Types Of Algebraic Expressions
The types of algebraic expressions are based on the variables found in that particular expression, the number of the terms of that expression, and the values of the exponents of the variables in each expression. Given below is a table that divides the algebraic expressions into five different categories. Let us have a look at the table.
| Types |
|---|
Adding And Subtracting Like Terms
We have seen that we can add to get
These three terms are called like terms because they all contain the same variable,.
We can also add. Because both terms have the variable, we can combine the terms using the operation that is given, which in this case is addition. The correct answer is:
We can also subtract like terms. We can simplify the expression \ using subtraction. The correct answer is:
When we collect or combine the like terms in this way, we are giving an expression in its simplest form, which is called simplifying an expression.
like terms Like terms contain the same variable or variables.
simplify an expression To simplify an expression is to give it in its simplest form. We do this by collecting like terms using addition or subtraction.
We can add or subtract any number of like terms.
For example:
Terms that do not have the same variables are called unlike terms. If we find an expression with unlike terms, we cannot add or subtract these terms. For example: contains two unlike terms. They have the same coefficient but not the same variable. This expression cannot be simplified further.
unlike terms Unlike terms contain different variables.
Using Generalisation To Find Misconceptions
When you see an expression like 2, you might spot immediately that this could be rewritten as , because it is an example of the law of distributivity where a = a × b a × c.
Spotting such patterns and generalisations is helpful in mathematics because it makes it easier to solve problems. The downside is that sometimes you might think something is a pattern and so you generalise it, when actually it is a special case and will only be true in some circumstances. The next activity gives some examples of writing generalised algebra from numerical expressions.
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How To Use Log Table: Step
To find the log value of a number using the log table, you must understand the process of reading the log table. We have provided a step-by-step process to find the values using an example:
Step 1: Identify the table. For different bases, different log table is used. The table provided above is for base 10. So, you can find the log value of a number to the base 10 only. To find natural logarithms or binary logarithms, you will have to use a different table.
Step 2: Find out the integer and decimal part of the given number. Suppose we want to find the log value of n = 18.25. So, first of all, we separate the integer and decimal.Integer Part: 18Decimal Part: 25
Step 3: Come to the common log table and look for the cell value at the following intersections:Row labeled with first two digits of nColumn header with the third digit of n In this example, log10 row 18, column 2 cell value 2601. So, the value obtained is 2601.
Step 4: Always use the common logarithm table with a mean difference. Now again go to row number 18 and column number 5 in the mean difference table. In this example, log10 row 18, mean difference column 5 cell value 12. Write down the corresponding value which is 12.
Step 5: Add both the values obtained in step 3 and step 4. That is 2601 + 12 = 2613.
Step 7: Combine both the Characteristic and the Mantissa part and you will get the final value which is 1.2613.
So, log10 = 1.2613
Frequently Asked Questions On Log Table Math
Here we have provided some of the FAQs related to online log tables that we have provided in this article.
| Q1: How do you read a log table?A: Take the first 2 digits of the number irrespective of the decimal and look for the row with that number. Next look for the column number corresponding to the third digit of the number. You may also need to look into the mean difference table to get the final value. The step-by-step process to read a log table is provided on this page. |
| Q2: What is the value of log 1 to 10?A: Log 1 to the base 10 is equal to 0. |
| Q3: What is the value of e in natural logarithm?A: e is an irrational and transcendental number approximately equal to 2.7182. |
| Q4: How do you calculate logs? A: The power to which a base of 10 must be raised to obtain a number is called the common logarithm of the number. To calculate the log values, we use the mathematics logarithm table. |
| Q5: What is the value of log 0?A: log 0 is undefined. Its not a real number, because you can never get zero by raising anything to the power of anything else. |
| Q6: How do you find the log of a number without a calculator?A: You can find the log of a number without a calculator using the logarithmic and mathematical tables provided on this page. |
Students can make use of NCERT Solutions for Maths provided by Embibe for your exam preparation.
|
Free Practice Questions and Mock Tests for Maths |
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Permutation And Combination Questions
Here are some practice questions on permutation and combination concepts for you to practice:
| Question 1: There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in a row. Find out the number of different arrangements possible. Question 2: In how many ways can a team of 5 persons be formed out of a total of 10 persons such that two particular persons should not be included in any team?Question 3: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chessboard? Question 4: Find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?Question 5: What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?Question 6: In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?Question 7: If nC8 = nC27, what is the value of n?Question 8: Find the number of triangles which can be drawn out of n given points on a circle?Question 9: In how many ways can 10 books be arranged on a shelf such that a particular pair of books will never be together? Question 10: How many numbers, between 100 and 1000, can be formed with the digits 3, 4, 5, 0, 6, 7 ? |
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Faqs Related To Probability Formula
Here we have provided some of the frequently asked questions related to statistical probability formulas:
Q1: What is the formula of probability?
