Math 1

Question 1

Real number

Answer 1

Any number on the number line including positive, negative, zero, fractions, decimals

Question 2

Integers

Answer 2

All positive and negative WHOLE numbers, including zero

Question 3

Commutative property

Answer 3

Switch order (addition and multiplication)

a+b=b+a
ab=ba

*can rewrite subtraction as addition of negative
7-4=7+(-4)=(-4)+7

Question 4

Associative property

Answer 4

Grouping (addition and multiplication)

A+(b+c)=(a+b)+c
a(bc)=(ab)c

Question 5

Distributive property

Answer 5

A(b+c)=ab +ac

A(b-c)=ab-ac

Question 6

Multiplying by zero

Answer 6

Anything times zero equals zero

Question 7

Zero product property

Answer 7

If product of two numbers is zero, one factor must be zero

If ab=0, then a=0 or b=0

Question 8

Dividing number by itself

Answer 8

If a doesn’t equal 0, then a/a=1

Question 9

(Negative) - (positive)

Or

(Negative) + (negative)

Answer 9

Factor out negative sign

(-46)-37 = -(46+37) = -83

Question 10

(Small positive) - (bigger positive)

Or

(Small positive) + (big negative)

Answer 10

Factor out negative and reverse order of subtraction

23-64= -(64-23)= -41

Question 11

Sign rules for multiplication/division

Answer 11

Same sign=positive

Different sign=negative

Question 12

Absolute values

Answer 12

Gives the distance of the number from the origin

|x-5|= distance of x from +5

|x+3|= distance of x from -3

Question 13

Order of operations

Answer 13

GEMDAS (grouping)

Always cancel before multiplying

Work from inside out with groups

Question 14

Multiplying decimals

Answer 14

Count number of digits to right of decimal and multiply as whole numbers

6.25 x 0.048 ; 2+3=5 decimal places
625 x 48 = 30000 = 0.3

Question 15

Decimal exponents

Answer 15

(0.3)^3=(0.03) x (0.03) x (0.03)

Then like multiplication rules: 6 places to the right of the decimal

3^3=27 ; .000027

Question 16

Dividing decimals

Answer 16

Slide decimal for both numbers to the right until you have two whole numbers (or until it’s easier to solve)

0.56/0.0007=5600/7=800

Question 17

Fractions to decimals

2/5

Answer 17

0.4

Question 18

Fractions to decimals

3/5

Answer 18

0.6

Question 19

Fractions to decimals

4/5

Answer 19

0.8

Question 20

Fractions to decimals

5/6

Answer 20

.8333 …

Question 21

Squaring multiple of 10

Answer 21

Square nonzero, then tack in two zeros at end

70^2 = 4900

Question 22

Squaring number ending in 5

Answer 22

1) remove the 5, leaving remaining digit(s)
2) add one to remaining digit(s)
3) multiply numbers from first two steps
4) put product in front of 25

35^2
3+1=4
3*4=12
35^2=1225

Question 23

If we know value of n^2, (if n is multiple of 5,10), we can get next square up, (n+1)^2, by adding n and (n+1)

41^2 = 40^2 +40 + 41

Answer 23

X

Question 24

Dividing by 5

Answer 24

Double N and divid by 10

235/5 = 470/10 = 47

Question 25

Equivalent fractions

Answer 25

Fractions with equal numerical value even tho they have different numerators and denominators

Question 26

Fraction in lowest terms

Answer 26

Equivalent fraction with lowest possible numerator and denominator (simplifying)

Question 27

Undefined fraction

Answer 27

Denominator equals zero

Question 28

Improper fraction

Answer 28

Numerator > denominator

5/3

Question 29

Mixed numeral

Answer 29

Integer part + fraction part

Question 30

Complex fraction

Answer 30

Large fraction with smaller fractions within its numerator, denominator

Question 31

Reciprocal fraction

Answer 31

Flipped over fraction

1/(3/7) = 7/3

Question 32

Adding fractions

Answer 32

Get common denominator

Question 33

Multiplying fractions

Answer 33

Multiply across in numerator and denominators

Cancel first

Question 34

Dividing by fractions

Answer 34

Multiply by its reciprocal

Question 35

Proportions

Answer 35

Equation in the form

Fraction=fraction

Question 36

Fraction word problems

Answer 36

"Is" = equals
"Of" = multiply

“What is 3/5 of $400?”
3/5400=3/5400/1=3/1*80/1=$240

Question 37

Multiplier

Answer 37

Decimal form of a percent

“What is 80% if 200?”

(0.80)*200=160

“56 is what percent of 800?”

56=800x
X=56/800=7/100=0.07=7%

Question 38

Percent increase

Answer 38

“Y increase by 30%” or “X is 39% greater than Y”

If Y increases by 30%, the whole original part of Y is still there plus 30% more

Multiplier for 30% increase: 1+0.3=1.3

Question 39

Percent decrease

Answer 39

“Y decreased by 30%” or “X is 30% less than Y”

If Y decreases by 30%, the whole original part of Y is still there except for 30% missing

Multiplier for 30% decrease: 1-0.3=0.7

Question 40

Attention: percent increase/decrease question phrasing

Answer 40

The price of an item increases from $200 to $800. What is the percent increase?

Not 400 but 300%! 4 is only multiplier, not final percent INCREASE!

Question 41

Multiple percent increases/decreases

Answer 41

Multiply multipliers together to get multiplier of percent increase/decrease

It increases by 20% and then decreased by 50% and finally increased by 40%. Percent change is:

(1.2)(0.5)(1.4)=0.84, 16% decrease

Question 42

Simple interest

Answer 42

Interest remains same amount based on principle every term

Bob receives $50 interest on $1000 every month. Always $50.

Question 43

Prime

Answer 43

A number with only two factors : 1 and itself

2,3,5,7,11 …

Question 44

Composite number

Answer 44

Has more than two factors (not prime)

Question 45

Prime numbers

Answer 45

Only two factors, 1 and itself

MEMORIZE

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59

Question 46

Undefined fraction

Answer 46

Denominator = 0