Equality Properties of Learning

Equality properties of learning:

Equal properties are the reasonable laws for actual numbers in arithmetic. These properties are used to control, stable the equations. Moreover, shorten the equations. In general, equality is defined as follows,

p = q denotes p is equal to q.
p ≠ q denotes p does not equal q.
Thus, the learning the properties of equality contain the following properties.

Based on balance equation:

a) Addition property

b) Subtraction property

c) Multiplication property

d) Division property

Based on equivalence:

a) Reflexive property

b) Symmetric property

c) Transitive property

Distributive property


1. Balance equation relation property:


The following properties are used for learning the equations with real numbers.

a) Addition property:

For learning the addition property let assume m, n, o are actual numbers. If m =n, then it can be written as m+o = n+o. similar number can add the equation of both side lacking of modifying the result of the equation.

b) Subtraction property:

For learning the subtraction property let assume x, y, z are real numbers. If x =y, then it can be written as x-z = y-z. Equal number can subtract the equation of all side without adjusting the result of the equation.

c) Multiplication property:

Let consider p, q, r are real numbers. If p =q, then it can be written as p*r = q*r. The equation of both sides can be multiplied by similar quantity without adjusting the result of the equation.

d) Division property:

Let consider p, q, r are real numbers(r =/ 0). If p =q, then it can be written as p/r = q/r. The equation of each side can be divided by same nonzero quantity without modifying the result of the equation.


2. Equivalence relation property:


a) Reflexive property:

Let consider ‘m’ is a real number, and then it reflects by itself. That the real number equals itself as, m = m.

b) Symmetric property:

For learning the symmetric property, let consider m and n are real numbers. If m = n, then it can be written as,

n =m. The order of equality is not considered.

c) Transitive property:

Let consider m, n, and o are real numbers. If m = n and n = o, then it can be written as,

m =o. Thus, the two quantities matching to the same extent are identical to each other

3. Distributive property:

From learning of distributive property, let consider p, q, r are real numbers. Then it states that as follows,

p(q+r) = pq+pr

Angle of Depression

Introduction to Angle of Depression Learning:

Angle of depression is a term used mainly in trigonometry where “depression” means “fall” or “drop”. Angle of depression means the angle between the horizontal and the line of sight to an object beneath the horizontal. The angle of depression is mainly used for learning or obtaining the distance of the two objects where we only know their angle and an object’s distance from the ground. I like to share this Pentagon Geometry with you all through my article.

Learning Angle of Depression:

Learning angle of depression plays one of the key roles for human’s day-to-day life. The angle of depression and angle of elevation is used for seeing objects where they are high above us or low below us. The human’s should able to differentiate what is angle of depression and angle of elevation and where to use them. The some examples of angle of depression are finding an angle from top of the building a man seeing a moving car, and a man seeing a stationary car from a moving train. Please express your views of this topic Picture of an Obtuse Angle by commenting on blog.

Example for Learning Angle of Depression:

Consider an example where the distance of a tree and the airplane is to find out where the distance from the ground and the airplane is given and also we know the angle between the tree and the airplane . But the airplane is flying above the tree here we want to find the distance from the airplane and tree. From using the given data’s we can find the angle of depression where the angle for the foot of the tree and airplane’s base is acting as an angle of depression. From the angle and the distance from the ground to the airplane we can find the distance from the tree to the plane using any one of the trigonometric identities. In the case where we have to find the distance between the foot of the ground and the airplane is obtained by the same trigonometric relations.

Math Makes Sense Grade 6

Introduction to Math makes sense grade 6:

Mathematics plays a vital role in the grade of 6. Elementary level of math are easy to learn and simple to solve.  Grade 6 math, consists of algebra, arithmetic calculations, sets, measurements and graphs. In arithmetic we use numerals and variables to represent equation. The grade 6 of mathematics also solves the linear equations and also the multiplication, subtraction, addition and division of the algebra. This grade 6 math sets as basic block for solving aptitude questions. Having problem with Laplace Transform Chart keep reading my upcoming posts, i will try to help you.


Math makes sense grade 6 in algebra sample problems:


On doing the sample problems they can also solve the advanced problems in the mathematics.

