作者：Marie Waddoups 10 年以前
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http://www.quickmath.com/webMathematica3/quickmath/graphs/equations/basic.jsp
http://www.mathsisfun.com/associative-commutative-distributive.html
36
Use distributive property to solve 6(9-3)
8 divided by 7971 equals
996 R 3
http://www.coolmath4kids.com/times-tables/times-tables-lesson-lattice-multiplication-1.html
Tom's diet allows only 1400 calories day. For breakfast Tom had skim milk 90 calories and a waffle with no syrup 120 calories and a bannana 119 calories. For lunch he had 1/2 cup of salad 185 calories with maynoise 110 calories and tea 0 calories. Then he had pecan pie 570 calories
can he have dinner consisting of Steak 250 calories and a salad with maynais and tea
No
Pam has 597 in her bank account. She uses her debit card to take out amounts of 52 71 and 124. Then she makes a 92 dollar deposit. How much is left in her account?
442
http://www.mathsisfun.com/associative-commutative-distributive.html
Associative, Communitive, and Distributive properties.
There is also the property that has to do with 0 and 1
Anything times 0 equals 0
Anything multiplied by 1 equals that number for example 8x1=8
Find the solution for 7+0=x
x=7
Write a related addition sequence for 16-z=2
Related Sequence: 16=z+2
Find the 9th term of the sequence
-2, 2, -2, 2
The ninth term of the sequence is -2
The nth term of the sequence is:
an=a1r ^n-1
an is the nth term
a1 is the first term
r is the common ratio
-2 * (-1) ^n-1
Determine the next term of the sequence and determine if the sequence is arithmetic, geometric, or neither.
9, 11. 13, 15, 17
The next term is 19
This is Arithmetic. 9=2=11, 11+2=13......
........................................................................................
growing deep population increases by 7 animals per year. If the current population is 46 animals, what will it be in 8 years?
In 8 years the population will be 102 animals.
Formula: an=a + (n-1)d
a. 1+2+3+4+ ... +999
b. 1+3+5+7+ ...+ 101
A. S= 1 + 2 + 3 + ... +997 +998 + 999
S=999+998+997 ...+ 3 + 2 + 1
2S=1,000 + 1,000 + 1,000 ... +1,000+ 1,0000 + 1,0000
2S = 999 * 1,000=
2S= 999,000
S=999,000/2
S=499,500
The sum of the sequence for a is 499,500
The sum of the sequence for b is 2,601
Consider the mathematical machine: a. What number would you have to use as input if you wanted 54 as the output B. What would you have to input to obtain an output of 61
Input: Add 5, Multiply by 7, Subtract 25, Divide by 2: Output
a. 14
b. 16
......................................
Jasmine can assemble 15 bikes in a week. Sheila who is new at the bike shop, can build only 7. If Jamine has assembled 75 bikes since Sheila was hired, how many has Sheila assembled?
35
(Jamine makes 8 more bikes than Sheila in 1 week is the key thing to remember for this problem)
If the cornerstone represents when a building was built and it reads MDCCXXXVI, when was the building built?
1736
M= 1 thousand D=500 C=100 X=10 V=5 I=1
......................................................................
Write in Roman Symbols 636
DCXXXVI
........................................
3 * 10^5 + 1 * 10^4 + 5 * 10^2 Rewrite the following as a base ten numeral
310,500
.........................................
Convert the following: 52 Months into years and months
(12 months in a year (52/4 to get 4 years..... and how many months)
4 years and 4 Months
Express the number as a percent
3.53
Answer 353%
Why?
Just move the decimal point to to the right to get this answer.
What is 8% of 24
Answer: 1.92
Why?
Take .08 and multiply it by 24
We got the .08 by moving the decimal point to to the right to make it a number.
A real estate commission rate is 6% what is the commission on the state of a 93,000 dollar home.
Answer 5,580 dollars
Why?
