Definition: Translating words into algebraic expression is the process of translating the word problems into an algebraic expression which can be used to solve the word problem and produce the solution for the given words problem.
Problems of translating words into algebraic expression:
Problem 1:
Flowers shop has thirty Roses and forty Lilly. How many pieces of flowers does flowers shop have?
Solution:
Let a = Total number of Flowers in the flowers shop. The sum of thirty Roses and forty Lilly is equal to the total number of flowers in the flowers shop. It translates the words problem into an algebraic expression. a = 30 + 40
Solve this expression.
Let a = Total number Pieces of Flowers in the flowers shop a = 70.
There are 70 Pieces of Flowers in the flowers shop.
Problem 2:
The sum of twice a number plus 20 is 86.Find the number.
Solution:
In words problem, the word is means equals and the word and means plus. Translating words problem into an algebraic expression the sum of twice a number and 20 equals 86. Write an expression
2X + 20 = 86
Solve this expression using the variable.
2X + 20 = 86 (Expression)
2X + 20 – 20 = 86 - 20 (subtract by -20 on both sides)
2X= 66
X = 33 (Divided by 2 on both sides we get the result)
Solution to the problem is 23.
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Ratio: Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent.
Proportion: a, b, c and d are said to be proportion if a : b = c : d. a and d are called the extremes, b and c are called the means. a, b, c and d are called first proportion, second proportion, third proportion and fourth proportion respectively.
Types Of Ratios and Proportion:
Ratios are classified in to six types:
1) Duplicate ratio:The ratio of the squares of the two numbers.Ex: 9:16 is the duplicate ratio of 3:4.
2) Triplicate ratio:The ratio of the cubes of the two numbers.Ex: 27:64 is the triplicate ratio of 3:4.
3) Sub-duplicate ratio:The ratio between square root of the two numbers.Ex: 4:5 is the sub-duplicate ratio of 16:25.
4) Sub-triplicate ratio:The ratio between the cube roots of the two numbers.Ex: 4:5 is the sub-triplicate of 64:125.
5) Inverse ratio:If the two terms in the ratio interchange their places,then the new ratio is inverse ratio of the first.Ex: 9:5 is the inverse ratio of 5:9.
6) Compound ratio:The ratio of the product of the first term to that of the second term of two or more ratios.Ex: 3/4,5/7,4/5 and 3/5 is 3/4 x 5/7 x 4/5 x 3/5 = 9/35.
Proportions are classified in to four types:
1) Continued proportion:In the proportion 8/12=12/18, 8,12,18 are in the continued proportion.
2) Fourth proportion:If a:b=c:x,then x is called forth proportion of a,b and c.The fourth proportion of a,b.c =bc/a
3) Third proportion:If a:b=b:x,then x is called third proportion of a and b.Third proportion of a,b =b^2/a
4) Second or mean proportion: If a:x=x:b,then x is called second or mean proportion of a and b.Therefore mean proportion of a and b =Root of(ab)
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.
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.
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.
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 offractions; the fraction should be written in its lowest terms. The following examples demonstratehow to convert decimals to fractions.