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Business Law I > CH R CH 01 Beginning Algebra by Lial Hornsby McGinnis > Flashcards

CH R CH 01 Beginning Algebra by Lial Hornsby McGinnis Flashcards

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1
Q

CH R.1

What are the natural (or counting numbers)?

A

1, 2, 3, 4…

P 01

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2
Q

CH R.1

What are the whole numbers?

A

0, 1, 2, 3, 4…

P 02

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3
Q

CH R.1

Name the parts of a fraction.

A

3/8

The 3 is the Numerator.

The / is the fraction bar.

The 8 is the Denominator.

(P 01)

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4
Q

CH R.1

What is a proper fraction?

A

The Numerator is less than the denominator. The value is less than 1.

(P 01)

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5
Q

CH R.1

What is an improper fraction?

A

The numerator is greater than or equal to the denominator. The values is equal to or greater than 1.

(P 01)

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6
Q

CH R.1

What does the fraction bar represent?

A

The fraction bar represents division.

P 01

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7
Q

CH R.1

In 3 x 6 = 18, the 3 and the 6 are ___________ of 18.

A

In 3 x 6 = 18, the 3 and the 6 are factors of 18.

P 02

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8
Q

CH R.1

What does factor mean (how do we factor)?

A

We factor a number by writing it as the product of two or more numbers.

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9
Q

CH R.1

What is a prime number?

A

A prime number is a number that can only be evenly divided by 1 and itself. It only has two factors, 1 and itself.

(P 02)

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10
Q

CH R.1

What is a composite number?

A

A composite number is a natural number greater than 1 and is not a prime number.
It is made of, or is a composite of, numbers that are factors.

(P 02)

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11
Q

CH R.1

Using a factorization tree, what kind of number do we start with, and what kind of number(s) do we factor down to?

A

We start with a prime number and factor down to only prime numbers in the tree.

(P 03)

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12
Q

CH R.1

True or False. The number 1 is considered a prime number.

A

False. The number 1 is considered to be neither prime nor composite.

(P 02)

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13
Q

CH R.1

Note: No matter which prime factor we start with when factoring, we will always obtain the same prime factorization.

(see a factorization tree)

(P 03)

A
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14
Q

CH R.1

Any nonzero number divided by itself is equal to ____.

A

Any nonzero number divided by itself is equal to 1.

P 03

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15
Q

CH R.1

Any nonzero number multiplied by itself is equal to _________.

A

Any number multiplied by 1 remains the same number. It does not change.

(P 03)

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16
Q

CH R.1

How do we write a fraction in lowest terms?

What is this called?

A

Step 1 - Write the numerator and denominator in factored form.

Step 2 - Replace each pair of factors in common to the numerator and denominator with 1.

Step 3 - Multiple the remaining factors in the numerator and denominator.

This is called “simplifying the fraction.”

(P 03)

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17
Q

CH R.1

What is a mixed number?

A

A mixed number is a number that represents the sum of a natural number and a proper fraction.

2 3/4 is a mixture of a natural number (2) and a proper fraction (3/4).

(P 04)

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18
Q

CH R.1

Write 59/8 as a mixed number.

The 59 is the numerator.
The 8 is the denominator.

A

59 divided by 8 is 7 with a remainder of 3.

The answer is 7 3/8. (Seven and three eighths.

(P 04)

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19
Q

CH R.1

Write 6 4/7 as an improper fraction.

A

6 4/7
Multiply the denominator of the fraction by the natural number and then
add the numerator to obtain the numerator of the improper fraction.

7 * 6 = 42.
42 + 4 = 46.

46/7 is the improper fraction for 6 4/7.

(P 04)

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20
Q

CH R.1

Note: Multiplying fractions. If a/b and c/d are fractions, then a/b * c/d = a*c over b * d.

Multiply their numerators and then multiply their denominators.

A
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21
Q

CH R.1

When writing in lowest terms, you can factor and divide out any common factors before multiplying.

(P 05)

A
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22
Q

CH R.1

Two numbers are reciprocals of each other if their product is __________.

A

Two numbers are reciprocals of each other if their product is 1.

3.4 * 4/3 = 12/12 or 1.

10/1 * 1/10 = 1.

(P 06)

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23
Q

CH R.1

Place value is used to write a decimal as a fraction.

Write each decimal as a fraction.

  1. 95
  2. 056
  3. 2095
A

0.95 is 95/100. 95 hundredths.
0.056 is 56/1000. fifty-six thousandths.
4.2095 is 4 and 2095/10,000 or four and two thousand ninety-five ten-thousandths, or
42,095/10,000.

(P 17)

24
Q

CH R.1

1 2/3 divided by 4 1/2.

A

Write each number as an improper fraction. (heavy on top)

Turn the second number into its reciprocal.

Multiply. Reduce if possible. This example cannot be reduced.

