Basic Rules of Algebra

Question 1

Formula for the Pythagorean Theorem

Answer 1

a² + b² = c²

Question 2

• Extension of the Pythagorean Theorem

Suppose a and b = 1

1² + 1² = c²
1 + 1 = c²
2 = c²

How to solve for c if c² = 2

Answer 2

Undo the squaring by taking the square root of both sides.

√2 = √c²
(Cancel out the Radical Sign and Squared on the right hand)
c = √2 or 1.414…

Further explanation: The square root operation is the inverse of squaring a number.

Question 3

Meaning of PEMDAS

Answer 3

• Parentheses
• Exponent
• Multiplication
• Division
• Addition
• Subtraction

Question 4

3 - 4 = 1 to Addition

Answer 4

3 + (-4) = 1

Question 5

3 / 4 to Multiplication

Answer 5

3 x 1/4 = 3/4

Question 6

Consider
x² + 1 = 0

Hint: Transpose

Answer 6

• x = √-1
• i = √-1

Solution:
x² = -1
√x² = √-1
x = √-1

Question 7

Additive Inverse of 5

Answer 7

• -5

Solution: 5 + (-5) = 0

Question 8

Additive Inverse of -7

Answer 8

• 7

Solution: -7 + 7 = 0

Question 9

Reciprocal of 23

Answer 9

• 1/23

Solution:
23/1
a/b → b/a

Question 10

Reciprocal of 64

Answer 10

• 1/64

Solution:
64/1
a/b → b/a

Question 11

Convert this to a fraction: 8

Answer 11

8/1

Question 12

Multiplicative Inverse of 5

Answer 12

• 1/5

Solution:
Reciprocal of 5
Convert 5 to a fraction
5/1
Multiply the converted number to the reciprocal
(5/1) (1/5)
5x1 and 1x5
5/5 = 1

Explanation: Can transform the first numerator and second denominator to 1’s because they are the same amount (Consider reciprocal).

Or just use 5x1, 1x5 = 1/1 = 1

Question 13

Multiplicative Inverse of -7

Answer 13

• • 1/7

Solution:
Reciprocal of -7
Convert -7 to a fraction
- 7/1
Multiply the converted number to the reciprocal
(- 7/1) (- 1/7)
-7x-1 and -1x-7
7/7 = 1

Explanation:
When multiplying fractions, just multiply the numerator to the numerator, and same with the denominator.

Question 14

Multiplicative Inverse of 3/5

Answer 14

• 5/3

Solution:
Reciprocal of 3/5
Multiply the converted number to the reciprocal
(3/5) (5/3)
3x5 and 5x3
15/15 = 1

Explanation:
When multiplying fractions, just multiply the numerator to the numerator, and same with the denominator.

Question 15

What is Commutative Property of Addition?

Answer 15

It means that however or wherever you put the given number, when added, sums up to the same answer.

Question 16

What is Commutative Property of Multiplication?

Answer 16

It means that however or wherever you put the given number, when multiplied, the product is the same.

Question 17

What is Associative Property of Addition?

Answer 17

Whichever you add first in a problem with three(3) numbers, it will sum up the same answer.

(1 + 2) + 3 = 1 + (2 + 3)
3 + 3 = 1 + 5
6 = 6

Question 18

What is Associative Property of Multiplication?

Answer 18

Whichever you multiply first in a problem with three(3) numbers, it will produce the same answer.

(2 x 3) x 4 = 2 x (3 x 4)
6 x 4 = 2 x 12
24 = 24

Question 19

What is Distributive Property?

Answer 19

This can be used to multiply a number to a binomial, starting from the closest to the farthest.

Example:
a(b + c) = ab + ac

Question 20

What is the Foil Method?

Answer 20

Using distributive property to multiply binomials meaning First, Outer, Inner and Last.

Example:
(a + b)(c + d)
ac + ad + bc + bd

Question 21

What is Additive Identity Property?

Answer 21

Adding zero to a number keeps the value of the number.

Question 22

What is Multiplicative Property?

Answer 22

Multiplying a number to 1 would result in the same number.