Example 1 to Math makes sense grade 6:

Solve the algebraic equation from 3(-3y - 2) - (y - 3) = -10(2y + 2) + 19

Solution:

Step 1:

Given equation is 3(-3y - 2) - (y - 3) = -10(2y + 2) + 19

Step 2:

Multiply the terms

-9 y -6 - y + 3= -20y – 20 + 19

Make them as a group

-10y -3= -20y - 1

-10y + 20y = 3 -1

10y = 2

y = 2/10

y = 0.2

The Answer Y = 0.2

Example 2 Math makes sense grade 6:


Solve the equation of grade 6:

2x + 5 = 4x (3) + 15

Solution:

Eliminate the braces:

2x + 5 = 12x + 15

Subtract -5 on both the sides:

2x +5 -5 = 12 x + 15 – 5

Simplify the equation:

2x = 12x + 10

Subtract – 10 from both the sides:

2x-10= 12x + 10 – 10

On simplifying the equation:

2x-10 = 12x

Subtract – 12x on both sides to get 0 on the right hand side:

2x – 10 – 12x = 12x – 12x

On simplifying the equation we get:

-10 –10x = 0

On adding 10 on both sides:

-10 -10x +10 = 0 +10

On simplifying the equation we get,

-10x = 10

Dividing by -10 on both the sides:

-10x / -10 = 10 / -10

After dividing we get:

X = -1

Thus we got the value of x by simplifying the equation.

Mental Math Techniques

Some people are born great at maths, most of us have to work hard. But why work harder than we need too, when we can often just use a better technique to improve our maths?

Here are some techniques and rules you can use in your maths to improve your maths skills. I like to share this Mental Math Problems with you all through my article.


Estimation

This is one of the most effective techniques to help you work out roughly what sort of answer you should have. So if you need to multiply 305 x 11, then it looks hard. But 300 x 11 is really easy, so do that first to get an idea of the answer - that's 3300. Having problem with Multiplicative Inverse keep reading my upcoming posts, i will try to help you.

Break It Down

Now we know that, we use the breakdown method: 305 x 11 is the same as 300 x 11 + 5 x 11. So to our 3300 we just add 55, to get 3355 as the answer, and we can see we've worked out 305 x 11 really easily!

Multiplying by 0 is always 0

Some sums that look really hard are actually really, check this one out: 26 x 54 - 15 x 576372 x 0 + 57

Looks hard? It's easy - the answer is '0' for any sum that contains multiplying by '0' and once you know that handy little fact such sums become the easiest ones there are!

Ratio Definition Math

Definition for ratio:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. I like to share this What is a Ratio? with you all through my article.

Example:

For every Spoon of sugar, you need 2 spoons of flour (1:2)

Source :Wikipedia

Ratio formula:

Let A and B be two given points. Let P be a point on the line segment `barA``barB` or on `barA` `barB` produced. Then P divides `barA` `barB` into two segments `barA` `barP` and `barP` `barB`. The lengths of `barA` `barP` and `barP``barB`  are AP and PB.

These lengths are in some ratio: n; that is AP : PB = m : n or  `(AP)/(PB)` `(m)/(n)`

If P lies inside `barA` `barB` we say that P divides `barA``barB` internally in the ratio m : n. If P lies outside `barA` `barB`, that is, P lies on `barA` `barB`  produced, then we say that P divides `barA``barB` externally in the ratio m : n. With a given ratio m : n, `barA``barB` can be divided either internally or externally. Understanding Dividing Radicals with Variables is always challenging for me but thanks to all math help websites to help me out.

Example for ratio:

Example :

Divide the line segment `barA` `barB` of length 16 units in the ratio 3:5

Solution:

i) Let C be the point inside `barA``barB` such that `(AC)/(CB)`= `(3)/(5)`. Since the numerator is smaller than the denominator, C is closer to A than to B . Then

5AC=3 BC or 5AC=3(AB–AC) or 8AC=3AB =3(16)=48

AC=6 units and so CB=AB–AC =16–6 = 10 units.

Hence C lies inside `barA` `barB` 6 units distance from A and 10 units distance from B. The point C is unique and it divides `barA``barB` internally in the given ratio 3:5.

ii) Let D be the point outside `barA``barB` such that `(AD)/(DB)`=`(3)/(5)`?. Since the numerator is smaller than the denominator, D is closer to A than to B. Now we have

5 AD = 3DB or 5 AD = 3(AD + AB) or 5 AD = 3AD + 3AB

2 AD = 3AB = 3(16) = 48 or AD = 24 Then DB = DA + AB = 24 + 16 = 40

Therefore, D lies outside `barA``barB` 24 units distance from A and 40 units distance from B. The point D is unique and it divides   `barA``barB` externally in the given ratio 3:5.

