Understanding Mathematical Expressions in Algebra
Explore how to translate English phrases into mathematical expressions in algebra. Learn key phrases for addition, subtraction, multiplication, and division, and practice writing expressions for various scenarios. This presentation includes examples and guidance for mastering algebraic concepts.
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Translating English to Mathematics As you read through this PowerPoint document, you will see a pencil on some of the pages. This is your cue to stop and try the exercise before moving on.
Key Phrases When we express algebraic concepts like addition, subtraction, multiplication, and division there are specific phrases that get used over and over again.
Phrases that mean a + b a increased by b b more than a the sum of a and b b added to a There are others that are context specific.
Write each phrase as a mathematical expression. The time, t, increased by 30 minutes Three ounces more than the weight, w The sum of the distance, d, and 45 miles
Write each phrase as a mathematical expression. The time, t, increased by 30 minutes t + 30 Three ounces more than the weight, w w + 3 The sum of the distance, d, and 45 miles d + 45
Phrases that mean a - b a decreased by b b less than a the difference between a and b b subtracted from a There are others that are context specific.
Write each phrase as a mathematical expression. Five less than the perimeter, p The height, h, decreased by 10 feet The difference between $50 and the cost
Write each phrase as a mathematical expression. Five less than the perimeter, p p 5 The height, h, decreased by 10 feet h 10 The difference between $50 and the cost 50 c
Multiplication and Division Phrases a b a multiplied by b the product of a and b a b a divided by b the quotient of a and b 1 b 2 a twice a a doubled 2 half of b b halved
Write each phrase as a mathematical expression. Twice the time The product of 5 and the price The rate divided by 12 The quotient of the distance and the time
Twice the time 2 t The product of 5 and the price 5 p The rate divided by 12 r 12 The quotient of the distance and the time d t
Each word in bold is a noun and means the result of the designated operation. Example: The sum of a and b is the number you get by adding a and b. The sum of a and b a + b The difference between a and b a - b The product of a and b a b The quotient of a and b a b
Write the phrase as a mathematical expression. Three times the sum of the time and 10 minutes
Write the phrase as a mathematical expression. Three times the sum of the time and 10 minutes 3(t +10) Explanation: The sum is the result of adding. The key here is to realize that three times the sum means that we add first then multiply by three.
Write each phrase as a mathematical expression. 4 more than the product of a number and 6 The difference between 8 and the product of a number and 7 10 less than the quotient of the time and 60
4 more than the product of a number and 6 6x + 4 The difference between 8 and the product of a number and 7 8 - 7x 10 less than the quotient of the time and 60 ? 60 10
Similar phrases can represent different expressions. Translate each pair of expressions. The height decreased by 10 feet 10 feet decreased by the height Four times a number, increased by 8 Four times a number increased by 8
Order matters in subtraction and division! The height decreased by 10 feet h 10 10 feet decreased by the height 10 h
A comma can make all the difference (in a perfect world everyone would avoid such ambiguous statements though). Four times a number, increased by 8 4x + 8 Four times a number increased by 8 4 (x + 8)
Identify the two related quantities. Define a variable to represent one of the quantity then represent the other quantities with an expression using your variable. One number is 3 less than another.
Identify the two related quantities. Define a variable to represent one of the quantity then represent the other quantities with an expression using your variable. One number is 3 less than another. Let n be another number.
Identify the two related quantities. Define a variable to represent one of the quantity then represent the other quantities with an expression using your variable. One number is 3 less than another. Let n be the second number. n 3 is the first number.
Identify the two related quantities. Define a variable to represent one of the quantities then represent the other quantity with an expression using your variable. Charlie and Ivan share a pizza. Ethan weighs twice as much as his little brother Ben. Debbie s weekly pay is $27.50 less than Stacy s weekly pay. The jeans were on sale for one-third off.
Charlie and Ivan share a pizza. Let n be the amount Ivan eats 1 n is the amount Charlie eats (they eat one pizza). Ethan weighs twice as much as his little brother Ben. Let B be the amount Ben weighs 2B is the amount Ethan weighs
Debbies weekly pay is $27.50 less than Stacy s weekly pay. Let S be Stacy s weekly pay in dollars. S 27.50 is Debbie s weekly pay. The jeans were on sale for one-third off. Let r be the regular price of the jeans r (1/3)r is the sale price.
Write the phrase as a mathematical expression. The price of a new sofa plus 7.5% sales tax
Write the phrase as a mathematical expression. The price of a new sofa plus 7.5% sales tax Let p be the price of the sofa in dollars. p + 0.075p
Working with Percent Express the percentage as a decimal by moving the decimal 2 places to the left. 7.5% = 0.075 40% = 0.40 120% = 1.20 A percent is always a percent of something. Which means we multiply. 25% of $16.00 = 0.25 (16) = $12.00 35% of the price = 0.35 p
Write each phrase as a mathematical expression. 75% as many calories as in a regular soft drink The price of a pair of jeans, marked down 25% A 40% increase in student interest The enrollment this year is up 6.25% Tobias is watching 30% less television this year than last year.
75% as many calories as in a regular soft drink Let c be the number of calories in a regular soft drink. 0.75c The price of a pair of jeans, marked down 25% Let p be the regular price of a pair of jeans. p 0.25p A 40% increase in student interest Let S be the previous level of student interest. S + 0.40 S The enrollment this year is up 6.25% Let n be last year s enrollment. n + 0.0625 n Tobias is watching 30% less television this year than last year. Let T be the amount of television Tobias watched last year. T 0.30 T
Applications An equation is the algebraic equivalent of a sentence. The equals sign is the verb in your mathematical sentence. As you work on application problems (AKA story problems), remember that one sentence usually makes one equation and the equals sign goes where the verb is.
