Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

MATHEMATICS > Algebraic expressions > Flashcards

Algebraic expressions Flashcards

1
Q

a symbol that we use to represent a certain number.

A

Variable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Example 2: Take a look at the expression x + y + z + 3. What are the variables in the expression?

A

Solution: x, y, and z are the variables used in the expression x + y + z.

x, y, and z represent certain quantities or numbers.

Since a variable represents certain quantities or values, this means that the value of a variable is not fixed. For instance, in x + y + z, the values of x, y, and z can be any number.

In the study of algebra, English letters are the most commonly used variables. Thus, in this reviewer, we will use letters to denote a variable that represents a certain value.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

a quantity with a fixed value.

A

cONSTANTS

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

If you multiply a variable by a certain number, the latter is called a

A

numerical coefficients

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Example 1: Determine the numerical coefficient and literal coefficient in ¼ y.

A

Solution: The numerical coefficient is ¼ since it is the number multiplied by the variable y. Meanwhile, y is the literal coefficient since it is a variable multiplied by a number.

If a variable has no number written on its left, it means the numerical coefficient is 1. For instance, consider the variable x. Note that there is no number written on its left. This does not mean that it has no numerical coefficient. Instead, its numerical coefficient is 1. Thus, x can also be interpreted as 1x or “1 times x”.

However, in algebra, if the numerical coefficient is 1, we do not write it because it is already understood that a certain variable has a numerical coefficient of 1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Example 2: Determine the numerical coefficient of the following:
3y
0.23x
w

A

Solution: For item 1, the numerical coefficient is 3. For item 2, the numerical coefficient is 0.23. Lastly, for item 3, the numerical coefficient is 1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

a mathematical expression that involves constants, variables, and arithmetic operations (addition, subtraction, multiplication, or division).

A

algebraic expressions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Example 1: Determine the variables, constant, coefficient, and operations involved in 9 + 3xy – z.

A

Solution: The variables are x, y, and z. The constant is 9. Meanwhile, the operations involved are addition, multiplication (3xy can be interpreted as 3 times x times y), and subtraction. Furthermore, 3 is a numerical coefficient of xy.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Example 2: Determine the variables, constants, and operations involved in the algebraic expression x⁄y – 2

A

Solution: Before we answer this, take note that in algebra, we usually indicate division as the ratio or a fraction between two numbers. Therefore, if we want to write x ÷ y, we write it as x/y instead.

Therefore, in x/y – 2, the variables are x and y, the constant is 2, and the operations involved are division and subtraction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Example 1: Translate this verbal expression into an algebraic expression: “18 minus a number equals 5”.

A

Solution: The phrase “a number” means that we are not sure what that number is. This means that we need to represent it using a letter or symbol. In other words, we need to use a variable to represent that unknown number.

Let us use the letter g to represent this unknown number. Thus, if we translate “18 minus a number is 5” into an algebraic expression, we will obtain:

18 – g = 5

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

The sum of 8 and a number

A

8 + x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

-6 plus a number

A

-6 + x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

A number increased by 7

A

x + 7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

3 more than a number

A

x + 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

The total of a number and -10

A

x + (-10)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Example 1: Translate “the sum of two numbers” into an algebraic expression.

A

Solution: The given sentence doesn’t explicitly state the values of two numbers. Thus, we need to use variables to represent them. Let us use the letters x and y to represent the numbers.

Since we have the keyword “sum”, it means that the numbers must be added.

Thus, the sentence can be translated as x + y

The answer is x + y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Example 2:Translate “a number more than 18 is equal to 25” into an algebraic expression.

A

Solution:Let us assignkas the variable that represents the unknown number in the sentence.

It’s stated that“a number more than 18 is equal to 25”. Since the keyword “more than” is used, it means theoperation of additionis involved.

Again, the keyword “more than” implies that the first number mentioned in the sentence was added to the second number mentioned. This means that when we translate the sentence into an algebraic expression, we need to write the second number which is 18 as the first addend.

Thus, we can translate the sentence as 18 +k= 25.

The answer is 18 +k= 25.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Thedifferencebetween a number and 15

A

x – 15

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

9subtracted bya number

A

9-x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

9subtracted froma number

A

x-9

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

15deducted bya number

A

15-x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

15deducted froma number

A

x – 15

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

A numberdecreased by6

A

x – 6

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

11minusa number

A

11 – x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Example 1:Translate “A number subtracted from – 19 is equal to 5” into an algebraic expression.

A

Solution:Let us use the letterpas the variable that represents the unknown number.

Recall that to translate a sentence with the keywordsubtracted frominto an algebraic expression,we are going to write it in the form <second> – <first>.</first></second>

Hence, the correct translation must be:– 19 – p = 5.

26
Q

Example 2:Translate “54 decreased by a number” into an algebraic expression

A

Solution:Let us use the letterqto represent the unknown number.