A: The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible. This basic definition of probability assumes that all the outcomes are equally likely to occur.
Q2: What are the 3 types of probability?
A: There are 3 types of probability: Theoretical Probability.
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Identifying Expressions And Equations
- Identify and write mathematical expressions using words and symbols
- Identify and write mathematical equations using words and symbols
- Identify the difference between an expression and an equation
- Use exponential notation to express repeated multiplication
- Write an exponential expression in expanded form
Algebraic Expression Explanation & Examples
Algebra is an interesting and enjoyable branch of mathematics in which numbers, shapes, and letters are used to express problems. Whether you are learning algebra in school or examining a certain test, you will notice that almost all mathematical problems are represented in words.
Therefore, the need to translate written word problems into algebraic expressions arises when we need to solve them.
Most of the algebraic word problems consist of real-life short stories or cases. Others are simple phrases such as the description of a math problem. This article will learn how to write algebraic expressions from simple word problems and then advance to lightly complex word problems.
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Coefficients Of Algebraic Terms
The number in the algebraic term is called the coefficient.
For example:For the term 4x, 4 is the coefficient
For the term 7y, 7 is the coefficient
The coefficient of 1 in an algebraic term is usually not written.
For example:1y can be written as simply y. So, 1y and y are the same.
Example:Find the coefficient and variable of each of the following terms:
a) 0.2m
a) 0.2m
b) 3p
c) and the variable is q)
d) z
e) and the variable is x)
Activity : What Could It Mean
Tell your students the following.
Below are some algebraic expressions adapted from textbooks:
- 30u + 44v
- three times Square root of four
- 18 left parenthesis three x plus one right parenthesis divided by six
- one divided by a plus one divided by b
Use your imagination and make up a story for what each expression could be about. What situation could the expression be modelling? What else could it be about?
You may also want to have a look at the key resource Storytelling, songs, role play and drama.
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Algebraic Expressions And Terms
Open sentences are made up of algebraic expressions. An algebraic expression is a mathematical phrase or statement that contains numbers, symbols, variables . Note that algebraic expressions do not have equals signs.
Here are some examples of algebraic expressions:
algebraic expression An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators. It does not have an equals sign.
Algebraic expressions are made up of terms that are separated by an addition or a subtraction
has 3 terms.
has 4 terms.
term A term can be a single number , or a variable, or one or more numbers and variables that are being multiplied together. Terms are separated by or
Here are some examples of single terms:
Here are some examples of algebraic expressions with two terms:
Here are some examples of algebraic expressions with five terms:
Identify Expressions And Equations
What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. Running very fast is a phrase, but The football player was running very fast is a sentence. A sentence has a subject and a verb.
In algebra, we have expressions and equations. An expression is like a phrase. Here are some examples of expressions and how they relate to word phrases:
| Expression | ||
|---|---|---|
| 3\text5 | the sum of three and five | |
| n – 1 | n minus one | the difference of n and one |
| 6\cdot 7 | 6\text7 | the product of six and seven |
| \frac | x divided by y | the quotient of x and y |
Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An equation is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:
| Equation | |
|---|---|
| 3+5=8 | The sum of three and five is equal to eight. |
| n – 1=14 | n minus one equals fourteen. |
| 6\cdot 7=42 | The product of six and seven is equal to forty-two. |
| x=53 | x is equal to fifty-three. |
| y+9=2y – 3 | y plus nine is equal to two y minus three. |
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Basic Algebraic Expressions Examples
Example 1: Write an algebraic expression for the math phrase the sum of a number and four.