Solving Mathematics Grind

Introduction for Solving Mathematics Grind:

Well experienced tutor (or) graduate Mathematics student offering Junior and Leaving Certificate grinds around Ireland. Grinds contains various subjects such as Mathematics, French, Accounting etc., in this math grind covers all level of students. They are providing explanation of theory with detailed examples with questions and answers. In this article we shall discuss about solving mathematics grind. The following examples are involved in solving mathematics grind. Is this topic Exponential Function Solver hard for you? Watch out for my coming posts.

Solving Mathematics Grind Example: 1

Solve the sum and find the value of ‘x’

50x + 40 = -200

Subtract 40 from both sides:

50x + 40 – 40 = -200 - 40

Simplify both sides:

50x = -240

Divide both sides by 50:

`(50x)/50` = `-240/50`

Simplify both sides:

x   =   `-24/5`

I have recently faced lot of problem while learning Place Value with Decimals, But thank to online resources of math which helped me to learn myself easily on net.

Solving Mathematics Grind Example: 2

Use Euclid’s algorithms solve the HCF of 2245 and 36548.

Solution:

Since 36548 > 2245, we apply the division lemma to 36548 and 2245, to get

36548 = 2245 × 16 + 628

Since the remainder 628 not equal to 0, we apply the division lemma to 2245 and 628, to get

2245 = 628 × 3 + 361

We consider the new divisor 628 and the new remainder 361, and apply the division lemma to get

628 = 361 × 1 + 267

We consider the new divisor 361 and the new remainder 267, and apply the division lemma to get

361 = 267 × 1 + 94

We consider the new divisor 267 and the new remainder 94, and apply the division lemma to get

267 = 94 × 2 + 79

We consider the new divisor 94 and the new remainder 79, and apply the division lemma to get

94 = 79 × 1 + 15

We consider the new divisor 79 and the new remainder 15, and apply the division lemma to get

79 = 15 × 5 + 4

We consider the new divisor 15 and the new remainder 4, and apply the division lemma to get

15 = 4 × 3 + 3

We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get

4 = 3 × 1 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 × 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 36548 and 2245 is 1.

Notice that 1 = HCF (3, 1) = HCF (4, 3) = HCF (15, 4) = HCF (79, 15) = HCF (94, 79) = HCF (267, 94) = HCF (361, 267) = HCF (628, 361) = HCF (2245, 628) = HCF (36548, 2245).

Meters to Inches

Meters to inches

Meter:

The metre (or meter), symbol m, is the base unit of length in the International System of Units (SI). It is defined as the distance travelled by light in a complete vacuum in 1/299,792,458 of a second.

Inch:

An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. I like to share this Alternate Exterior Angles with you all through my article.

(Source: wiki)

Let us see how to convert meters to inches in this article.

Formula for meters to inches

1 meter = 39.3700787 inches

Meters to Inches – Examples:
Meters to inches – Example 1:

Convert 5 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches:

1 meter = 39.3700787 inches

Step 2:

So to find 5 meter

Step 3:

Multiply 5 with 39.3700787 = 196.8503935

Step 4:

Therefore, 5 meter = 196.8503935 inches

Meters to inches – Example 2:

Convert 11 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 11 meter

Step 3:

Multiply 11 with 39.3700787 = 433.070866 inches

Step 4:

Therefore, 11 meter = 433.070866 inches

Meters to inches – Example 3:

Convert 15 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 15 meter

Step 3:

Multiply 15 with 39.3700787 = 590.551181 inches

Step 4:

Therefore, 15 meter = 590.551181 inches

Meters to inches – Example 4:

Convert 26 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 26 meter

Step 3:

Multiply 26 with 39.3700787 = 1 023.62205 inches

Step 4:

Therefore, 26 meter = 1 023.62205 inches

Meters to inches – Example 5:

Convert 0.50 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 0.501 meter

Step 3:

Multiply 0.501 with 39.3700787 = 19.7244094 inches

Step 4:

Therefore, 0.501 meter = 19.7244094 inches

Meters to inches – Example 6:

Convert 0.81 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 0.81 meter

Step 3:

Multiply 0.81 with 39.3700787 = 810

Step 4:

Therefore, 0.81 meter = 31.8897638 inches


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Meters to Inches – Practice Problems

Practice problem -1

Convert 6.5 Meters to inches?

Answer:

255.905512 inches

Practice problem -2

Convert 0.6 Meters to inches?

Answer:

23.6220472 inches