This document defines key mathematical terms related to subsets, properties, ratios, proportions, percentages, and interest. It includes: - Definitions of natural numbers, whole numbers, and integers as subsets of numbers - Explanations of closure, commutative, associative, and identity properties - How to calculate ratios, rates, and use proportions - Conversions between decimals, fractions, and percentages - A formula for calculating simple interest (I=PRT) and an example using it The document provides concise explanations and examples of fundamental mathematical concepts.

1. Prepared by
RONALDO Z. ONGOTAN

5. Subsets Definition
Natural Numbers (N)  Consist of the numbers 1, 2,3…
Whole Numbers (W)  Consist of the Natural numbers zero
Integers  Consist of the natural numbers, their
negatives, and zero

7. Property Definition Examples
Closure Property
 When we add or multiply any element in a set of
numbers, the sum or product is a unique real
number which belongs to that same set.
14+25+44+52+135
23×14×10= 3 220
Commutative
Property
 States that changing the position of the addends or
the factors does not affect the sum or the product.
33×10=10+33
18×9= 9×18
Associative Property  The sum of any number and zero
Addition is the same number.
•0 is the identity
(5+6) + 7=5+ (6+7)
2× (4×6)= (2×4)×6
Identity Property The product of any number and one is
Multiplication the same number.
1 is the identity.
512×1 = 512
Distributive Property
of Multiplication over
Addition/Subtraction
 states that multiplication distributes over addition
and subtraction
7(9+12)=7(9)+7(12)

19. Addition and Subtraction
Of Similar Fractions:
Just add/subtract the numerators and
copy the denominator.
Examples:
2 + 4 = 6
7 7 7
Of Dissimilar Fractions:
Convert the fractions first to similar fractions. Then
add/subtract the numerators and keep the denominators.
Reduce to lowest terms if necessary.

22. a) Addition and Subtraction
b) Multiplication
c) Division

23. Ratio Rate Proportion
A comparison of two or
more amounts or
quantities, such as a and b,
can be expressed in the
following equivalent ways:
a:b, a/b, a
b
Refers to a ratio whose
two amounts represent
different quantities
Examples:
35mi/h’ 5m/s
An equation or statement
that expresses the
equality of two ratios.
May be expressed as:
1) a =c, or
b d
1) a: b = c:d
In each form, b and c are
called means, and a and d
are called extremes.

24. As one quantity increases, the other also increases.
As one quantity increases, the other quantity decreases, and
vice versa.
 One quantity is being partitioned into different proportions.
Example:
A piece of wood 150cm long is cut in the ration 2:3:5. Find the
measure of each part.

25. When working with scale models, the scale is often given as the ratio:
Example:
If the scale model of a boat measures 6 inches and the model has a
scale of 1:20, what is the actual measurement of the boat?
Solution: model length = 1 = 6
Actual length 20 x
1 = 6
20 x
x=120
Answer: The actual measurement of the boat is 120 in., or 10 ft.

26. •When figures have corresponding sides that are in proportion
with one another and corresponding angles with the same measure,
the figures are similar.
•Proportion can be used to determine that figures are similar, and
calculate the missing part/s of known similar figures.
Example:
Find the missing side of the larger triangle.
A
10 cm
B
C
6 cm
x
15 cm
D
E F
Solution:
AB = BC 10 = 6
DE EF 15 x
10x = 90
x = 9

27. •Literally meaning ‘per hundred’, it refers to a special ratio that
compares a numerical quantity to 100.
•CONVERSATIONS
Between Decimals and Percent Between Fractions and Percents
A. Percent to Decimal
 Remove the percent symbol (%) and
move the decimal point two places to
the left.
A. Decimal Percent
1. Multiply the decimal by 100; or
2. Move the decimal point two places to
the right and write a percent symbol.
A. Percent to Fraction
 Use the proportion x = a, and cross
multiply
100 b
to solved for the variable x.
A. Fraction to Percent
 Remove the percent symbol (%) and
multiply the number by 1
100

28. To increase a number by a certain percent, (1) add
100% to the given percent, (2) convert
the sum to a decimal, and (3) multiply the number by
that decimal.
Example: increase 40 by 45%
Solution: 45% + 100% = 145% =1.45
40 x 1.45 = 58

29. I = Prt I interest charged or paid out
P principle amount that is saved or borrowed
r percentage rate written as a decimal
t time in years

30. If Cedric borrows P15,000 at an interest rate
of 17% for 18 months, how much will he have paid
in simple interest at the end of the 18 months?
Solution:
I=Prt
I=(P15,000) (17%) (1.5)
I= P3,825
P P15,000
r 17%
t 18 months = 1.5 years