Take 93,000 and multiply it by 0.06
See above for explanation on how to change a percent to a number.
http://www.mathgoodies.com/lessons/vol4/meaning_percent.html
http://www.math.com/school/subject1/lessons/S1U1L7GL.html
Find a decimal representation of 2/3
Answer: 0.6 forever
Why?
Do 3 divided by 2 .000 to get your answer.
Find a rational number between 2/5 and 0.40 forever
Answer: 0.4022
Why?
Divide 5 by 2 to get .4 which is equivalent to 2/5
We now know that the third number right of the decimal point has to be between 0 and 4 to work.
Find a decimal representation of 1/9
Answer: 0.1 forever
Why?
Just divide 9 into 1 and you will get the answer.
http://dictionary.reference.com/browse/nonterminating+decimal
^ Definition
http://www.math-only-math.com/non-terminating-decimal.html
Hannah went to the store and bought a chair for 6.18, a rake for 12.45, a spade for 11.12, a mower for 141.03, and two six packs of water for 2.02 each. What was the bill?
Answer: $184.82
Why?
Add up all the different prices to get this answer.
Careful to make sure you add 2.02 twice since you are buying two packs instead of one.
The water in a tank weighs 693.75 lb. One cubic foot of water weighs 62 lb. How many cubic feet of water does the tank hold.
Answer: 11.1 cubic feet of water
Why?
Divide 693.75 by 62 to get 11.189.
In this instance we do not round up because it the tank can not hold any more than that. So we round down to 11.1 cubic ft to be safe.
Convert to decimal notation
8.6x10 to the -7th
Answer=.00000086
Why?
go back 7 places from the decimal point like the question says to get your answer.
Round 617.788
Nearest 100th
617.79
Nearest 10th
617.8
Nearest unit 618
These are pretty easy you are just rounding up by what place the question dictates
Nearest ten (TENS PLACE) (COUNTING BY 10's to get this one)
620
Nearest hundred (NEAREST HUNDRED COUNTING ROUNDING BY HUNDREDS TO GET THIS ONE)
600
https://www.khanacademy.org/math/arithmetic/decimals
http://www.adaptedmind.com/categorylist.php?categoryId=17
Write the following as a sum, using powers of 10 to show place value: 0.279
=2x10 to the -1st +7x10 to the -2nd +9x10 to the -3rd
Without performing the actual division determine whether the following represents a terminating decimal.
19/40
Yes! It is a terminating decimal.
Why?
You can't reduce it any farther.
Write as a decimal 1/8
Answer: 0.125
Why?
To get this answer divide 8 into 1 adding .000
Arrange in order from smallest to largest
0.6928
0.74
0.7651
Answer: They are in order
Line up the decimals so that you can clearly see that one number is bigger than another. The smaller number means that that decimal is bigger than a larger number.
http://www.mathsisfun.com/decimals.html
https://www.youtube.com/watch?v=2FH6YiLWIuE
Multiply. Write the answer in the simplest form.
4/25x5/24
Answer: 1/30
Why?
You do not have to find common denominators so you can just multiply right across to get your answer. You reduce 20/600 to 1/30 to get your answer by dividing by 20.
Solve using the multiplication principle
2/15t=-1/4
Answer: t=-15/8
Why?
Just cross multiply everything together. If you do it successfully you will get.
8t=-15
Divide both sides by 8 to get t by itself and you will get the answer t=-15/8
Perform the proper calculations. Reduce your answer whenever possible.
14x1 and 1/2
Answer: 21
Why?
Take 1 and 1/2
Take 2x1+1 to get 3/2 This changes the number and fraction to just a fraction
You can then just multiply 14/1 by 3/2 to get 42/2
Reduce this to get your answer of 21
Choose the number that best approximates each of the following
2 and 1/3x 9 and 5/6
Answer 20
2 and 1/3 is about 2
9 and 5/6 is about 10
10x2=20
Multiply and simplify
9 to the ninth x 9 to the fourth
Answer: 9 to the 13th
Add the number above the nine which are the nine and four to get 13. This makes the answer 9 to the 13th
https://www.brainpop.com/math/numbersandoperations/multiplyinganddividingfractions/preview.weml
https://www.youtube.com/watch?v=B7MtFQW7i_I
Subtract 61/75 from 27/35
Answer: 22/525
Why?
