Week 8 Review: Practice Exercises and Problems

After learning how to solve number problems, let’s have some practice exercises.

Week 8 Review: Practice Exercises and Problems

1.) One number is 3 more than the other. Their sum is 27. What are the numbers?

2.) One number is 5 less than the other. Their sum is 51. What are the numbers?

3.) One number is 3 times the other number. Their sum is 48. What are the numbers?

4.) One number is 5 times the other number. Their difference is 52. What are the numbers?

5.) The sum of three numbers is 36. The second number is 5 more than the first number and the third number is 8 less than the first number. What are the three numbers?

6.) The sum of three numbers is 98. The second number is twice the first number and the third number twice the second number. What are the three numbers?
7.) One number is two more than thrice the other. Their sum is 26. What are the two numbers?

8.) One number is thrice the other. When 3 is added to the larger and 7 is subtracted from the smaller, their sum becomes 32. What are the two numbers?

9.) The sum of two positive consecutive numbers is 91. What are the two numbers?

10.) The sum of two positive consecutive EVEN integers is 66. What are the two numbers?

11. ) The sum of two positive consecutive ODD integers is 36. What are the two numbers?

12.) The sum of three positive consecutive ODD integers is 81. What are the three integers?

13.) The sum of the smallest and the largest of five positive consecutive integers is 108. What is the third integer?

14.) The average of four positive consecutive EVEN integers is 19. What is the largest integer?

15.) The average of seven positive consecutive integers is 31. What is the smallest integer?

Enjoy solving!

PCSR REVIEW SERIES WEEK 8: Number Problems

This is what everybody has been waiting for. After learning all the basic math from Week 1 to 7, we are now ready to solve some problems. Let’s start with some Number Word Problems. Read the articles below and watch the videos and later, we are going to have some practice exercises.

ARTICLES

How to Solve Consecutive Number Problems

VIDEOS

How to Solve Number Problems Mentally

How to Solve Number Problems 

Consecutive Number Problems

Enjoy learning!

Week 7 Review: Answers and Solutions

Below are the answers to the Week 7 Review Exercises and Problems. Since I cannot align the decimals using this platfrom, I just wrote the answers. You can check your answer using a calculator.

Exercise 1
a.) 1.2 + 3.02 + 4.003 (Answer: 8.223)
b.) 1.05 + 0.006 + 4.501 (Answer: 5.55)
c.) 12.1 – 4.25 (Answer: 7.85)
d.) 11.8 – 2.005 (Answer: 9.795)
e.) 12.1 – 21.53 + 2.563 (Answer: -6.867)

Exercise 2
a.) 3 × 0.41 (Answer: 1.23)
b.) 0.02 × 0.56 (Answer: 0.0112)
c.) 5.1 × 0.45 (Answer: 2.295)
d.) 5.8 × 4.25 (Answer: 24.65)
e.) 2.8 × 3.2 × 0.6 (Answer: 5.376)

Exercise 3
a.) 3 ÷ 0.2 (Answer: 15)
b.) 5.1 ÷ 0.3 (Answer: 17)
c.) 6.4 ÷ 4 (Answer: 1.6)
d.) 8.1 ÷ 0.009 (Answer: 900)
e.) 0.125 ÷ 0.25 (Answer: 0.5)

Problems

1.) Convert 0.25 to fraction. (Answer: 1/4)

2.) Convert 1/8 to decimal. (Answer: 0.125)

3.) Convert 3/4 to percent. (Answer: 75%)

4.) Convert 35% to fraction. (Answer: 7/20)

5.) Convert 20% to decimal. (Answer: 0.2)

Enjoy your review!

Week 7 Review: Practice Exercises and Problems

Now that we have learned how to operate with decimals and percents and how to convert from one representation to another, let’s have some exercises.

Exercise 1
a.) 1.2 + 3.02 + 4.003
b.) 1.05 + 0.006 + 4.501
c.) 12.1 – 4.25
d.) 11.8 – 2.005
e.) 12.1 – 21.53 + 2.563

Exercise 2
a.) 3 × 0.41
b.) 0.02 × 0.56
c.) 5.1 × 0.45
d.) 5.8 × 4.25
e.) 2.8 × 3.2 × 0.6

Exercise 3
a.) 3 ÷ 0.2
b.) 5.1 ÷ 0.3
c.) 6.4 ÷ 4
d.) 8.1 ÷ 0.009
e.) 0.125 ÷ 0.25

Problems

1.) Convert 0.25 to fraction.

2.) Convert 1/8 to decimal.

3.) Convert 3/4 to percent.

4.) Convert 35% to fraction.

5.) Convert 20% to decimal.

Enjoy your review!

PCSR REVIEW SERIES WEEK 7: Conversion of Decimals, Percent, and Fractions Operations

After learning about solving quations, let’s learn about operations on decimals. Let’s also learn the conversion among decimals, fractions, and percent. Below are the articles and videos about these topics. Exercises and problems will be posted later.

ARTICLES

Operations on Decimals

Conversion

YOUTUBE VIDEOS

Conversion

Enjoy!

Week 6 Review: Answers and Solutions

PCSR WEEK 6 Review: Solving Equations
Practice Exercise: Find the value of x.
1.) x + 5 = 8 => x = 8 – 5 => x = 3
2.) x – 3 = 6 => x = 6 + 3 => x = 9
3.) x + 8 = 0 => x = 0 – 8 => x = -8
4.) 4x = 12 => x = 12/4 => x = 3
5.) x/2 = -6 => x = -6(2) => x = -12

PCSR WEEK 6 Review: Solving Equations. In each equation, find the value of x.
1.) 2x – 1 = 5

2x = 5 + 1
2x = 6
x = 6/2
x = 3

2.) x – 12 = – 2x

x + 2x = 12
3x = 12
x = 12/3
x = 4

3.) x + 6 = 3x – 5

x – 3x = -5 – 6
-2x = -11
x = -11/-2
x = 11/2 or 5 1/2

4.) 5x + 12 = 3x – 6

5x – 3x = -6 – 12
2x = -18
x = -18/2
x = -9

5.) 2(5 – x) = 13

By distributive property, (2)(5) – (2)(x) = 13
10 – 2x = 13
-2x = 13 – 10
-2x = 3
x = 3/(-2)
x = -1 1/2

6.) 3(x + 8) = 15 + 6x

(3)(x) + (3)(8) = 15 + 6x
3x + 24 = 15 + 6x
3x – 6x = 15 – 24
-3x = -9
x = -9/-3
x = 9/3 or 3

7.) -2(3x – 4) = 2(1 – x)

(-2)(3x) – (-2)(4) =(2)(1) -(2)(x)
-6x – (-8) = 2 – 2x
-6x + 8 = 2 – 2x
-6x + 2x = 2 – 8
-4x = – 6
x = -6/(-4)
x = 6/4 or 3/2 or 1 1/2

8.) 4(x + 2) – 5 = x + 6

4(x) + 4(2) – 5 = x + 6
4x + 8 – 5 = x + 6
4x + 3 = x + 6
4x – x = 6 – 3
3x = 3
x = 3/3 or 1

9.) 3x/4 = 18

3x = 18(4)
3x = 72
x = 72/3
x = 24

10.) x/4 + 6 = 16

x/4 = 16 – 6
x/4 = 10
x = 10(4)
x = 40

11.) x/2 – 7 = 5 – 2x

To eliminate the fraction, we multiply both sides of the equation by 2.
2(x/2 – 7) = 2(5 – 2x)
2(x/2) – 2(7) = 2(5) – 2(2x)
x – 14 = 10 – 4x
x + 4x = 10 + 14
5x = 24
x = 24/5 or 4 4/5

12.) (x + 5)/2 = x – 3

To eliminate the fraction, we multiply both sides of the equation by 2.

2[(x + 5)/2] = 2(x – 3)
x + 5 = 2(x) – 2(3)
x + 5 = 2x – 6
x – 2x = -6 – 5
-x = -11
x = -11/-1
x = 11

13.) (2x – 3)/2 = (x + 2)/3

To eliminate the fraction, we multiply both sides of the equation by the LCM of 2 and 3 which is 6.

6[(2x – 3)/2] = 6[(x + 2)/3]
(6/2) (2x – 3) = (6/3) (x + 2)
(3)(2x – 3) = (2)(x + 2)
(3)(2x) – (3)(3) = (2)(x) + (2)(2)
6x – 9 = 2x + 4
6x – 2x = 4 + 9
4x = 13
x = 13/4
x = 3 1/4
14.) 8 – (x + 3)/4 = (x + 8)

4(8) – 4[(x + 3)/4] = 4(x + 8)
(32) – (x + 3) = (4)(x) + (4)(8)
32 – x – 3 = 4x + 32
29 – x = 4x + 32
-x – 4x = 32 – 29
-5x = 3
x = 3/(-5)
x = – 3/5

15.) 3(x -9)/4 = 2(x + 6)/5

[(3)(x) – (3)(9)]/4 = [(2)(x) + (2)(6)]/5
(3x – 27)/4 = (2x + 12)/5

To eliminate the fraction, we multiply both sides of the equation by the LCM of 2 and 3 which is 6.

20 [(3x – 27)/4 = (2x + 12)/5]

(20/4)(3x – 27) = (20/5)(2x + 12)
5(3x – 27) = 4(2x + 12)
(5)(3x) – (5)(27) = (4)(2x) + (4)(12)
15x – 135 = 8x + 48
15x – 8x = 48 + 135
7x = 183
x = 183/7 or 26 1/7

Week 6 Review: Practice Exercises and Problems

PCSR WEEK 6 Review: Solving Equations
Practice Exercise: Find the value of x.
1.) x + 5 = 8
2.) x – 3 = 6
3.) x + 8 = 0
4.) 4x = 12
5.) x/2 = -6

Practice Problems
Find the value of x.

1.) 2x – 1 = 5

2.) x – 12 = – 2x

3.) x + 6 = 3x – 5

4.) 5x + 12 = 3x – 6

5.) 2(5 – x) = 13

6.) 3(x + 8) = 15 + 6x

7.) -2(3x – 4) = 2(1 – x)

8.) 4(x + 2) – 5 = x + 6

9.) 3x/4 = 18

10.) x/4 + 6 = 16

11.) x/2 – 7 = 5 – 2x

12.) (x + 5)/2 = x – 3

13.) (2x – 3)/2 = (x + 2)/3

14.) 8 – (x + 3)/4 = (x + 8)

15.) 3(x -9)/4 = 2(x + 6)/5

PCSR REVIEW SERIES WEEK 6: Solving Equations

Solving equations is the most important part of problem solving and algebra in general. In solving word problems, you will have to set up equations and solve for unknowns. Be sure to master this concept.

ARTICLES

VIDEOS (Taglish)

More videos

In the next post, we are going to answer some problems and exercises.

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