MATHEMATICS Flashcards
Integer Definition
Any (+) or (-) whole #, including zero. Does not include fractions (1/3), decimals (0.56), or mixed #’s (7 3/4).
Prime #
Any whole # greater than 1 that has only 2 factors, itself and 1. A # that can be divided evenly only by 1 and itself. Ex: (2=2x1,1x2), (5=5x1,1x5)
Composite #
Any whole # that is not a prime #, has more +2 different factors. Ex: (4=2x2), (6=2x3)
Binary
Base 2, # system, used by computers, which uses only the #’s 0 and 1.
Rational #’s
Include all integers, decimals, & fractions. Any terminating or repeating decimal #’s is a rational #.
Irrational #’s
Cannot be written as fractions or decimals because the # of decimal places is infinite & there is no recurring patterns of digits within the #. Ex: pie-3.141592
Real #’s
The set of all rational & irrational #’s
Place value: Write the place value of each digit in the following # - 14,059.826
1: ten thousands
4: thousands
0: hundreds
5: tens
9: ones
8: tenths
2: hundredths
6: thousandths
Writing #’s in Word Form:
1.) Write each # in words: (29), (478), (9,435), (98,542), (302,876)
2.) Write each decimal in words: (0.06), (0.6), (0.009), (0.113), (6.0), (0.901)
1.) (29: twenty-nine), (478: four hundred seventy-eight), (9,435: nine thousand four hundred thirty-five), (98,542: ninety-eight five hundred forty-two), (302,876: three hundred two thousand eight hundred seventy-six)
2.) (0.06: six hundredths), (0.6: six tenths), (0.009: nine thousandths), (0.113: one hundredths, thirteen thousandths), (6.0: six), (0.901: nine hundredths one thousandths)
Equivalent fractions
Two fractions that have the same value, but are expressed differently
Improper fraction
A fraction whose numerator is greater than its denominator
Proper fraction
A fraction whose denominator is greater than its numerator.
Any improper fraction can be written as a?
Any improper fraction can be written as a MIXED #.
How do you convert from a decimal to a percentage?
Moving the decimal point two places to the right. Ex: (0.23->23%), (5.34->534%), (0.007->7%)
How do you move from a percentage to a decimal?
Moving it two places to the left. Ex: (700%->7.00), (86%->0.86), (0.15%->0.0015)
When performing order of operations, do you do multiplication & division, in what direction first?
Perform multiplication & division from left to right.
Converting Percentages, Fractions, & Decimals:
1.) Write 15% as a fraction & as a decimal.
2.) Write 24.36% as a fraction & as a decimal.
3.) Write 4/5 as a decimal & as a percentage.
4.) Write 3 2/5 as a decimal & as a percentage.
1.) (15%=15/100->divide by 5->3/20), (15%->0.15)
2.) (24.36%=24.36/100 or 2436/100 x100 = 609/2500), (24.36%->0.2436)
3.) (4/5=0.8), (4/5->0.8->80% or 4/5 x20 = 80/100 =80%)
4.) (3 2/5->17/5 x20 = 340/100=3.4 or 3 2/5-> 2 divided by 5= 0.4+3(whole #)=3.4), (3.4x100=340%)
When performing order of operations, do you do addition & subtraction, in what direction first?
Perform addition & subtraction from left to right.
A negative exponent is the same as what?
A negative exponent is the same as THE RECIPROCAL OF A (+) EXPONENT. Ex: a^-2->1/a^2
The reciprocal of a (+) exponent is the same as what?
The reciprocal of a (+) exponent is the same as A (-) EXPONENT. Ex: a^-2->1/a^2
Reciprocal
the same way as the other fraction. Ex: 4/3<–>3/4
Absolute Value:
1.) Show that |3|=|-3|
=3
Absolute Value
The distance away from zero, always (+) & is written as |x|.
What is the product if there is an odd # of (-) factors?
If there are an odd # of (-) factors, then the product is (-). Ex: (-4) x (-8) x (-2) = -64
How would you subtract signed #’s?
Change the sign of the # after the minus symbol & then follow the same rules used for addition. Ex: (+4) - (+8)->(+4) + (-8) = -4
What is the product if there is an even # of (-) factors?
If there is an even # of (-) factors, then the product is (+). Ex: (+4) x (-8) x (-2) = +64
In a division problem w/ decimals, what must be converted into a whole #?
In a division problem w/ decimals, the divisor must be converted into a whole #.
1.) Order the following rational #’s from least to greatest: (0.55), (17%), (square root of 25), (64/4), (25/50), (3)
2.) Order the following rational #’s from greatest to least: (0.3), (27%), (square root of 100), (72/9), (1/9), (4.5)
1.) (0.55), (17%->0.17), (square root of 25->5), (64/4->16), (25/50->1/2->0.5), (3)
= LEAST (17%->0.17) -> (25/50->1/2->0.5) -> (0.55) -> (3) -> (square root of 25) -> (64/4->16) GREATEST
2.) (0.3), (27%->0.27), (square root of 100 = 10), (72/9 = 8), (1/9=0.11111…), (4.5)
= GREATEST (square root of 100=10), (72/9 = 8), (4.5), (0.3), (27%->0.27), (1/9=0.111…)
Evaluate the expression 5+20 divided by 4 x (2+3)-6
= 24
(2/10), (3/15), (4/20), (5/25) are all what types of fractions?
(2/10), (3/15), (4/20), (5/25) are all equivalent fractions. They can also be reduced or simplified to 1/5.
Decimal -> Fraction
- Write 0.24 as a fraction.
0.24 -> 24% -> 24/100, can be reduced to 6/25.
Fraction -> Percentage:
1.) Write 7/10 as a percentage.
2.) Write 1/4 as a percentage.