Basically we are trying to find a common denominator. Lots of guessing, but what you find is that both the denominators have a common denominator of 525.
(75x7)=525 and (35x15)=525
With both of these what you do to the bottom you have to do to the top.
(61x7)=427 and (27x15)=405
What we have now...
427/525-405/525=22/525
This can't be reduced so it's our answer.
Change the following fraction to a mixed number. 23/3
Answer: 7 and 2/3
Why?
How many 3's can go into 23. The answer is 7.
7x3=21
23 is our total so 23-21=2 we have 2 left over.
So therefor that 2 is part of the thirds so it is our left over 2/3
So our whole number 7
And our fraction 2/3
Our answer is 7 and 2/3
Estimate the following as a whole number, as 1/2, or as a mixed numeral where the fractional part is 1/2
7/451+7/13+5/9
Answer is approximately 1
7/451 is closes to 0
7/13 is closest to 1/2
and 5/9 is closes to 1/2
So add them all up
1/2+1/2+0
Equals approximately 1 or 1
Find two fractions equivalent to the following fraction. 2/7
Answer: 4/14 and 12/42
Why:
Multiply 2/7 by 2/2 to get 4/14
Multiply 2/7 by 6/6 to get 12/42
Write the fraction in lowest terms: 24/42
Answer: 4/7
Why: Take 24/42 and divide the numerator and denominator by 2 and then by 3 to reduce the fraction to 4/7.
Determine if the following pairs are equal by changing both to the same denominator: 15/24 and 20/21
Answer: Not Equal
Why: They are not equal because you can't reduce them to the same fraction. They do not equal the same even if they are reduced or are given common denominators.
Find a value for x so that 16/12=-4/x
You need to cross multiply here
You will get 16x/16=-48/16 dividing by 16 here
After this you will get
x=-3
Arrange each of the following in decreasing order: 11/14, 11/21, 11/23
They are already in order.
Why?
Think of a pie...
Each time 11 pieces are given to you out of a certain number of pieces.
One will get a bigger piece with a smaller total amount of slices (denominator) than a larger denominator. This means that there are more pieces, but overall you will get less (decreasing order)
Rule: If numerator is the same, the smaller the denominator is bigger/more than a larger one
For practice on 5-1 and 5-2 click the hyperlink attached to 5-1.
Find the opposite (additive inverse) of -86Opposite is just 86 positive=862. -4 – (-7)Is the same as -4 + 7=33.Determine the common difference and the next two terms of the arithmetic sequence8. 3, -2, -7…a. The common difference is -5 (subtracting five each time)b.Next two numbers (subtracting five) are -12 and -174. Solve the equation and check the solution-3+x=25Add three onto the 25X=28
Divide if possible. Check your answer-22 divided by (-11)=22. Simplify.(-496 divided by 62) divided by (-8)Start with first half-8 (because of the sign) divided by -8It’s going to be a positive 1=1
Using the divisibility tests, answer each of the following.Can 148 passengers be assigned to 3 flights so that each flight has the same number of passengers? (Yes or No)No (Dividing 3 into 148 does not come out evenly)Can a parking lot designed to accommodate 4916 cars be divided into 11 equal rows?No (does not divide equally)Can a theater charging six dollars per person for admission to a play take in exactly 1476 dollars for a night’s performance?1479/6=246YES2. Use divisibility tests to determine whether 4,805,235 is divisible by 15(YES OR NO?)Just divide the number by 15 to check and see if it works outYES IT DOES
Find the prime factorization of 2,205.The prime factorization is ____a.Use a factor treeb.2,205=5*441c.FIVE IS PRIMEd.441=3*147e.THREE IS PRIMEf.3*49g.THREE IS PRIMEh.SEVEN SQUAREDi.(FIVE)(THREE)(THREE)(SEVEN)(SEVEN)2. Find the prime factorization of 33 fifths* 39 * 4 twelthsa. 2 twelths* 3 sixths * eleven fifths* 13b.2 twenty fourths* 3 sixths * 11* 13c.2 twenty fourths* 3 sixths* 11 fifths* 13d.2 twenty fourths* 3 fifths* 11 fifths* 1333 fifths = (11x3) fifths so (11x11x11x11x11)(3x3x3x3x3)39=13x34 twelths is 2 twenty fourthsSo the answer should be2 twenty fourths x 13 x 3 sevenths x 11 sixthsTake away one eleven and one 3Answer is C(Still confused why you take away certain numbers)
Find the greatest common divisor (GCD) and the least common multiple (LCM) of the following.