The keyword “decreased by”implies that a number was subtracted from 54.

Thus, the correct translation should be54 – q

27
Q

Theproductof a number and 5

A

5x

28
Q

-3multiplied bya number

A

-3x

29
Q

Twiceof a number

A

2x

30
Q

Thriceof a number

A

3x

31
Q

½ofa number

A

½x

32
Q

7timesa number

A

7x

33
Q

Example 1:Translate “20% of a number is equal to 50”into an algebraic expression.

A

Solution:The keyword “of” indicates multiplication. Thus, the correct translation is 20%x = 50.You can also express the given percent into decimal. This means that 0.20x =50 is also a translation for the given sentence.

34
Q

Example 2:Translate “The product of two numbers is equal to twice of another number” into an algebraic expression.

A

Solution:We have three unknown numbers involved. Thus, we need to use three letters as variables. Let us use the lettersx, y,andz.

The product of two numberscan be translated asxy. Meanwhile, since the keywordtwiceindicates that a number is being doubled or multiplied by 2, thentwice of another numbercan be translated as 2z. Hence, the correct translation of the given sentence should bexy = 2z.

35
Q

Thequotientof 8 and a number

A

8 ÷xor 8⁄x

36
Q

A numberdivided by4

A

x ÷4or x⁄4

37
Q

Theratio ofa number and 2

A

x÷2or x⁄2

38
Q

A number issplit equallyinto 3

A

x÷3orx⁄3

39
Q

Example 1:What is “The sum of twice a number and 9” as an algebraic expression?

A

Solution:Let us start with the first keyword mentioned in the problem which is thesum. Recall that if the keywordsumis used in a sentence, it implies that there are numbers being added. The question now is:What are the numbers that are being added according to the given verbal expression?

Let us read again the given verbal expression:The sum of twice a number and 9. It is clearly stated that there are two quantities that will be added–the quantitytwice a numberand 9.

We can now express our translation in this form for a while:twice a number + 9

Now, let us translatetwice a numberinto an algebraic expression. Again, the wordtwiceimplies that a certain number is being doubled or multiplied by 2. Let us usexto represent the unknown number. Thus, twice ofxis simply, 2x.

Therefore, our final translation forThe sum of twice a number and 9is 2x+ 9.

40
Q

Example 2:Translate “Twice the difference between two numbers” into an algebraic expression.

A

Solution:Let us start with the keywordtwice. This keyword implies that a certain quantity or number will be multiplied by 2.What is this quantity that will be multiplied by 2 according to the given verbal expression?

Let us read the given problem again:Twice the difference between two numbers. The statement tells us the difference between the two numbers is what will be multiplied by 2.

Hence, we can translate it this way: 2(difference between two numbers). We use parenthesis to indicate multiplication.

Now, let us translate thedifference between two numbersinto an algebraic expression. We have two unknown numbers so let us use x and y to represent them. Thus, we can translate thedifference between two numbersasx – y.

We replace the expressiondifference between two numbersin 2(difference between two numbers)withx – y.

Hence,Twice the difference between two numbersis 2(x – y).

41
Q

Example 3:Write “the ratio of two numbers increased by 5” as an algebraic expression.

A

Solution: Let us start with the keywordratio. The phrasethe ratio of two numberstells us that two numbers are involved in a division process. Letxandybe these two numbers. Hence, we can translatethe ratio of two numbersasx÷yor x⁄y. For this problem, let us use x⁄y.

The next keywordincreased byinthe ratio of two numbers increased by 5tells us that the number 5 will be added to x⁄y. This means that we need to add 5 to our translation. Thus,

x⁄y+ 5

Therefore, ifthe ratio of two numbers increased by 5will be written as an algebraic expression, you will have x⁄y+ 5

42
Q

Thesquare rootof a number
Cube rootof a number

A

√x
∛x

43
Q

A numberraised to5
Square ofa number
Cube ofa number

A

x5
x2
x3

44
Q

4 isequal toa number
3 plus a numberyields9
7 minus a numberis0

A

4 =x
3 +x = 9
7 –x= 0

45
Q

5 isnot equal toa number
7 isgreater thana number
7 isless thana number
0 isgreater than or equal toa number
0 isless than or equal toa number
5 plus a number isat least9
3 minus a number isat most24 =x
3 +x = 9
7 –x= 0
0 ≥x
0 ≤x
5 +x≥ 9

A

4 =x
3 +x = 9
7 –x= 0
0 ≥x
0 ≤x
5 +x≥ 9
3 –x≤ 2

46
Q

Example 1:Write “the sum of the square of a number and 3 is at least 9” as an algebraic expression.

A

Solution:The keywordsumtells us that certain quantities will be added. These quantities are the square of a number and 3.

Let us usexto represent the unknown number. Its square can be represented asx2.

Thus, the quantities that will be added arex2and 3.

