BUHI ST. JOSEPH’S ACADEMY INC. (BSJAI)
San Pedro Buhi, Camarines Sur
S/Y 2021-2022
JUNIOR HIGH SCHOOL DEPARTMENT
Mathematics 7
MODULE 2 (3rd QUARTER)
NAME: _________________________________________
SUBJECT TEACHER: MS. MARIEL JOY I. AZON
GRADE AND SECTION: GRADE 7- ____________
CONTACT NUMBER: 09076352637-SMART
MULTIPLYING
RATIONAL
NUMBERS
I. INTRODUCTION
Like. with any set of numbers, rational numbers can be added and subtracted. In this lesson, you will
learn techniques in multiplying and dividing numbers. Techniques include changing rational numbers into
various forms convenient for the operation as well as estimation and computation techniques.
II. OBJECTIVES
At the end of the lesson, the learners should be able to:
1. Multiply rational numbers;
2. Solve problems involving multiplication of rational numbers.
III. DISCUSSION
A model that we can use to illustrate multiplication and division of rational numbers is the area model.
1
What is 4
1
3? Suppose we have one bar of chocolate represent 1 unit.
Divide the bar first into 4 equal parts vertically. One part of it is
Then, divide each fourth into 3 equal parts, this time horizontally to make the divisions easy to see. One part of
the horizontal division is .
1
3
There will be 12 equal-sized pieces and one piece is
from elementary mathematics to mean
1
3
1
4
1
12
1
. But, that one one piece is
3
of
1
4
, which we know
1
.
4
Greatest common factor
FINDING THE GREATEST COMMON FACTOR (GCF)
Finding the GCF is a prerequisite skill in simplifying fractions. This is the reason why you need to recall this concept.
Example 1: Find the GCF of 12 and 18.
Answer:
Write all factors of 12 and 18, then get the greatest common factor.
12 → 1, 2, 3, 4, 6, 12
18 → 1, 2, 3, 6, 9, 18
The common factors are 1, 2, 3, and 6. The greatest is 6.
So, the GCF (12, 18) = 6.
MULTIPLYING FRACTION
To multiply fractions, simply multiply the numerators then the denominators. In symbols,
Example 2. Find the product of
and
.
.
Answer: Using a model, we have:
1
2
Figure 2
Figure 1
Multiplying (Figure 1) and
and
2
6
2
3
(Figure 2) is the intersection of the two figures as shown in Figure 3. Thus, the product of
. Simplifying, we have
By using the rule,
Figure 3
x
.
; divide the numerator and
denominator by the GCF 2 to
express the product in its simplest
form
Example 3. Find:
Answer:
; simplify by dividing the numerator and denominator by the
GCF of 4 and 10 which is 2
Example 4. Multiply
Answer:
and
x
;
x
;
.
write
in improper fraction
multiply the numerators, then the denominators
;
simplify by dividing the numerator and denominator by the GCF
of 36 and 24 which is 12
Example 5. In a city,
of the people own pets. Of those who own pets, own goldfish.
What fraction of the people in the city owns goldfish?
Answer:
A fraction of something means multiplication. So multiply
and .
x
simplify,
Important Rules to Remember
The following are rules that you must remember. From here on, the symbols to be used for multiplication are any of the
following: , x, , or
1. To multiply rational numbers in fraction form simply multiply the numerators and multiply the denominators.
where b and d are NOT equal to zero, ( b ≠ 0; d ≠ 0 )
In symbol,
Example:
Multiply the following and write your answer in simplest form.
The easiest way to solve for this number is to change mixed
numbers to an improper fraction and then multiply it. Or use
prime factors or the greatest
common factor, as part of the multiplication process.
a.
b.
Divide:
=
Take the reciprocal of , which is then multiply it with the first fraction.
Using prime factors, it is easy to see that 2 can be factored out of the
numerator then cancelled out with the denominator, leaving 4 and 3 as the
remaining factors in the numerator and 11 as the remaining factors in the
denominator
MULTIPLYING DECIMAL
1. Multiply the numbers using the rules in multiplying whole numbers. Ignore first the decimal points.
2. Count the total number of digits that are located at the right side of the decimal points in the factors.
3. Locate the decimal point of the product by moving the decimal point of the whole number to the left that number
of times as the total number of digits in step 2.
4. Insert zero as needed.
Example 6. Multiply .214 and–.12.
Answer: .214 x –.12 = – .02568
Solution:
.214 ; there are 3 digits after the decimal point
5 digits after the decimal point
x–.12 ; there are2 digits after the decimal point
428
2 14
00
.0 2 5 6 8 ; insert 0 in the extra space since there should be 5 digits after the decimal point
Product: –.02568 ; there are 5 digits after the decimal point
Example 7. There are 2.54 centimeters in an inch. How many centimeters are there in 9.5 inches?
Answer: Since 1 inch is equivalent to 2.54 centimeters, multiply 2.54 by 9.5.
Thus,
2.54 x 9.5
one digit after the decimal point
two digits after the decimal point
22
2.54
x 9.5 1 1
12 7 0
2 286
24.1 3 0
= 24.130 cm
three digits after the decimal point or
= 24.13 cm
Example 8. Rio buys 3 yards of red ribbons. Each yard costs PhP15.75. How much did Rio spend for the ribbons?
Answer: 15.75 x 3 = PhP 47.25
V. REFERENCES
K-12 Curriculum Guide Mathematics(Grade 1-10) Revised August 2016 from
Dep-Ed Mathematics 7 Learner’s Guide First Edition 2013 from
file:///D:/SCHOOL%20FILES/GRADE%207%20MODULE/MATHEMATICS%20QUARTER%201%20A
ND%202.pdf
file:///D:/DEPED%20NEW%20MODULES/GRADE%207%20MODULES/G7-Q1-M2.pdf
https://www.youtube.com/watch?v=Lpjz-FxKwvE
Monitored by:
_____________________________
Signature over printed name of Parent
Prepared by:
MARIEL JOY I. AZON
Mathematics Teacher
Checked by:
DAZIEL ANN C. MARAVILLO
JHS Academic Coordinator
BUHI ST. JOSEPH’S ACADEMY INC. (BSJAI)
San Pedro Buhi, Camarines Sur
S/Y 2021-2022
JUNIOR HIGH SCHOOL DEPARTMENT
Activity Sheet
ACTIVITY2SHEET
(Module 3)
MODULE
(3rd QUARTER)
NAME: __________________________________________ GRADE AND SECTION: GRADE 7-________________
MODULE NUMBER: 2
QUARTER: 3rd
SUBJECT: MATHEMATICS
DATE ACCOMPLISHED: _________________________
IV. ACTIVITIES
ACTIVITY 1: Math Meaning
Direction: Give the complete name of the following abbreviation.
1. Important Rules to Remember in Multiplying Fractions
2. Important Rules to Remember in Multiplying Decimals
ACTIVITY 2: Mathinik on Adding and Subtracting Decimals
Direction: Perform the indicated operations and express your answer in simplest form.
1. 1,902 × 21.36
4. 5.44 × 4.97
2. 45.08 × 30.545
5. 700.125× 678.891
3. 676.34× 78.003
ACTIVITY 3: Mathinik on Adding and Subtracting Fractions
Direction: Perform the indicated operations and express your answer in simplest form.
1.
2.
3.
2
3
×9
9
6
5
2
5
×
3
5
7
× 10
16
6
4. 24 × 12
5
2
5. 2 12 × 3