Solution: The word sum immediately gives us the hint that we are going to add here. Notice that we want to add two quantities: one unknown number and the number 4. Since we dont know what the value of the number, we can use a variable to represent it. You may use any letters of the alphabet. In this case, lets agree to use y for the variable.
When we add the variable y and 4, we have y + 4. It is also okay to write your answer as 4 + y because addition is commutative that is, switching the order of addition doesnt change its sum.
The final answer is y+4.
Example 2: Write an algebraic expression for the math phrase 10 increased by a number.
Solution: The keywords increased by imply addition. This means that an unknown number has been added to 10. Using the letter k as the variable, we can translate the statement above as 10 + k. Since addition is commutative, we can rewrite it as k + 10. Either of the two above is a correct answer.
The final answer is k+10.
Example 3: Write an algebraic expression for the math phrase the difference of 1 and a number.
The final answer is 1 – x.
Example 4: Write an algebraic expression for the math phrase a number less than 8.
In other words, we are going to subtract the unknown number from the number 8. If we choose our variable to be the letter a, we get 8 a.
The final answer is 8 – a.
The final answer is 5m.
\LARGE
\LARGE
Permutation And Combination: Definition Formula Examples
Permutation and Combination: Permutation and Combination are two separate ways to represent a group of elements. Both are different and many students get confused between the two. When the order of arrangement doesnt matter then we call it a combination. If the order does matter then we have a permutation. It can be rightly said that a permutation is an ordered combination. Let us understand the difference between permutation and combination with an example.
Take a number lock. When we try to open it with a password, say, 1-2-3, then the order is very important. You cant open it with 2-1-3 or 3-1-2. Thus, it is a permutation. All the permutations of 1, 2, and 3 are:
| 123, 132, 213, 231, 312, 321 |
If it was a true combination lock, it would open by entering any of the permutations above. In fact, a number lock should rightly be called a permutation lock and not a combination lock!
We have explained in detail all the permutation and combination formula on this page. Also, we have provided you with solved examples and practice questions on permutation combination.
Here we have given the mathematical definition of permutation and combination:
What is Permutation?
A permutation is an arrangement in a definite order of a number of objects taken some or all at a time. With permutations, every little detail matters. It means the order in which elements are arranged is very important.
There are two types of permutations:
What is Combination?
There are two types of combinations:
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Solved Examples On Probability Formulas Class 12
Here we have provided some probability solved examples.
Question 1: A coin is thrown 3 times. What is the probability that at least one head is obtained?
Solution: Sample space = Total number of ways = 2 × 2 × 2 = 8. Favorable Cases = 7 P = No. of Favourable Outcomes/Total number of outcomes= 7/8
Question 2: Two cards are drawn from the pack of 52 cards. Find the probability that both are diamonds or both are kings.
Solution: Total no. of ways = 52C2Case I: Both are diamonds = 13C2Case II: Both are kings = 4C2 P = / 52C2 = 14/221
Question 3: Calculate the probability of getting an even number if a dice is rolled.
Solution: Sample space = n = 6Let E be the event of getting an odd number, E = n = 3So, the Probability of getting an odd number is:P = /= n/n= 3/6= 1/2
Question 4: What is the probability of getting a sum of 22 or more when four dice are thrown?
Solution: Total number of ways = 64 = 1296 Number of ways of getting a sum 22 are 6,6,6,4 = 4! / 3! = 4 and 6,6,5,5 = 4! / 2!2! = 6. Number of ways of getting a sum 23 is 6,6,6,5 = 4! / 3! = 4 Number of ways of getting a sum 24 is 6,6,6,6 = 1.Fav. Number of cases = 4 + 6 + 4 + 1 = 15 ways.P = 15/1296 = 5/432
Question 5: Find the probability that a leap year has 52 Sundays.
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| Differentiation Formulas |
Probability Formula: Definition Of Probability
The uncertainty/certainty of the occurrence of an event is measured by the probability. Though probability started with gambling, it is now used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. Probability for Class 10 is an important chapter for students and it explains all the basic concepts.
To find the probability of a single event to occur, first, we should know the total number of possible outcomes. For example, when we toss a coin, either we get a Head or a Tail, i.e. only two possible outcomes are possible . If we want Head to come, our favorable outcome is H. So, we denote the probability of getting Head on the toss of a coin is:
= 1/2
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