2. WHAT IS 2 + 3 X 4 – 9 ÷ (5 - 2)
PEMDAS (Parenthesis, Exponents, Multiplication & Division, Addition &
Subtraction)
2 + 3 x 4 – 9 ÷ (5 -
2)
2 + 3 x 4 – 9 ÷ (3) Simplify the terms inside the
parenthesis
2 + 12 – 9 ÷ (3) Multiplication or Division from left
to right
2 + 12 – 3 Multiplication or Division from left
to right
14 – 3 Addition or Subtraction from left to
right
11 Addition or Subtraction from left to
right
2 + 3 x 4 – 9 ÷ (5 -
2)
2 + 3 x 4 – 9 ÷ (3)
2 + 12 – 9 ÷ (3)
2 + 12 – 3
3. WHICH OF THE FOLLOWING IS DIVISIBLE BY 2,
4, AND 5?
A. 144
B. 1280
C. 2205
D. 27225
4. WHICH OF THE FOLLOWING IS DIVISIBLE BY 6?
I. 479112 II. 792114 III. 749121 IV.
912714
A. I ONLY
B. I AND II ONLY
C. I, II AND IV
D. I, II, III, AND IV
5. WHICH OF THE FOLLOWING IS A PRIME
NUMBER?
A. 2
B. 4
C. 6
D. 9
6. WHAT IS THE SUM OF COMPOSITE NUMBERS
BETWEEN 1 AND 10?
• 27
• 15
• 19
• 14
7. WHAT IS THE PRIME FACTORIZATION OF 75?
A. 3 X 5 X 7
B. 32 X 7
C. 5 X 15
D. 3 X 52
8. FIND THE LEAST COMMON MULTIPLE (LCM)
OF 12 AND 28.
A. 42
B. 84
C. 7
D. 64
9. FIND THE LEAST COMMON MULTIPLE (LCM) OF 12
AND 28.
12 = 4 x 3 = 2 x 2
x 3
Get the prime factors of each
number
28 = 4 x 7 = 2 x 2 x
7 = 2 x 2 x 3 x 7
Align the common prime factors of
each number
Multiply the factors
= 4 x 21 = 84
10. FIND THE GREATEST COMMON FACTOR (GCF)
OF 30, 40, AND 65.
A. 4
B. 5
C. 6
D. 10
11. FIND THE GREATEST COMMON FACTOR (GCF) OF
30, 40, AND 65.
30 = 10 x 3 = 5 x 2
x 3
Get the prime factors of each
number
40 = 10 x 4 = 5 x 2 x
2
65 = 5 x 13= 5 x
13
Align the common prime factors of
each number
Determine the factors common to the
numbers
12. Ronald and Tim both did their laundry today. Ronald does
laundry every 6 days and Tim does laundry every 9 days.
How many days will it be until Ronald and Tim both do
laundry on the same day again?
Multiples of 6 = 6, 12, 18, 24,
30
Multiples of 9 = 9, 18, 27, 36,
45
6 = 2 x 3
Finding the LCM
9 = 3 x 3
Listing the Multiples
= 2 x 3 x 3 = 18
13. There are 28 girls and 42 boys from 6 sections registered to
participate in a science quiz bee. The quiz master divided the
participants into teams with the same number of boys and
girls on each team. How many teams will there be? How many
boys and girls are on each team?
A. 7 TEAMS WITH 4 GIRLS AND 6 BOYS IN EACH TEAM
B. 7 TEAMS WITH 6 GIRLS AND 4 BOYS IN EACH TEAM
C. 8 TEAMS WITH 4 GIRLS AND 6 BOYS IN EACH TEAM
D. 8 TEAMS WITH 6 GIRLS AND 4 BOYS IN EACH TEAM
14. There are 28 girls and 42 boys from 6 sections registered to
participate in a science quiz bee. The quiz master divided the
participants into teams with the same number of boys and
girls on each team. How many teams will there be? How many
boys and girls are on each team?
28 = 4 x 7 = 2 x 2
x 7
42 = 6 x 7 = 2 x 3
x 7
Find the GCF
Divide both
numbers by 7
28 ÷7 = 4
42 ÷7 = 6
15. Carina has 24 apples, 36 bundles of bananas and 12 lemons.
She wants to put all of the fruit into plastic containers, each
with the same number of pieces of fruit in it. What is the
greatest number of pieces of fruit she can put in each plastic
container?
