers;
2. arrange real numbers in increasing or decreasing order and on a number line; and
3. represents real-life situations and solves problems involving real numbers
 Value Standards: My Priorities for them; Advocacy for persons who are poor and
Compassionate Service
 Evidence of Learning: Drills, Summative Quiz

Link Start True or False?

Write T if the statement is True and write F if the statement is False.
_______1. In Mathematics, it is often useful to represent whole numbers by points on a line called
the Number line.
______ 2. Zero (0) is a natural number.
______ 3. (2 + 3) + 4 = 2 + (3 +4) is under Addition Associative Property.
______ 4. 2, 4, 6, and 8 are odd numbers.
_______5. Addition, Subtraction, Multiplication and Division are the four fundamental
operations in Mathematics.
______ 6. Sum: Addition, Quotient: Subtraction
25 1
______ 7. The simplest form of is .
100 4
_____ 8. -12 + 13 = 1
______ 9. The product of two negative numbers is positive numbers.
1
______ 10. is equal to 0.333 which is an example of repeating decimal.
3
Fractions 4 5 2 1
, , ,2
9 6 9 3
Decimals 1.5 , 0.5 , 0.2, 22.3 , 1.222222

Game On
The set of real numbers is a collection of rational and irrational numbers.

Illustration
1ST QUARTER | MODULE 6 IN MATHEMATCS 7: REAL NUMBERS|MR. FELIX JONES B. BANARES | 30
 UNIVERSIDAD DE STA. ISABEL PILI CAMPUS
San Agustin, Pili, Camarines Sur
SY 2020 - 2021

(Visual representation of Subsets of Real Numbers)

Real Numbers
Real Numbers are the numbers that can be represented on a number line, that is, a real
number has only one fixed point on the number line.
One can see that there are many other numbers in between any two integers. Since a number
may also be a negative, the number line can be extended to the left as shown below:

-1
1
-

The length between two integers on the number line as shown is divided into five equal parts.
1 3 1
The numbers -1 , - ,1 ,have been marked on the number line. In fact, an infinite quantity
2 4 4
of such numbers can be marked on this number line. For example, -1
1 2 1 1 1 3 4
4 ,−10 ,−6 ,−1 ,0 ,1 ,5 , 10 , etc .
2 3 4 2 2 5 9
Example:
Mark each of the following points on a number line.
1
a. −2 b. 2.4
5

2
c. d. -0.6
5

Solution:
The number line shows the order in value of the numbers in ascending order (from the
smallest to the greatest). The numbers arranged in ascending order are as follows:

Example:
Arrange the following real numbers in ascending order (that is, from the smallest to greatest)

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 UNIVERSIDAD DE STA. ISABEL PILI CAMPUS
San Agustin, Pili, Camarines Sur
SY 2020 - 2021
11.5, 1 , 3, 3
−2 −5 , 4 , 0 ,−8 , 7.6
Solution: 3 4

8 0 3 4

The real numbers arranged in ascending order are as follows.

3 1
−8 , −5 ,−2 , 0 , 3 , 4 , 7.6 , 11.5
4 3
Properties of Real Numbers

1. The sum, difference, and product of two real numbers are real numbers
2. The division of a real number by a nonzero real number gives a real number.
3. Every real number has a corresponding negative real number. The number zero is neither
positive nor negative. Zero is its own opposite, sa +0 = -0, that is zero’s step to the right is the same
as zero steps to the left.
4. The sum, difference, product and quotient of a rational numbers and an irrational number
are irrational.
For example:
,∧2
2 is rational and √ 5 is irrational, but 2+ √ 5 ,2−√ 5 ,2 √ 5 are all irrationals.
√5
5. The sum, difference, product and quotient of two irrational numbers need not be irrational.
For example:
( 2+ √ 3 ) +¿ = 4, which is not irrational.
( √ 3+5 ) +( √ 3−5) = 10, which is not irrational.
( 3+ √ 2 ) (3−√ 2) = 9-2 = 7, which is not irrational.
√ a = a ,∧¿. Note: a cannot be negative.
6. Given two real numbers a∧b,√ a × √ b=√ ab ,
√b b √
Real Life Problems Involving Real Numbers
There are many instances in real life when you need to use real numbers to solve everyday
problems. Just like other word problems that you have encountered before, the key step in solving these
problems is in properly representing the conditions in the problem by mathematical expression. To do this,
you must read the given conditions carefully to ensure that you have understood the problem correctly, and
in order to properly convert the problem statement into the correct mathematical equation
Example:
1. Ana has a piece of rope 34.6 meters long which he wants to cut into five pieces of
equal length. What would be the length of each part?
Solution:
The length of each piece of rope is
34.6 ÷ 5 = 6.92 meters
Example:
2. For her quarterly project in mathematics, Miya bought the following items from
the bookstore: 40 sheets of bond paper for 27.50 pesos, 5 folders at 9.75 pesos each
and 3 pieces of cartolina at 10.25 pesos each. If he gave 200 pesos to pay for her
purchases, how much change did he receive?
Solution:

1ST QUARTER | MODULE 6 IN MATHEMATCS 7: REAL NUMBERS|MR. FELIX JONES B. BANARES | 32

 UNIVERSIDAD DE STA. ISABEL PILI CAMPUS
San Agustin, Pili, Camarines Sur
SY 2020 - 2021
The total amount of his purchase is
27.50 + (5 × 9.75) + (3 × 10.25)=
27.50 + 48.75 + 30.75 = 107
Thus, his change is given by 200 – 107 = 93 pesos
Example:
3. The table below shows the mean temperature in America by month from 2001-2002.
January -6.4oC May 13.7oC September 12.6oC
o o
February -7.6 C June 16.9 C October 6.0oC
o o
March -0.8 C July 21.0 C November 0.5oC
April 6.8oC August 18.4oC December -4.9oC

Plot each temperature point on the number line and arrange it ascending order.
Solution:

References:
Yvette, Lim F., et al. Mathematics for Engaged Learning Grade 11. Quezon City: Sibs Publishing House, Inc.,
2016

STUDENT
CODE:

MATHEMATICS 7| Module 6 Worksheet

Name: _______________________________Grade and Section: _______________Date:___________

I. Mark the numbers on a number line.

1 1
1. -9.5, - , 0, 2 , 3.9, 4, 9
2 5

1 1
2. -5.5, -4 , - 3.5, 1, 2 , 2.6
3 4

II. Arrange the following numbers in ascending order.

2 3 1 −1 1 1 −1 4 4
1. ,− , ,8 3. , , , , ,−
5 4 2 2 2 3 3 5 7

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 UNIVERSIDAD DE STA. ISABEL PILI CAMPUS
San Agustin, Pili, Camarines Sur
SY 2020 - 2021
−2 −4 1 1
2. ,-3.5, 2, , 4. 0.5, -3.6, 1.8, 0, 1,
9 5 7 2
III. Arrange the following numbers in descending order.
−1 −7 2 1
1. ,-5.5, 2.3, , 3. 3.3, -4.6, 1.6, 0, 1, −1
9 9 9 2
4 4 3 −1 1 2 −2 3 3
2. ,− , , 7 4. , , , , ,−
5 5 5 5 5 5 5 5 5
IV. Direction: Solve the following worded problem below. Write your answer on a separate sheet of paper
and attach it on the last page of this module.
1. Suppose that eggs of a certain size weighing 48.4 grams each are packed in egg cartons. Each carton
contains a dozen eggs. How much will eggs in 8 cartons weigh in kilograms?
2. The group of dancer in USI Pili Campus will participate in a competition. They will wear costume
1
of which each member requires 2 meters of fabric. If the group consists of 12 members, how
2
much fabric will be needed for their costume?
3. Suppose that with a certain airline company, the round trip airfare going to a certain country costs
US$1,500. If the exchange rate is 49.5 pesos to one dollar, how much is the airfare in pesos?

I. Let’s Reflect:

My Priorities for Them

Real Numbers are the numbers that can be represented on a number line. The number line
shows the order in value of the numbers in ascending order (from the smallest to the greatest). In
arranging the real numbers, it may also use a descending order which is from the greatest to the smallest.

If you’re belong to a wealthy family and you have a good heart to help others especially
the poor people like the Vincentian’s Saints and Blesseds did. How could you help and give hope to
them. Through the use of number line that shows order of value, what is your smallest to greatest priority
to be focus on helping the poor people?

Smallest Priority Greatest Priority

1ST QUARTER | MODULE 6 IN MATHEMATCS 7: REAL NUMBERS|MR. FELIX JONES B. BANARES | 34

 UNIVERSIDAD DE STA. ISABEL PILI CAMPUS
San Agustin, Pili, Camarines Sur
SY 2020 - 2021
How did you perform on the activities in this module? Assess yourself by ticking the box of your
answer below:
I am confident and proud of my work.
You have reached the end of Module
I did well on some parts of the module.
6. Detach this answer sheet
/worksheet from the set. It was fine. Only this sheet
will be returned to your I will do better next time. teacher on the
next scheduled dropping of modules.

1ST QUARTER | MODULE 6 IN MATHEMATCS 7: REAL NUMBERS|MR. FELIX JONES B. BANARES | 35