(P 07)

25
Q

The result of adding two numbers is the ______ of the numbers.

A

The result of adding two numbers is the sum of the numbers.

P 07

26
Q

CH R.1

Note: Add fractions.

If a/b and c/b are fractions, then a/b + c/b = a + c / b.

To find the sum of two fractions having the same denominator, add the numerators and keep the same denominator.

If they do not have the same denominator, rewrite with one common denominator.

3/4 = ?/12. 4 goes into 12 3 times, 3 * 3 = 9/12. or:

3/4 * 1 = 3/4 * 3/3 or 9/12. Can be reduced back to 3/4.

A
27
Q

CH R.1

Note: The process of writing and equivalent fraction is the reverse of writing a fraction in lowest terms.

A
28
Q

CH R.1

Finding the lowest common denominator, or least common denominator.

Step 1 - Factor each denominator using prime numbers.

Step 2 - The LCD is the product of every (different) factor that appears in any of the factored denominators. If a factor is repeated, use the greatest number of repeats as factors of the LCD.

Step 3 - Write each fraction with the LCD as the denominator.

A

4/15 + 5/9.

Factor each denominator using prime factors. 15 = 5 * 3, 9 = 3 * 3.
The LCD is 5 * 3 * 3 or 45.
Write each fraction with 45 as the denominator. 4/15 * 3/3 = 12/45. 5/9 * 5/5 = 25/45. Therefore,
4/15 + 5/9 = 12/45 + 25/45, or 37/45. If the answer can be reduced, reduce.

(P 08)

29
Q

CH R.1

3 1/2 + 2 3/4.

A

3 1/2 + 2 3/4 equals 7/2 + 11/4.
2 goes into 4 a total of 2 times. 2 * 7 = 14 which makes 14/4.
14/4 + 11/4 = 25/4. 25 divided by 4 equals 6 1/4. The 6 1/4 is reduced and is a mixed number.

(P 08)

30
Q

What is the addition property of 0?

A

0 plus any number equals the number.

31
Q

What is the commutative property of addition?

A

Changing the order of the two addends does not change the sum.

32
Q

What is the associative property of addition?

A

You can change the grouping of numbers without changing the sum.

33
Q

What is the perimeter of a polygon?

A

Distance around the polygon, or the sum of the lengths of its sides.

34
Q

What are the minuend, the subtrahend and the difference?

A

The minuend is the number being taken away from the subtrahend. The difference is the result.

35
Q

What are the subtraction properties of 0?

A

A number minus the same number is 0.

The difference of any number and 0 is the same number.

36
Q

What is the multiplication property of 0?

A

Any number multiplied by 0 is 0.

37
Q

What are factors in multiplication?

A

The number you are multiplying.

38
Q

What is the result of multiplying?

A

The product.

39
Q

What is the multiplication property of 1.

A

1 times any number is the same number.

40
Q

What is the commutative property of multiplication?

A

The order of the factors can change without changing the product.

41
Q

What is the associative property of multiplication?

A

The grouping of the numbers can be changed without changing the product.

42
Q

What is the distributive property of multiplication?

A

Multiplication distributes over addition.

43
Q

What is the bar in long division?

A

The divisor is separated from the dividend by a right parenthesis ⟨)⟩ or vertical bar ⟨|⟩; the dividend is separated from the quotient by a vinculum (i.e., an overbar). The combination of these two symbols is sometimes known as a long division symbol or division bracket. (Google)

44
Q

What is a fraction bar?

A

It is the bar separating the numerator and the denominator in a fraction.

45
Q

What is the division property of 1?

A

Any number divided by itself is 1.

Any number divided by 1 is that number.

46
Q

What is the division property of 0?

A

The quotient of 0 any any number is 0, also known as undefined.

47
Q

How do you find an average?

A

An average is the sum of numbers over the number of numbers.

48
Q

What is the result called:

In addition?
In subtraction?
In multiplication?
In division?

A

In addition: the sum.
In subtraction: the difference.
In Multiplication: the product.
In Division: the quotient.

49
Q

How do you calculate the area?

A

The length times the width.

50
Q

What is the square root?

A

On of the two identical factors of a number.

51
Q

What is the Associative Property of Addition?

A

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

signs stay the same.

52
Q

What is the associative property of multiplication?

A

(a * b) * c = a * (b * c)

signs stay the same

53
Q

What is the identity property?

A

The Identity property involves the number 0.

a + 0 = a

sign stays the same

54
Q

What is the Identity property of multiplication?

A

The Identity property involves the number 1.

a * 1 = a

sign stays the same

55
Q

What is the Inverse Property of Addition?

A

a + (-a) = 0

opposite signs.

56
Q

What is the Inverse Property of Multiplication?

A

1 * 1/a = a/a = 1

signs stay the same

57
Q

What is the Distributive Property?

A

PEMDAS

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

Business Law I (13 decks)

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