A. 6
B. 8
C. 12
D. 18
Find the GCF
24 = 4 x 6 = 2 x 2 x 2 x 3
36 = 6 x 6 = 2 x 2 x 3 x 3
12 = 2 x 6 = 2 x 2 x 3
12 = 2 x 6 = 2 x 2 x 3 = 12
16. The 3 bells ring at the factory at intervals of 3, 6
and 10 minutes simultaneously starting at 8:00 in
the morning. At what time will the three bells ring
together at the same time?
A. 8:15
B. 8:24
C. 8:30
D. 8:36
Find the LCM
3 = 3 x 1
6 = 2 x 3
10 = 2 x 5
= 2 x 3 x 5 = 30 min
8:00 + 30 min = 8:30
17. Recently the men’s basketball team at the University of
Maryland won 24 of the 36 games they played. What fraction
represents the number of games won?
A. 1/3
B. 2/3
C. 1/2
D. 6/8
2
4
3
6
=24÷6
36÷6
= 4÷2
6÷2
= 2
3
Reduce to lowest term by dividing the
numerator and denominator by the
same factors
18. There are 60 minutes in 1 hour. What fraction of an hour
is 15 minutes?
A. 1/2
B. 1/3
C. 1/4
D. 1/15
1
5
6
0
=15÷5
60 ÷5
= 3÷3
12÷
3
= 1
4
Reduce to lowest term by dividing the
numerator and denominator by the
same factors
19. Which of the following is arranged in increasing order?
A. 1/2, 2/5, 3/7,
4/9
B. 1/8, 3/7, 2/3,
4/5
C. 2/9, 5/7, 3/4,
7/8
D. 5/6, 3/5, 2/7,
1/4
2
9
<
5
7
3
4
14 45
<
5
7
20 21
<
<
3
4
7
8
24 28
<
<
20. WHAT IS 3/5 OF 1/3 OF 15?
A. 3
B. 6
C. 9
D. 15
OF implies
multiplication
3
5
1
3
1
5
1
x x = 3 x 1 x
15
5 x 3 x
1
1
1
1
3
=
3
1
= 3
Cancel common
factors before
multiplying
You can cancel only
numbers from opposite
side of the fraction bar
21. WHAT IS THE QUOTIENT OF 4/5 AND 16/25?
A. 5/4
B. 4/5
C. 20/25
D. 4/25
QUOTIENT implies division
4
5
÷1
6
2
5
= 4
5
2
5
1
6
x
Write the reciprocal of the divisor
Proceed to multiplication
= 4 x 25
5 x 16
1
4
Cancel common factors before multiplying
1
5
= 5
4
22. If 6/7 yard of material is needed to make A
blanket, how many blankets can be made from 12
yards of material?
A. 1/7
B. 2/7
C. 14
D. 7
The problem requires division
1
2
1
÷ 6
7
= 1
2
1
x 7
6
12 x 7
1 x 6
=
1
2
= 1
4
1
= 𝟏𝟒
23. WHAT IS THE PRODUCT OF 2 ½ AND 3?
A. 5 ½
B. 6 ½
C. 7 ½
D. 7 1/3
2
1
2
𝑥 3 =
Product implies multiplication
Change the mixed fraction to improper
fraction
2
1
2
𝑥 3 =
5
2
𝑥
3
1
=
5 𝑥 3
2 𝑥 1
= 7
1
2
15
2
=
24. A recipe calls for 2/3 cup of flour and ¾ cup
of sugar. What is the total amount of flour
and sugar called for in the recipe?
A. 5/7 CUPS
B. 1 5/12
CUPS
C. 1 7/12
CUPS
D. 1 ¾ CUPS
TOTAL implies
ADDITION
2
3
+ 3
4
= 8
12
+ 9
12
Get the LCD (lowest common denominator)
Get the equivalent fractions using
the LCD
= 17
12
= 1
5
12
25. A pair of jeans is 32 ½ inches long. How long
are the jeans after they have been washed if
they shrink 1 1/3 inches?
A. 30 1/6 INCHES
B. 31 1/6 INCHES
C. 32 1/3 INCHES
D. 33 5/6 INCHES
26. A clothing manufacturer has two rolls of
cloth. One roll is 35 ½ yards, and the other is
62 5/8 yards. What is the total number of
yards in the two rolls?
A. 97 6/10
B. 97 1/8
C. 98 1/8
D. 98 6/10
27. Find the difference between 13 1/6 and 12
5/8.
