Elementary Algebra, ratio word problems

In Elementary Algebra practice , a ratio expresses the magnitude of quantities relative to each other rather. 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. Mathematically, a proportion is defined as the equality of two ratios. However in common usage the word proportion is used to indicate a ratio, especially the ratio of a part to a whole.Let's see an example from 4th grade math algebra word problems with solution

Question:-

Find two numbers such that their difference ,sum and product are in the ratio 1:4:15 respectively.

Answer:-

This solution will explain how to understand ratio word problems

Let the numbers be x and y

By the problem

(x-y) : (x+y) : (xy) = 1 : 4 : 15

x-y = k ----- 1

x+y = 4k ----- 2

xy = 15k -------- 3

Where k is the constant of proportionality

From 1+2 , we get x = 5k/2

Substitute this in eq 2 , we get y = 3k/2

By substituting this x and y values in eq 3

We get k = 4

If we put this k value in x = 5k/2 , we get x = 10

If we put k value in y = 3k/2 , we get y = 6

So the numbers are 10,6

How to find Slope of parallel lines

Slope is used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line or pair of straight lines. It is also always the same thing as how many rises in one run.The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.The larger the absolute value of a slope, the steeper the line. A horizontal line has slope 0, a 45° rising line has a slope of +1, and a 45° falling line has a slope of -1. A vertical line's point slope form
is undefined meaning it has "no slope."

Question:-

How to find the slope of the line parallel to x+2y=10

Answer:-

Point to remember:- Parallel lines will have same slope
So we just have to find the slope of the given line.

x+2y = 10

subtract 'x' on both sides

2y = -x+10

divide by 2 on both sides

y = -x/2 + 5

So the slope is -1/2 for both the lines.

same way,we can also find all points having an x-coordinate of 2 whose distance from the point 2 1 is 5

What is a Natural number

In mathematics, from number theory tutorial there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century.

Natural numbers have two main purposes: counting ("there are 3 apples on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively. (See English numerals.) A more recent notion is that of a nominal number, which is used only for naming.

Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics.

When we add two natural numbers

we also get a natural number

Let's have a look at a simple problem from numeric and algebraic operations



2 is a natural number

5 is also natural number

2+5=7

7 is also a natural number.

We represent natural numbers with W

w={ 0,1,2,3.....}

If you know the basics of this you can get any math answers

How to convert Decimal into Fraction

Topic: Fraction

A fraction is a mathematical expression relating two quantities or numbers, one divided by the other. The numbers may be whole numbers integers- this is a rational number. For example, 1/2 is a fraction. They can also be polynomials - this is a rational function.

Let's have a look at the answer which have done by online algebra tutor
The process of decimal to fraction conversion involves the use of the fundamental rule of fractions; the fraction should be written in its lowest terms. The following examples demonstrate how to convert decimals to fractions.

Here is example of a 7th grade math equations




For similar problems of this type purple math will guide you.

Rules of Exponents

Topic: Exponents
Exponentiation is a mathematical operation, written aⁿ, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication:

Here are some examples:

1.)Addition:An exponent can be added only when they have the same number.

For example: 2x1 + 2x1 = 4x1

   3x2 - 2x2 = 5x2


2.)Subtraction:The rule is same for subtraction.


3.)Multiplication:While multiplying, multiply the numbers and add the exponents.

For example: 3x1 * 2x1 = 6x2 (Add)

    4x2 * 3x3 = 12x5 (Add)


4.)Division:While dividing the exponents, the denominator takes the opposite sign and m

and mover to the numerator. The numbers should be divided as usual.

For example:

    36x8-4
 ___________ = 6x4
      64


     48x2+4
 ___________ = 8x6
     6x-4           

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problem on simple interest

Topic:- simple interest

Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money or, money earned by deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements.

Let's see a problem on this.

Question:

Greg invests $1200 at an annual rate of 6.5%. How long will it take until Greg earns $195 in interest?

Solution:

Formula to find the interest is

I = PTR/100

here p = profit=1200
   t = time
   r = rate=6.5

Substitute the values in formula,so that

        (1200 x T x 6.5)
195 = -----------------
             100

         T = 2.4

Greg will earn $195 in interest in 2.5 years.

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