Ysabelle's Algebra Post

Algebra

Algebra- branch of mathematics that involves expressions with variables

variable- a symbol which represents any unknown number

constant- integer in an Algebraic expression expression or equation

equation- only has one answer, has an equal sign

expression- has pattern, many answers

Steps to solve:

1. Isolate the variable.
2. Cancel the constant using zero pairs.
3. Balance by doing the same operations on each side.
4. Verify to check.

One-Step Equations

5) m+4=-12

Solution:

m+4=-12
m=-12-4
m=-16

Verify:

m+4=-12
-16+4=-12
-12=-12

9) v-15=-27

Solution:

v-15=-27
v=-27+15
v=-12

Verify:

v-15=-27
-12-15=-27
-27=-27

19) 21=-7n

Solution:

21=-7n
21/-7=-7n/-7
-3=n

Verify:

21=-7n
21=-7(-3)
21=21


27) v/7=8

Solution:

v/7=8
v/7(7)=8(7)
v=56

Verify:

v/7=8
56/7=8
8=8



Two-Step Equations




9) 5x-1=9

Solution:

5x-1=9

5x=9+1

5x=10

5x/5=10/5

x=2

Verify:

5x-1=9

5(2)-1=9

10-1=9

9=9

21) 9+9n=9

Solution:

9+9n=9

9n=9-9

9n=0

9n/9=0/9

n=0

Verify:

9+9n=9

9+9(0)=9

9=9

Ysabelle's Term 2 Reflection

Term 2 Math Reflection

In term 2, I learned about surface area,volume, and percent. I think I did well on surface area and volume. I find it easy to memorize the formulas. I struggled on some word problems involving volume. Some questions were really confusing and I can’t solve them. I also struggled on converting some units. I would do better next term by practicing more. I will also comment on blogs more often. I will try to participate in class to improve my grades. I learned how to solve surface area and volume of prisms. I learned how to apply percents, surface area and volume in my daily life.

Ysabelle's Great Big Book of Integers

Grade 7 Integer Review

Integers

An integer is a number that is not a fraction. An integer is any of the natural numbers (positive or negative) or zero.

positive-red

negative-blue

Brackets are training wheels.

Examples:

-4-(-8)

-4+8 ---> standard form

4-(+9)

4-9 ---> standard form

-7+(-8)

-7-8 ---> standard form

A zero pair is a pair of number with a positive and negative sign whose sum is zero. (+,-)

Examples:

-6 and +6

-4 and +4

-10 and +10

When subtracting something that isn't there, use a zero pair.

Here are the * questions:

-3-(-7)=4

-3-7=-10

3-7=-4

3+7=10

-3+7=4

Chapter 2
Sign Rule:
Even- When you have an even number of negative factors the product is positive.
Odd- When you have an odd number of negative factors the product is negative.

(+2) x (+3)= 6
2 groups of positive 3

(+2) x (-3)= -6
2 groups of negative 3

(-2) x (+3)= -6
remove 2 groups of positive 3

(-2) x (-3)= 6
remove 2 groups of negative 3

Chapter 3
Dividing Integers

Partitive Division
You are trying to find out how many times a number contains another number.

Examples:
6÷2=3


-6÷(-2)=3


Quotative Division
Sharing equally with groups.

Example:
-6÷2=-3




Multiplicative Inverse can help you solve 6÷(-2)= by checking your answer. When you found out what the quotient is, switch its place with the divisor's place.

6÷(-2)=-3 ---> 6÷(-3)=-2

Sign Rule
When you divide two integers with the same signs, the quotient would be positive.
When you divide two integers with different signs, the quotient would be negative.

6÷2=3 - positive because they have same signs
-6÷(-2)=3 - positive because they have same signs
(-6)÷2=-3 - negative because they have different signs
6÷(-2)=-3 - negative because they have different signs



Chapter 4 Order of Operations with Integers

(+5) x (-3) + (-6) ÷ (+3)=
You could solve this problem by using BEDMAS-brackets, exponents, division, multiplication, addition, subtraction.
- Perform division and multiplication as they occur from left to right.
- Perform addition and subtraction as they from left to right.

(+5) x (-3) + (-6) ÷ (+3)= -15+(-2)
(+5) x (-3) + (-6) ÷ (+3)=-15-2
(+5) x (-3) + (-6) ÷ (+3)=-17

Ysabelle's Surface Area Scribe

Pages 186-187

7. Do you prefer to find the surface area of a cylinder by using the sum of the area of each face or by using a formula? Give at least two reasons for your choice.