A. 1 ½
B. 1 11/24
C. 1 13/24
D. 13/24
28. Which is the fraction equivalent of 0.625?
A. 3/7
B. 4/5
C. 5/7
D. 5/8
0.62
5
= 625
1000
= 625÷
25
1000÷
25
= 25÷ 5
40÷ 5
5
8
=
29. SUBTRACT 0.194 FROM 82
A. 81.906
B. 82.194
C. 81.306
D. 81.806
82. 0 0
00. 1 9
4
1 9 91
81. 8 0
6
30. THE MASS OF A JAR OF SUGAR IS 1.9 KG.
WHAT IS THE TOTAL MASS OF 13 JARS OF
SUGAR?
A. 0.247
B. 2.47
C. 24.7
D. 247
31. Brad studied a total of 24.4 hours over a
period of four days. On average, how many
hours did. Brad study each day?
A. 4.2 HOURS
B. 5.3 HOURS
C. 6.1 HOURS
D. 7.4 HOURS
32. If each kilo of chicken cost Php 250.75, how
much does 3 ¼ kilos cost? Round to the
nearest hundredths.
A. 814.94
B. 814.95
C. 815.00
D. 815.94
33. What is the equivalent value of 3.4% in
decimal?
A. 0.0034
B. 0.034
C. 0.34
D. 3.4
DECIMA
L
PERCEN
T
3.4%
0 0 3.4%
0 .034
0 .0 3 4
34. What is the percent equivalent of 0.04?
A. 0.04%
B. 0.4%
C. 4%
D. 40%
35. WHAT IS THE FRACTION EQUIVALENT OF 2%?
A. 1/50
B. 2/50
C. 1/5
D. 2/5
36. WHAT IS THE FRACTION EQUIVALENT OF 2
¼%?
A. 9/400
B. 9/200
C. 2 ¼
D. 2 1/5
2
1
4
% =
9
4
% =
9
4
÷ 100 =
9
4
x
1
100
=
9
400
37. WHAT 3 3/4 IN PERCENT?
A. 0.375%
B. 3.75%
C. 37.5%
D. 375%
3
3
4
=
15
4
=
15
4
𝑥 100 =
15 𝑥 100
4
=
2
5
1
375
38. WHAT NUMBER IS 25% OF 32?
A. 4
B. 8
C. 12
D. 16
25% x 32 =
25
100
x 32 =
1
4
8
8
39. WHAT PERCENT OF 50 IS 5?
A. 5%
B. 10%
C. 15%
D. 20%
N% x 50 = 5
𝑁
100
x 50 = 5
50𝑁
100
= 5
𝑁 = 5x
100
50
𝑁 = 10
40. 10 IS 20% OF WHAT NUMBER?
A. 20
B. 40
C. 50
D. 100
10 = 20% x N
10 =
20
100
x N
10 x
100
20
= N
50 = N
41. On a 120-question test a student answered
90 correctly. What percent of the problems
did the student work correctly?
A. 60%
B. 70%
C. 75%
D. 80%
42. There are 3,200 students at a university. If
52% of them are female, how many female
students are there at the university?
A. 1646
B. 1466
C. 1664
D. 1644
43. If a person earns php240,000.00 a year and
gets a 10% increase in salary, what is the new
salary?
A. PHP
242,400.00
B. PHP
264,000.00
C. PHP
284,000.00
D. PHP
480,000.00
240,000 x 0.1 = 24,000
240,000
+ 24,000
264, 000
Method 1 Method 2
240,000 x 1.1 = 264,000
44. The enrolment in a certain school was 800 in
2020. In 2021, the enrolment in the same school
was 600. What is the percent decrease in the
enrolment from 2020 to 2021?
A. 15%
B. 25%
C. 33%
D. 75%
800 − 600
800
x 100
=
200
800
x 100
=
2
8
x 100
=
1
4
x 100
= 25%
45. During a clearance sale, a t-shirt that usually
sells for Php300 is marked “15% off.” What is
the sale price?
A. PHP 45
B. PHP 55
C. PHP 245
D. PHP 255
300 x 15%
300 x
15
100
3 x15 = 45
Discounted amount
300 − 45 = 255
Sale price
46. A pair of pants which was originally priced at Php
1,200 was sold at a discounted price of Php 900.
What is the discount rate for the pair of pants?
