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.

Week 5 Review Answers and Solutions

This is the full solutions for the problems and exercises about operations on integers, order of operations, and PEMDAS rules.

Practice Exercises 1

a.) 12 + (-4) = 8
b.) (-9) + 3 = – 6
c.) (-7) + (- 5) = -12
d.) 8 + 3 + (-11) = (8+3) + (-11) = (11) + (-11) = 0
e.) 6 + (-10) + (-2) = 6 + (-10 + -2) = 6 + (-12) = -6

Practice Exercises 2

a.) 3 – 5 = (3) + (-5) = -2
b.) -9 – 4 = (-9) + (-4) = -13
c.) (-7) – (- 8) = (-7) + (8) = 1
d.) – 2 – 6 = (-2) + (-6) = -8
e.) 1 – (-10) = (1) + (10) = 11

Practice Exercises 3

a.) 4 × (- 5) = -20
b.) (-2) × (- 4) = 8
c.) 6 × (- 3) = -18
d.) 8 × 2 × (-1) = -16
e.) (-3) × (2) × (-7) = 42

Practice Exercises 4
a.)-20 ÷ 4 = -5
b.) 18 ÷ (- 6) = -3
c.) (-16) ÷ (- 2) = 8
d.) 0 ÷ 8 = 0
e.) 9 ÷ 3 = 3

1.) 2 + 3 × 5

2 + 3 × 5
= 2 + 15
= 17

2.) (2 + 3) × 5

(2 + 3) × 5 = (5) × 5
= 25

3.) 3 × (-3) + 4 × (-2)

= 3× (-3) + 4× (-2)
= (-9) + (-8)
= -17

4.) 3(5^2 – 8)

3(5 × 5 – 8)
= 3(25 – 8)
= 3(17)
= 51

5.)  2(5 – 8)^2
= 2(-3)^2
= 2(-3 × -3)
= 2(9)
= 18

6.) 16 + (-4) + 12 + (-8 x 3)

= 16 + (-4) + 12 + (-24)
= (16 + 12) + (-4 + -24)
= (28) + (-28)
= 0

7.) (3^2 + 2^2)^2 = ?

= (3 × 3 +2× 2)^2
= (9 + 4)^2
= (13)^2
= 13 × 13
= 169

8.) 6 + 3 × 2 – 5 = ?

= 6 + (3 × 2) – 5
= 6 + 6 – 5
= 12 – 5
= 7

9.) 8 – 12(3 – 4) + (-5 × 2)

= 8 – 12(3 – 4) + (-5 × 2)
= 8 – 12(-1) + (-10)
= 8 – (-12) + (-10)
= 20 + (-10)
= 10

10.) 7 + 3 × (-5) – 9 / 3 = ?

= 7 + 3 × (-5) – 9/3
= 7 + (-15) – 3
= 7 + (-18)
= -11

Week 5 Review: Practice Exercises and Problems

In the previous post, we learned about operations on integers, order of operations, and PEMDAS rules. Below are the exercises and problems about these topics.

PCSR WEEK 5 Review: Operations on Integers

Practice Exercises 1

a.) 12 + (-4)
b.) (-9) + 3
c.) (-7) + (- 5)
d.) 8 + 3 + (-11)
e.) 6 + (-10) + (-2)

Practice Exercises 2

a.) 3 – 5
b.) -9 – 4
c.) (-7) – (- 8)
d.) – 2 – 6
e.) 1 – (-10)

Practice Exercises 3

a.) 4 × (- 5)
b.) (-2) × (- 4)
c.) (6) × (- 3)
d.) 8 × 2 × (-1)
e.) (-3) × (2) × (-7)

Practice Exercises 4
a.)-20 ÷ 4
b.) 18 ÷ (- 6)
c.) (-16) ÷ (- 2)
d.) 0 ÷ 8
e.) 9 ÷ 3

Practice Problems

1.) 2 + 3 × 5
2.) (2 + 3) × 5
3.) 3 x (-3) + 4 ×(-2)
4.) 3(5^2 - 8)
5.) 2(5 - 8)^2
6.) 16 + (-4) + 12 + (-8 × 3)
7.) (3^2 + 2^2)^2
8.) 6 + 3 × 2 – 5
9.) 8 – 12(3 – 4) + (-5 × 2)
10.) 7 + 3 × (-5) – 9 / 3

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