1.) 7/10 x 10 = 70/100 -> 70%
2.) 1/4 x 25 = 25/100 -> 25%
Percentage -> Decimal
1.) Write 700% as a decimal.
2.) Write 86% as a decimal.
3.) Write 0.15% as a decimal.
1.) 700% -> 7.00
2.) 86% -> 0.86
3.) 0.15% -> 0.0015
Percentage -> Fraction
1.) Write 60% as a fraction.
2.) Write 96% as a fraction.
1.) 60% -> 60/100 -> 6/10, simplified to 2, = 3/5
2.) 96% -> 96/100 = 24/25
Decimal -> Percentage
1.) Write 0.23 as a percentage.
2.) Write 0.007 as a percentage.
1.) 0.23 -> 23%
2.) 0.007 -> 0.7%
What do you need to do when adding or subtracting decimals?
When adding & subtracting decimals, the decimal points must always be aligned.
Order Of Operations:
- Evaluate the expression 5+20, divided by 4, x (2+3)-6
=24
Adding & Subtracting Decimals:
- 4.5 + 2
= 6.5
Multiplying Decimals:
- 12.3x 2.56
= 31.488
Dividing Decimals:
- 24.5 divided by 4.9
= 5
Operations w/ Fractions:
1.) 1/2 + 1/4
2.) 1/3 x 2/3
3.) 2/3 divided by 3/4
1.) 1/2 + 1/4, multiply numerator & denominator of the 1st fraction by 2, -> 2/4 + 1/4 = 3/4
2.) 1/3 x 2/3 = 2/9
3.) 2/3 divided by 3/4 -> 2/3 x 4/3 = 8/9
What does the term rational mean? And what does a set of rational #’s includes?
The term rational simply means that the # can be expressed as a ratio or fraction. The set of rational #’s includes integers & decimals.
What is the least common multiple of 3/4 & 5/6
The least common multiple of 3/4 & 5/6 is 12.
- 3/4 & 5/6, (4x3=12), (6x2=12)
Common factor
An common factor is a # that divides exactly into 2 or more other #’s.
What is the common factors of 12 & 15?
- 12 (1, 2, 3, 4, 6, 12)
- 15 (1, 3, 5, 15)
Ray earns $10 an hour. This can be given w/ the expression 10x, where x is equal to the # of hrs that Ray works. Ray makes $360 so, how many hrs did he work to make $360?
10x=360, divide 10 on both sides, -> x=36
What is 14.5% of 96?
14.5% -> 14.5/100 = 0.145 x 96 = 13.92
Solve for x in the following equation: (45%/12% = 15%/x)
(45%/12%=15%/x) -> 45x=180, divide both sides by 45, -> x=4%
One Variable Linear Equation
ax+b=0, a & b are integers
A solution to an equation is called a what?
A solution to an equation is called a root. Ex: (5x+10=0)->subtract both sides by -10, -> (5x = -10), divide both sides by 5, -> x=-2. The root of the equation is -2.
Solve for x in the following equation: (40/8 = x/24)
(40/8 = x/24) -> 8x = 960, divide both sides by 8, -> x=120
At a hospital, 3/4 of the 100 beds are occupied today. Yesterday, 4/5 of the 100 beds were occupied. On which day were more of the hospital beds occupied & by how much more?
(3/4 x 100 = 75), (4/5 x 100 = 80) -> 80-75=5 beds. Therefore, 5 more beds were occupied yesterday than today.
Solve for x in the following equation: (0.50/2 = 1.50/x)
(0.50/2 = 1.50/x) -> 0.50x = 3, divide both sides by 0.50, -> x=6
A pt. was given pain med. at a dosage of 0.22 grams. The pt.’s dosage was then increased to 0.80 grams. By how much was the pt.’s dosage increased?
0.80 - 0.22 = 0.58
A pt.’s age is thirteen more than half of 60. How old is the pt.?
(1/2 x 60 + 13) -> (30 + 13) = 43. The pt. is 43 yrs. old
Jane ate lunch at a local restaurant. She ordered a $4.99 appetizer, a $12.50 entree, & a $1.25 soda. If she wants to tip her server 20%, how much money will she spend in all?
$4.99 + $12.50 + $1.25 = $18.74 x 20%->0.2 = $22.49
At a hospital, 40% of the nurses work in labor & delivery. If 20 nurses work in labor & delivery, how many nurses work at the hospital?
(40% x n = 20) ,divide 40% on both sides, -> (n = 20/40%) -> (n=20/.40) = (n=50). 50 nurses work at the hospital.
1.) A pt. was given blood pressure med. at a dosage of 2 grams. The pt’s dosage was then decreased to 0.45 grams. By how much was the pt’s dosage decreased?
2.00 - 0.45 = 1.55
Two weeks ago, 2/3 of the 60 pts. at a hospital were male. Last week, 3/6 of the 80 pts. were male. During which week were there more male pts.?
(2/3 x 60 -> 120/3 = 40), (3/6 x 80 -> 240/6 = 40). The # of male pts. was the same for both weeks.
What are the three equations of a percentage problem?
1.) % = P/W
2.) P = W x %
3.) W = P/%
In a school cafeteria, 7 students choose pizza, 9 chose hamburgers, & 4 choose tacos. Find the % that chooses tacos.
7+9+4=20 -> 4/20 -> x5 -> 20/100 = 20%
A pt. was given 100 mg of a certain med. The pt.’s dosage was later decreased to 88 mg. What was the % decreased?
(100-80 = 12) -> (12/100 x 100) -> (1,200/100) = 12%
- The % decreased to 12%.
What is 150% of 20?
150% -> 150/100 = 1.5 x 20 = 30
What is 30% of 120?
30% -> 30/100 = 0.3 x 120 = 36