A. 20%
B. 25%
C. 30%
D. 75%
1200 − 900 = 300 Discounted amount
300
1200
=
3
12
=
1
4
= 0.25 = 25%
Discounted rate
47. The value of a cellphone depreciated to
29,400 pesos after 3 year. If the original
price is 42,000 pesos, by how many percent
has the value decreased?
A. 10.8%
B. 28%
C. 30%
D. 60%
48. Clarissa paid Php 1500 for a handbag that
was sold to her at a 25% discount. What is the
original price of the handbag?
A. PHP 1750
B. PHP 2000
C. PHP 2250
D. PHP 2500
P = B x
r
1500 = B x 75%
𝟏𝟓𝟎𝟎
𝟎.𝟕𝟓
=
𝑩 𝒙 𝟎.𝟕𝟓
𝟎.𝟕𝟓
𝟏𝟓𝟎𝟎
𝟎.𝟕𝟓
=
𝑩
𝟐𝟎𝟎𝟎 = 𝑩
49. A ribbon 72 meters long is cut into two pieces. If
the ratio of the lengths of the pieces is 3:6, how
long is the shorter piece?
A. 12
B. 18
C. 24
D. 48
72
m
=
72
9
= 8 𝑚 1 unit
= 8𝑥3 = 24𝑚 3 units
3
parts
6
parts
50. A motorcycle covers 112.5 km in 2.5 hours.
How far can he go in 1 ¾ hours?
A. 78.75 KM
B. 78.25 KM
C. 62.5 KM
D. 62.25 KM
112.5 ÷ 2.5 = 45
45 𝑥 1.75 = 78.75
51. A certain recipe calls for 6 eggs, 3
tablespoons of sugar, and 1 cup of water.
What is the ratio of sugar to egg?
A. 6:1
B. 2:3
C. 2:1
D. 1:2
suga
r
egg
to
3 : 6 Simplify to lowest
term
1 : 2 Note: the order
matters
52. DIVIDE 35 IN THE RATIO OF 2:5
A. 7:25
B. 7:35
C. 10:25
D. 14:35
Get the measurement for 1 unit
35/7 = 5 1 unit
2 : 5 Multiply the ratio by the measurement
per unit
x
5
x
5
10 : 25
53. The number of hours spent by drew studying for
his exams in Math, Science, and English is in the
ratio 5:3:2. If in total he spent 3 hours and 20
minutes, how much time did he spend studying
English?
A. 40 MINUTES
B. 1 HOUR
C. 1 HOUR AND 40
MINUTES
D. 20 MINUTES
Convert hours to minutes
3 x 60 + 20 = 180 + 20 = 200
200/10 = 20
Get the amount per unit
Multiply the per unit amount to the desired part
in the ratio
20 x 2 = 40
54. EXPRESS ¾ TO ¼ AS A RATIO.
A. 3 : 1
B. 1 : 3
C. 4 : 1
D. 1 : 4
3
4
÷
1
4
=
3
4
𝑥
4
1
=
3
1
55. A solution contains 8 pints of antifreeze and 5
pints of water. How many pints of water must be
added to 24 pints of antifreeze to get a solution
with the same concentration?
A. 12
B. 15
C. 18
D. 20
This is an example of direct
proportion
antifree
ze
to water
8 : 5
24 N
:
Solution number 2
8 : 5 = 24 :
N
5 x 24 =
8N 8
8
3
15 = N
56. The scale on a map indicates that 1 cm
corresponds to an actual distance of 50 km. Two
cities are 4.5 cm apart on the map. What is the
actual distance between the two cities?
A. 200 KM
B. 225 KM
C. 250 KM
D. 275 KM
57. The manager of Stuart siding company found that the
number of workers used to side a house varies inversely
with the number of hours needed to finish the job. If four
workers can side the house in 48 hours, how many hours
will it take 6 workers working at the same speed to do the
same job?
A. 32
B. 36
C. 42
D. 72
This is an example of indirect
proportion
Workers t
o
Tim
e
4 : 48
Workers t
o
Tim
e
6 : N
4 : 48 = 6 : N
4 x 48 = 6 x
N 6
6
8
4 x 8 =
N 32 = N
58. The number of students, N, is inversely proportional to
the time, T days, required to complete a project. It takes
12 students 20 days to complete a project. Find the
number of days it would take for 15 students to complete
the same project.
A. 12
B. 16
C. 25
D. 30
