Chapter 3- Learning Outcome 1_Mathematics for Technologists

21st
Century Mathematics for
the Industrial Technology
Learners: Automotive
Technology
BABY 'RLENE I. BAYOC

Fractions,
Ratio and Proportion
Chapter
III
21st
Century Mathematics for the Industrial Technology Learners: Automotive Technology

CHAPTER III: Fractions, Ratio and Proportion
Learning
Outcome 1:
Defined, compared, and simplified
common fractions and perform
arithmetic and conversion with
fractions;

A fraction is defined as part of an entire object. Formally defined,
if p and q are algebraic expressions, the quotient, or ratio, p/q is
called a fractional expression or a fraction with numerator p and
denominator q, read as p over q. Note that the denominator of a
fraction cannot be zero. If q=0, the expression p/q is not defined.
Therefore, whenever we use a factional expression, we shall
automatically assume that the denominator is nonzero.
Fractions
Define, compare, and
simplify common
fractions

Fractions
A fraction is proper when the numerator is less than the
denominator or improper when the numerator is equal or greater than
the denominator also similar (like) fractions if they have the same
denominator or dissimilar (unlike) fractions when they different
denominator. Two fractions are equivalent fraction if they have the
same value. To compare similar fractions, the fraction with the
greatest numerator is the largest fraction and the fraction with the
least numerator is the smallest fraction. When comparing dissimilar
fractions, we have different solutions. First is by division; second is by
making them similar fractions by the LCD (least common
denominator); and third is by cross multiplication.
Fractions
Define, compare, and
simplify common
fractions

Solutions in Comparing Dissimilar Fractions.

There are rules that we have to follow when applying the four fundamental
operations with fractions, likewise in conversion of fractions to decimals and
percent.
1. Adding/Subtracting Fractions with the Same Denominator:
To add/subtract two fractions with the same denominator, add/subtract the
numerators for the numeratorand copy the denominator.
Example 1. 3/11 + 2/11
= (3+2)/11
= 5/11
Example 2. 3/11 – 2/11
= (3 -
2)/11
= 1/11

2. Adding/subtracting Fractions with Different Denominators:
To Add/subtract Fractions with different denominators, find the Least
Common Denominator (LCD) of the fractions. Rename the fractions to
have the LCD. Add/subtract the numerators of the fractions. Simplify
the fraction until it is in its simplest form.
Example 1. 3/5 + 2/15
= (9+2)/15
= 11/15
Example 2. 3/8 - 2/12
= (9 -
4)/24
= 5/24

3. Multiplying fractions: To multiply fractions, multiply the
numerators then multiply the denominators. Then simplify if
possible.
Example 1. i/r x f/z
= if/rz
Example 2. 2/8 x 5/12
= 10/96
= 5/48

4. Dividing fractions: To divide fractions, multiply the extremes over the means or
use the reciprocal of the divisor then proceed to multiplication. Simplify your final
answer.
Note that before multiplying or dividing fractional expressions in general, try to factor
the numerators and denominators completely to reveal any factors that can be
canceled.
Fractions
Define, compare, and simplify common
fractions
Example 1. i/r ÷ f/z
= iz/rf
Example 2. i/r ÷ f/z
= i/r x z/f
= iz/rf

5. Converting Fractions to Decimals:
A. The simplest method is to use a calculator by just dividing the numerator by the
denominator.
B. The method used when there is no calculator is by long division.
C. Another Method is to make the denominator equal to 10, 100, 1000 ...
Step 1: Find a number that when you multiply your denominator by that number then
your denominator becomes 10, 100, 1000, .... or any 1 followed by 0’s.
Step 2: Multiply both the numerator and the denominator by that number.
Step 3. Then count the number of zero/es in your denominator and it would be
the number of decimal places in your numerator.
Example 1. 3/5 = 3/5 x 2/2 = 6/10 = 0.6
Example 2. 50/250 = 50/250 x 4/4 = 200/1000 = 0.2

5. Converting Fractions to Decimals:
The diagram represents the
conversion of fractions to decimals,
decimals to percent, percent to
fractions and percent to decimals.
Note that if we convert fractions
to percent, we have to convert it first
to decimals.
For decimals to fractions,
convert it first to percent then to
fraction. There is other way to do this,
write it the way you read it.

6. Converting recurring decimals to fractions:
Step 1: Let x = recurring decimal in expanded form.
Step 2: Let the number of recurring digits = n.
Step 3: Multiply recurring decimal by 10n.
Step 4: Subtract (1) from (3) to eliminate the recurring part.
Step 5: Solve for x, expressing your answer as a fraction in its simplest form.
Examples of recurring decimal are 1/3 = 0.333333..., 1/7 = 0.142857142857...
A recurring decimal exists when decimal numbers repeat forever.

6. Converting recurring decimals to fractions:
Example 1. Convert 0.111111…
to fraction.
Solution: Let x = 0.1111111… = 0.1̅
10 x = 1.1̅
10x – x = 1.1̅ - 0.1̅
9x = 1
X = 1/9
Example 2. Convert 0.1212121212…
to fraction.
Solution: Let x = 0.1212121212… = 0.1̅2̅
100x = 12.1̅2̅
100x – x = 12.1̅2̅ - 0.1̅2̅
99x = 12
x = 12/99 or 4/33.

REFERENCES
https://www.emathzone.com/tutorials/algebra/multiplication-and-division-of-
fractions.html#ixzz6K8M3Cn7b
https://www.emathzone.com/tutorials/algebra/addition-and-subtraction-of-
fractions.html#ixzz6K8LmeWJl
https://www.cimt.org.uk/projects/mepres/book7/bk7i17/bk7_17i2.htm
https://www.mathsisfun.com/converting-fractions-decimals.html
https://www.aaamath.com/fra16_x2.htm
https://www.emathzone.com/tutorials/algebra/fractions.html#ixzz6K8LMdp5x
https://www.khanacademy.org/math/arithmetic/fraction-arithmetic
https://www.onlinemathlearning.com/recurring-decimals-fractions.html

Thank you

Chapter 3- Learning Outcome 1_Mathematics for Technologists

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