This document provides examples and explanations of key concepts for translating between verbal and algebraic expressions, including:
1) Definitions of variables, expressions, operations like addition, subtraction, multiplication and division.
2) Examples of writing algebraic expressions to represent verbal phrases like "7 times a number decreased by 13" and vice versa.
3) Explanations of exponents and powers, and examples of evaluating expressions like 21, 22, 23, and 2n7.
4) Practice identifying equivalent expressions and evaluating whether expressions are equal, like 35 and 53.
Properties of Square Numbers (Class 8) (Audio in Hindi)Parth Nagpal
This presentation was created by me for the Scholars for Change Campaign, IIM Ahmedabad for the underprivileged children.
Scholars for Change is a campaign of Education Innovation Bank at IIM Ahmedabad. This campaign seeks to give to underprivileged children access to high quality, interesting content in Science and Math, so that they can learn on their own, in their own language, with fun and play.
Applying Knowledge of Square Numbers and Square Roots jacob_lingley
Using their knowledge of square numbers and square roots, students will be separated into colour coded groups to practice a concept, then return to their original groupings to teach that concept to fellow classmates.
Properties of Square Numbers (Class 8) (Audio in Hindi)Parth Nagpal
This presentation was created by me for the Scholars for Change Campaign, IIM Ahmedabad for the underprivileged children.
Scholars for Change is a campaign of Education Innovation Bank at IIM Ahmedabad. This campaign seeks to give to underprivileged children access to high quality, interesting content in Science and Math, so that they can learn on their own, in their own language, with fun and play.
Applying Knowledge of Square Numbers and Square Roots jacob_lingley
Using their knowledge of square numbers and square roots, students will be separated into colour coded groups to practice a concept, then return to their original groupings to teach that concept to fellow classmates.
Algebraic Expression and Expansion.pptxMisbahSadia1
Algebraic expressions are fundamental mathematical constructs that play a crucial role in representing and solving a wide range of mathematical and real-world problems. They are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions are a bridge between the abstract world of mathematics and the practical world of problem-solving.
Key components of an algebraic expression:
Variables: These are symbols (usually letters) that represent unknown values or quantities. Common variables include "x," "y," and "z." Variables allow us to generalize mathematical relationships and solve problems with unknowns.
Constants: These are fixed numerical values that do not change within the expression. Examples include numbers like 2, 5, π (pi), or any other specific constant value.
Mathematical Operations: Algebraic expressions include operations like addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^ or **). These operations define how the variables and constants interact within the expression.
Coefficients: Coefficients are the numerical values that multiply variables. For example, in the expression 3x, 3 is the coefficient of the variable x.
Algebraic expressions can take various forms, from simple linear expressions like 2x + 3 to more complex ones like (x^2 - 4)(x + 1). They are used in a wide range of mathematical contexts, including equations, inequalities, and functions.
Expansion of Algebraic Expressions:
Expanding an algebraic expression involves simplifying it by removing parentheses and combining like terms. This process is essential for solving equations, simplifying complex expressions, and gaining a better understanding of the underlying mathematical relationships.
Here's how to expand algebraic expressions:
Distribute: When an expression contains parentheses, you distribute each term within the parentheses to every term outside the parentheses using the appropriate mathematical operation (usually multiplication or addition).
Example: To expand 2(x + 3), you distribute the 2 to both terms inside the parentheses: 2x + 6.
Combine Like Terms: After distributing and simplifying, you look for like terms (terms with the same variable(s) and exponent(s)) and combine them.
Example: In the expression 3x + 2x, you combine the like terms to get 5x.
Remove Parentheses: If there are nested parentheses, continue to distribute and simplify until no parentheses remain.
Expanding algebraic expressions is a crucial step in solving equations and simplifying complex expressions. It allows mathematicians and scientists to manipulate and analyze mathematical relationships efficiently, making it an essential tool in various fields, including physics, engineering, and computer science.
G7 Math Q2-Week 3- Translating Math Phrase to English.pptx
Expressions
1. Objective
The student will be able to:
translate verbal expressions into
math expressions and vice versa.
SOL: A.1
Designed by Skip Tyler, Varina High School
2. What is the area of a rectangle?
Length times Width
If the length is 3 meters and the width is 2
meters, what is the area?
A = L x W
A = 3 x 2 = 6 meters2
A, L and W are the variables. It is any
letter that represents an unknown number.
4. In expressions, there are many
different ways to write multiplication.
1) ab
2) a • b
3) a(b) or (a)b
4) (a)(b)
5) a x b
We are not going to use the multiplication symbol
any more. Why?
6. Throughout this year, you will hear many
words that mean addition, subtraction,
multiplication, and division. Complete the
table with as many as you know.
Addition Subtraction Multiplication Division
7. Here are some phrases you may have listed.
The terms with * are ones that are often
used.
Addition Subtraction Multiplication Division
sum* difference* product* quotient*
increase decrease times divided
plus minus multiplied ratio
add subtract
more than less than
total
8. Write an algebraic expression for
1) m increased by 5.
m + 5
2) 7 times the product of x and t.
7xt or 7(x)(t) or 7 • x • t
9. 3) 11 less than 4 times a number.
4n - 11
4) two more than 6 times a number.
6n + 2
5) the quotient of a number and 12.
12
x
10. Which of the following expressions represents
7 times a number decreased by 13?
1. 7x + 13
2. 7x - 13
3. 13 - 7x
4. 13 + 7x
Answer Now
11. Which one of the following expressions
represents 28 less than three times a number?
1. 28 - 3x
2. 3x - 28
3. 28 + 3x
4. 3x + 28
Answer Now
12. Write a verbal expression for:
1) 8 + a.
The ratio of m to r
Do you have a different way of writing
these?
The sum of 8 and a
2) m
r
.
13. Which of the following verbal expressions
represents 2x + 9?
Answer Now
1. 9 increased by twice a number
2. a number increased by nine
3. twice a number decreased by 9
4. 9 less than twice a number
14. Which of the following expressions represents
the sum of 16 and five times a number?
Answer Now
1. 5x - 16
2. 16x + 5
3. 16 + 5x
4. 16 - 5x
15. base
and 3 is called the
exponent or power.
103
means 10 • 10 • 10
103
= 1000
When looking at the expression
103
, 10 is called the
16. How is it said?
21
Two to the first power
22
Two to the second power or two squared
23
Two to the third power or two cubed
2n7
Two times n to the seventh power
17. Which of the following verbal expressions
represents x2
+ 2x?
Answer Now
1. the sum of a number squared and
twice a number
2. the sum of a number and twice the
number
3. twice a number less than the
number squared
4. the sum of a number and twice the
number squared
18. Which of the following expressions
represents four less than the cube of a
number?
Answer Now
1. 4 – x3
2. 4 – 3x
3. 3x – 4
4. x3
– 4
19. Evaluate.
21
2
22
2 • 2 = 4
23
2 • 2 • 2 = 8
2n7
We can’t evaluate because we don’t
know what n equals to!!
20. Is 35
the same as 53
?
Evaluate each and find out!
35
= 3 • 3 • 3 • 3 • 3 = 243
53
= 5 • 5 • 5 = 125
243 125≠
They are not the same!