Algebraic expressions are a series of arithmetic operations consisting of the four operations, numbers, variables, parentheses and other mathematical symbols (square roots, powers, factors…).
These algebraic expressions are abstracted from physical concepts so that we can see their applications in all fields.
As we said earlier, algebraic expressions mainly consist of the four operations, numbers, variables, parentheses and various mathematical symbols that we will discuss as follows:
- Numbers: They are fixed values such as
- Operations Symbols: These are addition(+), subtraction(-), multiplication() and division()
- Variables: These are the unknowns that we usually express with letters such as
- Grouping Symbols: It contains other expressions such as
- Other Mathematical Symbols: such as square roots, exponents,
Convert texts to algebraic expressions
Let’s take some exemples:
Example1:
Sum of two unknown numbers.
Solution:
Let the first number be and the second number be .
So their sum is
Example2:
The sum of twice and
Solution:
Let the first number be , the twice of is .
So the sum is
Example3:
The difference of the number and the triple of the number .
Solution:
The variables are already defined and . the triple of is .
So the difference is
Example4:
The difference of the product of and , and the quotient of and
Solution:
The product of and is
The quotient of and is
So the difference is
Example5:
The product of two consecutive numbers.
Solution:
Let be the first number. then the second number is .
So, the product of this two numbers is
Example6:
The product of the sum of the numbers and and the sum of the numbers and twice of .
Solution:
The sum of and is
The sum of and the twice of is
The product is
Example7:
The sum of the square root of a number and the number next of it
Solution:
Let the unknown number. then the square root of is .
The number next of is .
The sum is
Lesson Description:
How to write an expression from a word problem
I show how to solve math problems online during live instruction in class. This is my way of providing free tutoring for the students in my class and for students anywhere in the world. Every video is a short clip that shows exactly how to solve math problems step by step. The problems are done in real time and in front of a regular classroom. These videos are intended to help you learn how to solve math problems, review how to solve a math problems, study for a test, or finish your homework. I post all of my videos on YouTube, but if you are looking for other ways to interact with me and my videos you can follow me on the following pages through My Blog, Twitter, or Facebook.
Questions answered by this video:
- How do you write an Algebraic expression from a word problem?
- If a used book store sells hardcover books for $2.50 and paperback books for $0.50, how do you write an expression for the cost of buying h hardcover books and p paperback books?
- How can you make a table for how much it costs to buy 1, 2, and 3 hardcover books at $2.50 each and 1, 2, and 3 paperback books at $0.50 each?
Examples, solutions, videos, worksheets, games and activities to help Algebra 1 or grade 7 students learn how to write algebraic expressions from word problems.
Beginning Algebra & Word Problem Steps
- Name what x is.
- Define everything in the problem in terms of x.
- Write the equation.
- Solve the equation.
Examples:
- Kevin’s age is 3 years more than twice Jane’s age. The sum of their ages is 39. How old is Kevin and Jane?
- The difference between two numbers is 7. Find the two numbers if the larger number is three times the smaller.
- Mary and Jim collect baseball cards, Mary has 5 more than 3 times as many cards as Jim. The total number of cards they both have is 253. How many cards does Mary have?
How to writing a word problem as an algebraic expression?
Example:
Last week, Shaun had half as many computer games as Johan. He purchased 3 more games this week. Write an expression that represents the number of games Shaun now has if j represents the number of games that Johan has?
Algebraic Word Problem
Example:
Devon is going to make 3 shelves for her father. She has a piece of lumber 12 feet long. She wants the top shelf to be half a foot shorter than the middle shelf, and the bottom shelf to be half a foot shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?
-
Show Step-by-step Solutions
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
Writing the phrase as an algebraic expression
Example
Write the phrase as an algebraic expression.
“Four less than twice ???x???”
The phrase “twice ???x???” means “???2??? times ???x???” which we know means to multiply, and so we can write it as ???2x???. Now we have
“Four less than ???2x???”
Less means subtraction, so we’ll subtract ???4??? from ???2x???.
???2x-4???
It may be tempting to write the ???4??? first and subtract ???2x???. Let’s use numbers to help us visualize this. When we say ???4??? less than ???10??? you know that you’d have to subtract ???4??? from ???10???, written out as ???10-4???. So ???4??? less than ???2x??? will be ???2x-4???.
Example
Find the value of the expression.
???frac{1}{4}??? of ???120???
In math, the word “of” (immediately after a proper or improper fraction) tells us to multiply. Therefore, the mathematical expression of the phrase will be
???frac{1}{4} cdot 120???
Because we were asked to actually find the value of the expression, we’ll perform the multiplication to get the simplified value.
???30???
Not only can we translate phrases into expressions, but we can write equations from some phrases as well.
For instance, suppose you wanted to use algebra to solve the following word problem:
John’s age is four less than twice Mary’s age. If Mary is ???18???, how old is John?