a. 20,15
b. B. 250, 100
a. GCD (20,15)=
b. 20=(1*20, 2*10, 4*5, 5*4, 10*2, 20*1)
c. 15= (1*15, 3*5, 5*3, 15*1)
d. Look for commons (GREATEST COMMON)
e. Answer= 5
LCM (20, 15)
a. 20, 40, 60, 80, 100, 120, 140, 160
b. 15, 30, 45, 60
c. BOTH HAVE 60 for the least they have in common!
GCD (250, 100)= 50
YES
a. 250=1*250, 2*125, 5*50, 10*25, CHECKED OUT
b. 100=1*100, 2*50, 4*25, 5*20, 10*10, 20*5 CHECKED OUT
c. WHAT IS THE MOST COMMON FOR BOTH
d. Answer= 50
LCM (250, 100)
a. 250, 500, 750, 1,000
b. 100, 200, 300, 400, 500 CHECKED OUT
c. Answer=500
2.
Calvin has three alarm clocks which sound at different intervals. Clock A goes off every 15 minutes, clock B every 20 minutes, and clock C every 25 minutes.
The three clocks sound together every____ minutes.
a. Use the prime factorization method.
b. 15=5*3
c. 20=5*4= 2 squared *5
d. 25=5*5
THE LCM (15, 20, 25)
(2 squared) ( three) (five squared) SINCE THERE ARE REPEATS BY THEMSELVES OF FIVE YOU HAVE FOUR ORIGINALLY AND YOU DELETE HALF? YOU DELETED TWO.
=300
The three clocks sound together every 300 minutes.
5-4 Prime and Composite Numbers
Find the prime factorization of 2,205.
The prime factorization is ____
a. Use a factor tree
b. 2,205=5*441
c. FIVE IS PRIME
d. 441=3*147
e. THREE IS PRIME
f. 3*49
g. THREE IS PRIME
h. SEVEN SQUARED
i. (FIVE)(THREE)(THREE)(SEVEN)(SEVEN)
2.
Find the prime factorization of 33 fifths* 39 * 4 twelths
a. 2 twelths* 3 sixths * eleven fifths* 13
b. 2 twenty fourths* 3 sixths * 11* 13
c. 2 twenty fourths* 3 sixths* 11 fifths* 13
d. 2 twenty fourths* 3 fifths* 11 fifths* 13
33 fifths = (11x3) fifths so (11x11x11x11x11)(3x3x3x3x3)
39=13x3
4 twelths is 2 twenty fourths
So the answer should be
2 twenty fourths x 13 x 3 sevenths x 11 sixths
Take away one eleven and one 3
Answer is C
(Still confused why you take away certain numbers)
5-3 Divisibility
Using the divisibility tests, answer each of the following.
Can 148 passengers be assigned to 3 flights so that each flight has the same number of passengers? (Yes or No)
No (Dividing 3 into 148 does not come out evenly)
Can a parking lot designed to accommodate 4916 cars be divided into 11 equal rows?
No (does not divide equally)
Can a theater charging six dollars per person for admission to a play take in exactly 1476 dollars for a night’s performance?
1479/6=246
YES
2.
Use divisibility tests to determine whether 4,805,235 is divisible by 15
(YES OR NO?)
Just divide the number by 15 to check and see if it works out
YES IT DOES
Find the greatest common divisor (GCD) and the least common multiple (LCM) of the following.a.20,15b.B. 250, 100a. GCD (20,15)=b.20=(1*20, 2*10, 4*5, 5*4, 10*2, 20*1)c.15= (1*15, 3*5, 5*3, 15*1)d.Look for commons (GREATEST COMMON)e.Answer= 5LCM (20, 15)a. 20, 40, 60, 80, 100, 120, 140, 160b.15, 30, 45, 60c.BOTH HAVE 60 for the least they have in common!GCD (250, 100)= 50YESa. 250=1*250, 2*125, 5*50, 10*25, CHECKED OUT b.100=1*100, 2*50, 4*25, 5*20, 10*10, 20*5 CHECKED OUT c.WHAT IS THE MOST COMMON FOR BOTHd.Answer= 50LCM (250, 100)a. 250, 500, 750, 1,000b.100, 200, 300, 400, 500 CHECKED OUT c.Answer=5002.Calvin has three alarm clocks which sound at different intervals. Clock A goes off every 15 minutes, clock B every 20 minutes, and clock C every 25 minutes.The three clocks sound together every____ minutes.a.Use the prime factorization method.b.15=5*3c.20=5*4= 2 squared *5d.25=5*5THE LCM (15, 20, 25)(2 squared) ( three) (five squared) SINCE THERE ARE REPEATS BY THEMSELVES OF FIVE YOU HAVE FOUR ORIGINALLY AND YOU DELETE HALF? YOU DELETED TWO.=300The three clocks sound together every 300 minutes.5-4 Prime and Composite NumbersFind the prime factorization of 2,205.The prime factorization is ____a.Use a factor treeb.2,205=5*441c.FIVE IS PRIMEd.441=3*147e.THREE IS PRIMEf.3*49g.THREE IS PRIMEh.SEVEN SQUAREDi.(FIVE)(THREE)(THREE)(SEVEN)(SEVEN)2. Find the prime factorization of 33 fifths* 39 * 4 twelthsa. 2 twelths* 3 sixths * eleven fifths* 13b.2 twenty fourths* 3 sixths * 11* 13c.2 twenty fourths* 3 sixths* 11 fifths* 13d.2 twenty fourths* 3 fifths* 11 fifths* 1333 fifths = (11x3) fifths so (11x11x11x11x11)(3x3x3x3x3)39=13x34 twelths is 2 twenty fourthsSo the answer should be2 twenty fourths x 13 x 3 sevenths x 11 sixthsTake away one eleven and one 3Answer is C(Still confused why you take away certain numbers)5-3 DivisibilityUsing the divisibility tests, answer each of the following.Can 148 passengers be assigned to 3 flights so that each flight has the same number of passengers? (Yes or No)No (Dividing 3 into 148 does not come out evenly)Can a parking lot designed to accommodate 4916 cars be divided into 11 equal rows?No (does not divide equally)Can a theater charging six dollars per person for admission to a play take in exactly 1476 dollars for a night’s performance?1479/6=246YES2. Use divisibility tests to determine whether 4,805,235 is divisible by 15(YES OR NO?)Just divide the number by 15 to check and see if it works outYES IT DOES
A=(c,e,j,k)
D=(8,3,6,9)
G=(4,6)
B=(x,y,z,w)
E= weird circle slash thing
H=(6,4)
C=(j,k,e,c)
F=(weird circle slash thing)
J= ( )
True or False
A=C True
E=F False
C=D False
E=J True
G=H True
A=B False
On a certain senate subcomittee there are five senators: Arturo, Beau, Casper, Dean, and Ellen. Three of these members are to be appointed to a subcomittee. How many possible subcommitees are there?
There will be 10 possible subcommittees.
