Brainscape's Knowledge GenomeTM

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


See full index

Prealgebra > AoPS Ch 1 Properties of Arithmetic > Flashcards

AoPS Ch 1 Properties of Arithmetic Flashcards

0
Q

Addition is commutative. What does this mean?

A

a + b = b + a

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

Order of operations: In what order do you perform the operations in an expression?

A
  1. Evaluate expressions inside parentheses first.
  2. Compute powers.
  3. Multiply and divide from left to right.
  4. Add and subtract from left to right.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is another way to write 3 + 7 using the commutative property of addition?

A

7 + 3

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

Addition is associative. What does this mean?

A

(a + b) + c = a + (b + c)

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

What is another way to write (2 + 5) + 3 using the associative property of addition?

A

2 + (5 + 3)

In other words, you can add 5+3 first to get 8 and then add 2 to get 10, instead of 2+5 to get 7 and then 7+3 to get 10.

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

Compute (35 + 13) + 27

A

Using the associative property:

35 + (13 + 27) = 35 + 40 = 75

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

Multiplication is commutative: What does this mean?

A

ab = ba

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

Multiplication is associative. What does this mean?

A

(ab)c = a(bc)

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

According to the commutative property, what does 7x35 equal?

A

7 x 35 = 35 x 7

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

Using the associative property, compute 25 x (12 x 8) in your head.

A

25 x (12 x 8) = (25 x 12) x 8 = 300 x 8 = 2400

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

Distributive Property: Multiplication distributes over addition. What does this mean?

A

a(b + c) = ab + ac

and

(b + c)a = ba + ca

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

Using the distributive property, what is 5 x 17?

A

5 x 17 = 5 x (10 + 7) = 5 x 10 + 5 x 7 = 50 + 35 = 85

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

Using the distributive property, compute (7 + 9) x 13.

A

(7 + 9) x 13 = (7 x 13) + (9 x 13) = 91 + 117 = 208

or

(7+9) x 13 = 16x13 = 16 x (10+3) = 16x10 + 16x3 = 160+48 = 208

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

What is the Negation Property?

A

-a + a = 0

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

What is the Reciprocal Property?

A

(1/a) x a = 1

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

What is the definition of SUBTRACTION?

A

a - b = a + (-b)

Subtraction is addition of the negation.

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

What is DIVISION?

A

(a/b) = a x (1/b)

Division is the same as multiplication by the reciprocal.

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

Negation of a negation says the -(-a) = ?

A

-(-a) = a

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

Negation of a sum says that -(a + b) = ?

A

-(a + b) = (-a) + (-b)

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

Multiplying by -1 means that (-1)a = ?

A

(-1)a = -a

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

Multiplying by a Negation means that (-a)b = ?

A

(-a)b = -(ab)

and

a(-b) = -(ab)

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

Negation times Negation means that (-a)(-b) = ?

A

(-a)(-b) = ab

22
Q

Compute (-3)(-2) =

A

(-3)(-2) = 6

23
Q

Compute (-3)(2) =

A

(-3)(2) = -6

24
Q

Compute (3)(-2) = ?

A

(3)(-2) = -6

25
Q

Compute (-1)(7) =

A

(-1)(7) = -7

26
Q

Subtracting from 0:

0 - a =

A

-a

27
Q

Self subtraction:

a - a =

A

0

28
Q

Subtracting 0:

a - 0 =

A

a

29
Q

Subtraction of negation:

a - (-b) =

A

a + b

30
Q

Subtraction from negation:

-a - b =

A

-(a+b)

31
Q

Negation of subtraction:

-(a - b) =

A

b - a

32
Q

Multiplication distributes over subtraction:

a(b - c) =

A

ab - ac

33
Q

Multiplication distributes over subtraction:

(b - c)a =

A

ba - ca

34
Q

Reciprocal of reciprocal:

If a is nonzero, then the reciprocal of (1/a) is ?

A

a

35
Q

Reciprocal of negation:

If a is nonzero, then (1/-a) =

A

-(1/a)

36
Q

Reciprocal of product:

If a and b are nonzero, then (1/ab) =

A

(1/a) x (1/b)

37
Q

Dividing into zero:

If a is nonzero, then 0/a =

A

0

38
Q

Self division:

If a is nonzero, then a/a =

A

1

39
Q

Dividing by 1:

a/1 =

A

a

40
Q

Dividing into 1:

If x is nonzero, then 1 divided by x is ?

A

1/x

41
Q

Dividing by reciprocal:

If b is nonzero, then a divided by (1/b) is

A

ab

42
Q

Dividing into negation:

If b is nonzero, then (-a)/b =

A

-(a/b)

43
Q

Dividing by negation:

If b is nonzero, then a/(-b) =

A

-(a/b)

44
Q

Negation divided by negation:

If b is nonzero, then (-a)/(-b) =

A

a/b

45
Q

Cancel common factor:

If a and c are nonzero, then (ab)/(ac) =

A

b/c

46
Q

Division by a number distributes over addition:

If c is nonzero, then (a + b)/c =

A

a/c + b/c

47
Q

Division by a number distributes over subtraction:

If c is nonzero, then (a - b)/c =

A

a/c - b/c

48
Q

Adding zero:

a + 0 =

A

a

49
Q

Multiplying by zero:

0 x a = 0a =

A

0

50
Q

Subtraction is neither commutative nor associative. What does this mean?

A

a - b does not necessarily equal b - a, and

a - (b - c) does not necessarily equal (a - b) - c

51
Q

You can’t divide by

A

Zero.

Division by zero is undefined. Before dividing by a number, be sure that the number is nonzero.

52
Q

Division is neither commutative nor associative. What does this mean?

A

a/b and b/a are not necessarily equal, and

a/(b/c) and (a/b)/c are not necessarily equal.

53
Q

We can use the distributive property to divide a sum by a number, but we can’t use the distributive property to divide a number by a sum. What does this mean?

A

(a + b)/c = a/c + b/c and (a - b)/c = a/c - b/c

but a/(b + c) is not necessarily equal to a/b + a/c       
and a(b - c) is not necessarily equal to a/b - a/c

Prealgebra (3 decks)

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