The first step in solving a word problem like this is to define the variables. What that means is to state the particular quantity that each variable stands for.
In this problem, we have two quantities: Mary’s age and John’s age. So we’ll define the variables by saying “Let ???x??? be Mary’s age, and let ???y??? be John’s age.” (We could use any letters of the alphabet for the variables, but people often use ???x??? for one of the variables, and if there are one or two additional variables, they tend to use ???y??? and ???z???, in that order.)
The next step in solving a word problem is to “translate” each word or phrase into mathematical symbols. Here, “John’s age” is translated as “???2x-4???.”
How about the word “is” (in “John’s age is four less than twice Mary’s age”)? Well, “is” is translated as an equals sign. To see this, it may help to think of the word “is” as having the same meaning (in math) as “is equal to.”
Combining all of these, we get the equation
???y=2x-4???
The third step in solving a word problem is to use the given data and solve the equation. Here, we’re given Mary’s age as ???18???, so we substitute ???18??? for ???x??? and then solve for ???y???.
???y=2(18)-4???
???y=36-4???
???y=32???
The final step is to answer the question that was asked. Here, we’re asked for John’s age. Since we defined ???y??? as John’s age, the answer is ???32???.
Suppose we’d been given the following word problem instead:
Currently, John’s age is four less than twice Mary’s age. If Mary is now ???18???, how old will John be seven years from now?
To solve this problem, it would be convenient to define ???x??? as Mary’s age now, and ???y??? as John’s age now, because we’re given a relationship between Mary’s age (now) and John’s age (now). Then in the last step (answering the question that was asked), we’d have to evaluate ???y+7??? (to get John’s age seven years from now), and our answer would be ???32+7=39???.
Get access to the complete Algebra 1 course
Presentation on theme: «Writing Expressions from Word Problems»— Presentation transcript:
1
Writing Expressions from Word Problems
Mrs. Breeding 6th Grade
2
Annie makes $5 and hour baby sitting one child, and $2 each for every additional child. Write and algebraic expression that can be used to find out how much Annie earn. If Annie babysits 3 children for 2 hours, how much will she earn?
3
5h + 2c $14.00
4
A pizza with cheese costs $12, and $1. 50 for extra topping
A pizza with cheese costs $12, and $1.50 for extra topping. Write and algebraic expression that can be used to find the cost of a pizza. How much will a cheese pizza with 2 extra toppings cost?
5
1.50n + 12 $15.00
6
It costs $7 for a movie ticket, and $2 for each box of candy you buy
It costs $7 for a movie ticket, and $2 for each box of candy you buy. Write and algebraic expression that can be used to find how much you will spend. If you buy 1 box of candy with your movie ticket, how much will you spend?
7
2c + 7 $9
8
Joel runs twice as far as John
Joel runs twice as far as John. Write an algebraic expression that can be used to find how far Joel runs. If John runs 10 miles, how many miles does Joel run?
9
2n 20 miles
10
Ashe has a coupon for a $5 discount if he buys 3 video games
Ashe has a coupon for a $5 discount if he buys 3 video games. Write an algebraic expression that can be used to find how much Ashe will spend. If the game costs $45 each, how much will Ashe spend?
11
3g – 5 $130
12
Steven is paid $1000 a month, plus $50 for every computer he sells
Steven is paid $1000 a month, plus $50 for every computer he sells. Write an algebraic expression that can be used to find how much Steven will earn in a month. If Steven sells 6 computers this month, how much will he earn?
13
Averie is three years less than 3 times as old as her sister
Averie is three years less than 3 times as old as her sister. Write an algebraic expression that can be used to find Averie’s age. If Averie’s sister is 5 years old, how old is Averie?
14
3s – 3 12 years old
15
Broc has $150 in savings now and plans to save $20 every month
Broc has $150 in savings now and plans to save $20 every month. Write and algebraic expression that can be used to find out how much Broc will save. If Broc saves for a year, how much money will he have?
16
20m + 150 $390
17
Natalie reads for 30 minutes every day
Natalie reads for 30 minutes every day. Write an expression that can be used to find how many minutes Natalie reads. How many minutes does Natalie read in one week?
18
30d 210 minutes
19
Lauren sells her bracelets for $3 each after spending $20 on supplies
Lauren sells her bracelets for $3 each after spending $20 on supplies. Write an algebraic expression that can be used to find how much Lauren makes selling bracelets. If Lauren sells 20 bracelets, how much money will she make?
20
3b – 20 $40
21
Gavin charges $10 each for mowing lawns
Gavin charges $10 each for mowing lawns. Write an algebraic expression that can be used to find how much Gavin earns. If Gavin mows 15 lawns, how much money will her earn?
22
10x $150
23
Andrew rides his bike at a rate of 10 miles an hour
Andrew rides his bike at a rate of 10 miles an hour. Write an algebraic expression that can be used to find how many miles Andrew rode. If Andrew rides for 3 hours, how many miles will he ride?
24
10h 30 miles