A: I prefer to use a formula because it is quicker and I'm less likely to miss a part of the calculation.

9. Kaitlyn and Hakim each bought a tube of candy. Both containers cost the same amount . Which container required more plastic to make?

Container A:
diameter- 7 cm
height- 122 cm

radius- 3.5 cm

SA=2.π.r.r+2.π.r.h
SA=2(3.14)(3.5)(3.5)+2(3.14)(3.5)(122)
SA=76.93+2681.56
SA=2758.49 cm²

Container B:
diameter- 11 cm
height- 85 cm

radius- 5.5 cm

SA=2.π.r.r+2.π.r.h
SA=2(3.14)(5.5)(5.5)+2(3.14)(5.5)(85)
SA=189.97+2935.90
SA=3125.87 cm²

Container B required more plastic to make.

10. Paper towel is rolled around a cardboard tube. Calculate the outside surface area of the tube.

radius-2 cm
height- 27.5 cm

outside SA=2.π.r.h
outside SA=2(3.14)(2)(27.5)
outside SA=345.4 cm²




Cylinder Volume and Volume Problems




Solution:

JUMBO
r= d/2 r=20/2 r=10 cm V= πrrh V= [(3.14)(10)(10)](40) V= (314cm²)(40cm) V= 12560cm³

POPCORN LOVER'S
r=d/2 r=30/2 r=15 cm V= πrrh V= [(3.14)(15)(15)](20) V= (706.5cm²)(20cm) V= 14130cm³

Martha should buy Popcorn's Lover if she wants more popcorn for her money.




Solution:
outside
r=d/2
r=1/2
r=0.5m

V=πrrh
V=[(3.14)(0.5)(o.5)](10)
V=(o.785m²)(10m)
V=7.85m³
inside
r=d/2
r=0.8/2
r=0.4m

V=πrrh
V=[(3.14)(0.4)(0.4)](10)
V=(o.5024m²)(10m)
V=5.024m³

7.85m³-5.024m³=2.862m³ or 2.9m³

The volume of the concrete required to make the culvert is 2.9m³.

Final Percent Post

Percent
-means out of 100
-another name for hundredths
-65% means out of 100 or 65/100 or 0.65
-a percent that includes a portion of a percent, such as 1/2% , 0.42%, 7 3/8%, 125 3/4%, 4.5%

4.1: Representing Percents


-To represent a percent,you can shade squares on a grid of 100 squares called a hundred grid. One completely shaded grid represents 100%.

-To represent a percent greater than 100%, shade more than one grid.

-To represent a fractional percent between 0% and 1%,shade part of one square.

-To represent a fractional percent greater than 1%, shade squares from a hundred grid to show the whole number and part of one square from the grid to show the fraction.

4.2: Fractions,Decimals and Percents

-Fractions, decimals and percents can be used to represent numbers in various situations.

-Percents can be written as fractions and decimals.
1/2% = 0.5% 42 3/4% = 42.75%

4.3: Percent of a Number

-You can use mental math strategies such as halving, doubling, and dividing by ten to find the percents of some numbers.

-To calculate the percent of a number, write the percent as a decimal and then multiply the number.
12 1/2% of 50= 0.125 x 50

4.4: Combining Percents

-Percents can be combined by adding to solve problems.
5%+7% = 12%

-To calculate the increase in a number,

-You can add the combined percent amount to the original number
12% of 100= 0.12 x 100 =12
100+12= 112

-You can multiply the original number by a single percent greater than 100
112% of 100= 1.12 x 100
= 112

Ysabelle's Percent Review Video

PERCENT

Percent means out of 100. Percent can be written in decimals and fractions. Percents can be used to represent numbers in various situations.

Percent Homework

Use mental math to determine each of the following.
a. 150% of $5 b. 0.1% of $1000 c. 1½% of $20000

Work:

a. 150% of $5



150% of $5 is $7.50.



b. 0.1% of $1000



0.1% of $1000 is $1.



c. 1½% of $20000



1½% of $ 20000 is $300.

Determine the percent of each number.
a. 160% of $53.27 b. ¾% of 135 c. 55 8/10% of 500

Work:

a. 160% of $53.27



160% of $53.27 is $85.23.



b. ¾% of 135



¾% of 135 is 1.01.



c. 55 8/10% of 500



55 8/10% of 500 is 279.

Sorry 'cause my post came late....