Week 2, Day 1: Basic Math

Question 1

What is PEMDAS stands for?

Answer 1

Parenthesis
Exponent
Multiply and Divide from left to right.
Add and Subtract from left to right.

Question 2

Answer this:
What is the value of 3+6×2.

A. 18
B. 15
C. 12
D. 9

Answer 2

B. 15

Solution:

Multiply first: 6×2=12
Then add: 3+12=15

Question 3

Find the value of 12−(6÷3+2)×2.

Choices:
A. 4
B. 6
C. 8
D. 10

Answer 3

A. 4

12−(6÷3+2)×2
12− (2+ 2) x 2
12 − 4 x 2
12− 8 = 4

Question 4

Is a process of obtaining prime numbers that must be multiplied together in order to get a particular number.

Answer 4

Prime Factorization

Question 5

Is a number greater than 1 an d has 2 factors: 1 and itself.

Answer 5

Prime Number

Question 6

What are the prime factors of 52?

A. 11x2x3
B. 13x2x2
C. 23x2
D. 2x2x2x3

Answer 6

B. 13x2x2
13x2 = 26
26x2= 52

Question 7

What are the 2 conditions must be met in prime factorization based on the previous question?

Answer 7

1. When you multiply the numbers, it should be equal to 52.
2. All numbers multiplied resulting to 52.

Question 8

Question:
What are the prime factors of 90?

A. 2 × 3 × 3 × 5
B. 2 × 5 × 9
C. 3 × 3 × 5 × 5
D. 2 × 3 × 15

Answer 8

A. 2 × 3 × 3 × 5

2x3= 6
6x3=18
18x5=90

Question 9

Is a smallest number divisible by all of the numbers in a set.

Answer 9

Least Common Multiple (LCM)

Question 10

Not a Question:

One technique in finding the LCM in a question is to look for the smallest number in the option that is divisible by all of the numbers in the question.

Another Tip:
From BOTTOM to TOP

Question 11

What is the least common multiple if 5 and 9?

A. 25
B. 40
C. 45
D. 50

Answer 11

C. 45

Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45

Multiples of 9:
9, 18, 27, 36, 45

Question 12

What is the least common multiple (LCM) of 125 and 150?

A. 250
B. 300
C. 450
D. 750

Answer 12

D. 750

Multiples of 125: 125, 250, 375, 500, 625, 750

Multiples of 150: 150, 300, 450, 600, 750

Question 13

Is the highest number that divides exactly two or more numbers.

Answer 13

Greatest Common Factor (GCF)

Question 14

Not a question:

One technique in finding a GCF in a question is find the biggest number in the option.

Tip: TOP to BOTTOM

Question 15

What is the GCF of 36 and 18?

A. 18
B. 3
C. 9
D. 6

Answer 15

A. 18

Solution:
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18

Factors of 18:
1, 2, 3, 6, 9, 18

The greatest common factor is 18.

Question 16

What is the greatest common factor (GCF) of 48 and 60?

Choices:
A. 6
B. 12
C. 24
D. 18

Answer 16

B. 12

Solution:

Factors of 48:
1, 2, 3, 4, 6, 8, 12

Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12

The greatest common factor is 12.

Question 17

Two streetlights blink at different intervals. One blinks every 18 seconds, and the other blinks every 24 seconds. After how many seconds will they blink together again?

Choices:
A. 72
B. 108
C. 144
D. 96

Answer 17

A. 72

Solution:
Find the LCM of 18 and 24.

Multiples of 18:
18, 36, 54, 72, 90, 108…

Multiples of 24:
24, 48, 72, 96…

The smallest common multiple is 72 seconds.

Question 18

A teacher has 84 pencils and 126 erasers. She wants to make packs so that each pack has the same number of items and there are no items left over. What is the greatest number of items in each pack?

A. 21
B. 42
C. 18
D. 36

Answer 18

B. 42

Solution:

Find the GCF of 84 and 126.

Factors of 84:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42

Factors of 126:
1, 2, 3, 6, 7, 9, 14, 18, 21, 42

The largest common factor is 42.

Question 19

Is a comparison of two quantities by division.

Answer 19

Ratio

Question 20

How can write ratio in different ways?

Answer 20

A is to B - in words
A:B - in colon form
A/B - in fraction form

Question 21

Note:
Always reduce the ratio in lowest terms.

Question 22

In a basket, there are 12 apples and 8 oranges. What is the ratio of apples to oranges?

A. 2:3
B. 3:2
C. 12:8
D. 4:3

Answer 22

B. 3:2

Solution:

Write the ratio of apples to oranges: 12:8

Simplify by dividing both numbers by their GCF (4): 12 ÷ 4 : 8 ÷ 4 = 3:2

Question 24

A warehouse has 360 boxes of apples and 240 boxes of oranges. What is the ratio of apples to oranges?

Choices:
A. 3:2
B. 2:3
C. 360:240
D. 240:360

Answer 24

A. 3:2

Solution:

Write the ratio of apples to oranges:
360:240

Simplify by dividing both numbers by their GCF (120): 360 ÷ 120 : 240 ÷ 120 = 3:2

Question 25

It is an equality of two ratios.

Answer 25

Proportion

Question 26

Example:

Answer 26

6/9 = 8/12

Question 27

What are the types of proportion?

Answer 27

1. Direct Proportion 2. Inverse Proportion 3. Partitive Proportion

Question 28

Both quantity increase or both decrease.

Answer 28

Direct Proportion

Question 29

Formula:​ ​

Answer 29

x1/y1 = x2/y2 Cross multiply. Then divide both sides.

Question 30

A printer prints 120 pages in 4 hours. How many pages will it print in 6 hours? Choices: A. 150 B. 160 C. 180 D. 200

Answer 30

C. 180 Solution: Cross multiply: 4/120 = 6/ x 4 times x = 4x 120 x 6 =720 or 4x = 720 Divide both sides by 4: 4x/ 4 = 1 or x 720/4 = 180 x = 180

Question 31

One quantity increases, the other decreases and vice versa.

Answer 31

Inverse Proportion

Question 32

Formula:

Answer 32

(x1) (y1) = (x2) (y2) Multiply the divide both sides.

Question 33

5 workers can complete a job in 12 days. How many days will 8 workers take to complete the same job? A. 6 B. 7.5 C. 8 D. 9

Answer 33

B. 7.5 days Solution: Multiply (5) (12) = (8) (x) 60 = 8x Divide: 8x/8 = 1 or x 60/8 = 7.5 x = 7.5

Question 34

One quantity is being partitioned into different proportions.

Answer 34

Partitive Porportion

Question 35

Question: A sum of 360 pesos is divided among 3 friends in the ratio 2:3:5. How much does the friend with the largest share get? A. 72 B. 108 C. 180 D. 200

Answer 35

c> 180 Solution: Given: 360 Total ratio = 2 + 3 + 5 = 10 Largest share = 5 Value of the largest share: 360 x 5 = 1800 1800/ 10 = 180​ =180 pesos