The sum of the square of a number and 3 is at least 9. This means thatx2+ 3 is greater than or equal to 9.

Hence, the correct translation isx2.+ 3≥9

47
Q

Example 1:Lea has 150 books that she collected during her college years. She decided to give some of her books to her friends. After giving some to her friends, 40 books were left to Lea. Write an algebraic expression that will illustrate Lea’s scenario.

A

Solution:It’s stated in the given scenario that Lea has 150 books. She gave some of her books to her friends. 40 books were left to Lea after giving some of them. This can be interpreted as 150 books minus the number of books given equals 40.

Let us usebto represent the number of books Lea gave to her friends.

Thus, we have this algebraic expression:150 – b = 40

48
Q

Example 2:A burger costs Php 32 each while a can of pineapple juice costs Php 25 each. Dario bought some burgers and cans of pineapple juice. Write an algebraic expression that shows how much Dario will pay for the burgers and cans of pineapple juice he bought.

A

Solution:It’s not specifically stated in the given scenario how many burgers and cans of pineapple juice Dario bought. Thus, we can use variables to represent the number of burgers and cans of pineapple juice he bought.

Letbrepresent the number of burgers that Dario bought. Meanwhile, letprepresent the number of cans of pineapple juice that Dario bought.

Each burger costs Php 32. Thus, the total amount that Dario will pay for the burgers can be represented as 32b.

Meanwhile, each can of pineapple juice costs Php 25. Thus, the total amount that Dario will pay for the cans of pineapple juice can be represented as 25p.

Combining the total amount he will pay for the burgers and cans of pineapple juice: 32b+ 25p.

Thus, the answer is 32b+ 25p.

49
Q

Example 1:Write x + 2 as a verbal expression.

A

Solution:The algebraic expression involves the operation of addition. Thus, you can use the keywords for addition in translatingx + 2.Moreover, just use the words “a number”to translate the variable.

Let’s use the keywordsum. We know thatsumis written before the quantities that are added. Thus, one possible translation could be “the sum of a number and 2”

Another possible translation is using the keyword “increased by”. You can translatex + 2as“A number increased by 2”.

50
Q

Example 2:Translate 4z + 5 into a verbal expression.

A

Example 2:Translate 4z + 5 into a verbal expression.

51
Q

Example 3:Translate y2≤ 2 into a verbal expression.

A

Solution:yrepresents a certain number. Thus, we can translate it as “a number”. Meanwhile,y2means that we squared that number. Hence,y2can be translated as “the square of a number”.

The symbol ≤ means less than or equal. We can use the phraseless than or equalfor this symbol or the phraseat most. In this problem, let us use the phraseat most.

Therefore, one possible translation fory2≤2could bethe square of a number is at most 2.

52
Q

Example 1:Evaluate x + 2if x = 2

A

Solution:The variable inx + 2isx. In this example, we have assigned a value toxwhich isx = 2.This means that we need to substitute or replacexwith 2.

Afterward, we perform the calculation to find the value of the algebraic expression whenx = 2.

Thus,x + 2 = 4ifx = 2.

53
Q

Example 2:Evaluate 5x + y if x = 2 and y = 0

A

Solution:We just substitute2forxand0foryin5x + y.Take note that 5xis multiplication between 5 andx. Thus, once you substitute 2 forx, you will have 5(2) which implies “5 times 2”.

Hence, the answer is 10.

54
Q

Example 3:Evaluate 2x – 3(y + z) if x = 10, y = 1, and z = 3

A

Solution:Plug in the assigned values forx, y, and zin the given algebraic expression:

Since, there are multiple operations involved, let use apply PEMDAS:

Therefore, the answer is 8.

55
Q

Example 4:Evaluate 8a – 3b if a = ½ and b = – 2

A

Solution:Let us plug in the values ofaandbto the given algebraic expression.

Performing the operations involved:

Thus, the answer is 10.

56
Q

1) Evaluate 2x
2y - 3xy + z at x = 1, y = 2, and z = - 1
a) - 1
b) - 2
c) - 3
d) - 4

A

C

57
Q

2) Write an algebraic expression that represents the phrase “the sum of a number and
one-fourth of it”.
a) x +
1
4
b) + x
1
4
1
4
c) x
1
4
d) x + x

A

D

58
Q

3) Translate into words.
3𝑥
2
a) The ratio of a number to thrice of it
b) Three times a number decreased by 2
c) Thrice the ratio of a number to 2
d) The ratio of thrice a number to 2

A

D

59
Q

4) What is if a = 1?
𝑎
3 − 𝑎
2
a) - ⅔
b) - ⅓
c) ⅔
d) ⅓

A

A

60
Q

5) What is “The sum of two numbers is at least 5” in symbols?
a) x + y < 5
b) x + y < 5
c) x + y > 5
d) x + y > 5

A

C

MATHEMATICS (21 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions