







An arithmetic sequence 
20190131 

From sara: if the 6th term of an arithmetic sequence is 8 and the 11th term is 2, what is the first term? Answered by Penny Nom. 





The number of terms in an arithmetic sequence 
20180615 

From Don: how many terms in arithmetic sequence are there if the first term and the last term are 3&59 respectively in common difference is 4? Answered by Harley Weston. 





Gauss' Addition of whole numbers. 
20180430 

From Brad: I found this on your site. Question: what is the sum of the first 100 whole numbers??
Is there a different formula if the numbers begin at a number other than one? For example
What is the series I want to add is goes from 7  53? Answered by Harley Weston. 





An arithmetic sequence 
20171130 

From yo: x; 2x+1; 11 are three consecutive terms of an arithmetic sequence.calculate x Answered by Penny Nom. 





An arithmetic sequence 
20170717 

From abbi: hi there im a student in 11 grade
ive been trying to do this task but i have no idea how to do it
the question is
Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030 Answered by Penny Nom. 





Why does 10x10x10 give 1,000.0000000000001? 
20170412 

From Randolph: Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy Answered by Penny Nom. 





Addition and subtraction base 5 
20170129 

From BABAWALE: Simplify 342five +132five223five Answered by Penny Nom. 





Which term of this sequence has value 8? 
20160720 

From Lauren: Hi there
Which term in the sequence 2; 5/3; 4/3 ; 1; ... has a value of 8.
Since term 2 and 3 of this sequence contain fractions which can be converted to recurring decimals. What is the best way to work out the common difference here.
I do however understand that to work out the nth term of an arithmetic series, the following formula Tn = a + (n1)d. In this series a = 2 Answered by Penny Nom. 





Calendar arithmetic 
20160214 

From Jenalee: January 1, 2001 is Julian Day 2 451 911 (the number of days that have passed since Day 0, January 1, 4713 BC).
If Julian Day 0 was a Monday, what day of the week was January 1, 2001? Answered by Victoria West. 





A sequence 
20160105 

From Mia: the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82, Answered by Penny Nom. 





Subtraction base 5 
20150829 

From nakita: can u explain the quinary subtraction ...
(3000) (2342) all the numbers are in quinary number system Answered by Penny Nom. 





1 + 2 + 3 + ... + (2n  1) 
20150101 

From Brian: Hi Maths Central
My wife presented me with a query which may have a simple answer, but one that I can’t deduce or explain.
Take the string of numbers, n=1,2,3,4,5…
It seems that n(2n1) = Sum((1…..(2n1))
e.g. for n=5, both 5 x 9 and Sum(1….9) equal 45, and so on for other values of n.
Could you please provide an explanation? Does it have an underlying reason and a name?
Look forward to your response.
Brian Answered by Penny Nom. 





An arithmetic progression 
20141119 

From Gbenga: In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression.. Answered by Penny Nom. 





The sum of the first 50 terms of an arithmetic progression 
20140726 

From Joshua: Hello ...my is Joshua...I'm a grade 11 student...I got a question
Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84 Answered by Penny Nom. 





An arithmetic progression 
20140331 

From Japheth: The 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the first term? Answered by Penny Nom. 





9,4,6,8,3,... 
20140331 

From Alynna: You are given the following pattern: 9,4,6,8,3,...
Create a formula for the nth figure.
I have trouble finding the formula, I need help trying to find it. Answered by Penny Nom. 





An arithmetic sequence 
20140320 

From Xabiso: The 10th term of an arithmetic sequence is 28 and the 7th term is 19. Calculate the common difference and the first term of the sequence. Answered by Penny Nom. 





An arithmetic sequence 
20140106 

From paris: find the twentyfifth term of an arithmetic sequence whose first term is 12 and whose common difference is 6 Answered by Penny Nom. 





Base 5 arithmetic 
20131127 

From samuel: Good day sir, please i don't understand when you say 4x4=13 in base five? In fact, am always having difficulties in addition, subtraction, division and multiplication of number in the same base other than base ten. Please can you give me one example each with details explainations? Answered by Penny Nom. 





Base 5 arithmetic 
20131012 

From Obassy: (4 2 4 3)(1 3 x 4)=( Y 3 4 4),find the value of x and y in the subtraction above carried in base five? Answered by Penny Nom. 





An Arithmetic Progression 
20131008 

From collins: In an A.P. the difference between the 8th and 4th term is 20 and the 8th is one and half times the 4th term... what is the common difference and the first term Answered by Penny Nom. 





Group the addends so that you can add mentally 
20131001 

From monica: the questions in the homework says change the order or group the addends so that you can add mentally ,find the sum and tell which property you used
120+37+280 and 25+25+30 Answered by Penny Nom. 





The sum of all whole numbers from 1 to X 
20130906 

From Tim: How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this Answered by Penny Nom. 





An arithmetic progression 
20130706 

From ashok: the 4th and 10th term a.p respectively 7 and 19 find its 15th term..... Answered by Penny Nom. 





A messy arithmetic expression 
20130224 

From niiaryee: (((((5^2*4^3)1/5+9^3/3)+(25+(4*5)/15)^210)/10/2)3))))) Answered by Penny Nom. 





An arithmetic progression 
20130206 

From loberto: the 3rd term of an a.p is 10more than the 1st term,while the 5th term is 15more than the 2nd term,find the sum of the 8th and 15th terms of the a.p if the 7th term is 7times the 1st term Answered by Penny Nom. 





Mod versus Rem in Turing 
20130101 

From Eric: I am a teacher teaching computer science using Turing. I am having
difficulty understanding why one would use the mod operator versus the rem
remainder operator.
Mod seems to make the resulting sign depend on the sign of the divisor,
whereas rem makes the resulting sign depend on the dividend.
Examples:
11 mod 5 = 1 and 11 rem 5 =1
11 mod 5 = 4 and 11 rem 5 = 1
11 mod 5 = 4 and 11 rem 5 =1
11 mod 5 = 1 and 11 rem 5 = 1
What I can't understand is why this would matter. For example, 11 / 5 =
2.2 and 11 / 5 = 2.2 get the same result.
So how is a remainder dependent on the sign of one of the parts?
What benefit would using one over the other have?
Any insight would be most helpful!
Eric Answered by Harley Weston. 





An arithmetic progression 
20120822 

From A student: the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term. Answered by Penny Nom. 





6/2(1+2)=? 
20120221 

From boyong: 6/2(1+2)=? Answered by Harley Weston. 





An arithmetic expression 
20120105 

From Jennifer: 1.8 + 3.2 / 0.4  4.375 x 0.2 Answered by Penny Nom. 





Mean and Average 
20120103 

From john: what is the difference between average and mean Answered by Robert Dawson. 





The 3rd term of an A.P is 10 more than the first term 
20111129 

From Olaniyan: the 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the A.P if the if the 7th term is 7 times the first term. Answered by Penny Nom. 





An arithmetic expression 
20111128 

From Muhmmad: 2/5*3/71/6*3/2+1/14*2/5 Answered by Penny Nom. 





Three consecutive terms of an arithmetic sequence 
20111030 

From Juliette: Find X when x, 1/2x + 7, 3x 1 are consecutive terms of an arithmetic sequence. Answered by Penny Nom. 





Modular arithmetic 
20111030 

From Kim: Hello,
I am editing a resource for students, and I think some of the answers may be incorrect.
The text I was given and my questions are in the attachment.
Any help you could give would be appreciated.
Thanks,
Kim Answered by Harley Weston. 





 16 x 6 / 2 
20110909 

From Nadiyah: i dont understand how to answer this question ;
 16 x 6 / 2
i still dont understand it with bedmas
/ = divison
please help! Answered by Penny Nom. 





(x^3 + 11x) is divisible by 6 
20100624 

From PT: Given that x is a nonzero integer,
how do you show that for all values of x,
(x3 + 11x) is divisible by 6?
I know it works but how do I answer the "all values of x" part?
Thanks in advance! Answered by Robert Dawson. 





4 + 10 + · · · + (6n − 2) 
20100421 

From Lan: Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How? Answered by Penny Nom. 





(24x3)+(7x8)(20/5)+(4x7) 
20091201 

From Marilyn: (24x3)+(7x8)(20/5)+(4x7)
Thought I had the answer but the form says no. Could you solve it for me please. Answered by Penny Nom. 





24 feet of pipe in 3 pieces 
20091009 

From Sam: I had a carpenter being a smarty pants with me. Question: I have a 20ft piece of pipe. I need three equal lengths cut. What is the measurement of each cut? He told me the answer right away because he knows the measuring tape like the back of his hand. The answer is 6'8". Is there an equation I can use to get the answer quicker than him looking at his tape measure? Answered by Penny Nom. 





How many terms are there in this sequence? 
20090928 

From tabby: How many terms are there in this sequence?
5,1,3,...,111 Answered by Penny Nom. 





Arithmetic Sum & Sequence 
20090901 

From Alice: Find the 24th term of this sequence
6.8,8.0,9.2...
Find the sum of the first 21 terms Answered by Janice Cotcher. 





Subtraction base 5 
20090809 

From Nikki: can you help me how to do subtraction in base 5 notation. example is 3434  51?
how do you do this in base 5?
can you please explain how you do this & the answer as i have no idea.
Thank you kindly
Nikki Answered by Harley Weston. 





Finding the Common Difference and Number of Terms of an Arithmetic Sequence 
20090724 

From Juan: In an arithmetic sequence, the first term is 2, the fourth term is 16 and the nth
term is 11,998
A. What is the common difference?
B. What is the value of n. Answered by Janice Cotcher. 





WHAT IS 8+4(227) 
20090505 

From ROB: WHAT IS 8+4(227)= Answered by Penny Nom. 





The middle term of an arithmetic sequence 
20081215 

From Leigh: Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92 Answered by Penny Nom. 





An arithmetic series 
20081017 

From Laura: In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have?
What formula do I use? Answered by Penny Nom. 





Bags of pennies 
20081011 

From paul: jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag? Answered by Penny Nom and Victoria West. 





Four weights 
20080825 

From Darla: A balance had known weights of 1/2 lb, 1/4 lb, 1/8 lb, and 1 oz. Edna's object weighted 2 oz. more than Paul's. Each used 3 known weights to weight his or her object. which know weights did each use? Answered by Penny Nom. 





The product of the digits of a four digit number 
20080726 

From Pete: I am a student preparing for a competition and this was one of the prep problems: The product of the digits of a four digit number is 6x5x4x3x2x1. how many such numbers are there with this property? Answered by Stephen La Rocque. 





Remainders 
20080630 

From vivek: what is the remainder when 2050*2071*2095 is divided by 23 ?
this question needs to be done in as less time as possible. Answered by Penny Nom. 





1?2?3?4 = 7 
20080425 

From john: 1 2 3 4 = 7
The numbers have to stay in order of 1234 and when added,subtracted,multiplied or divided they have to equal 7. Answered by Stephen La Rocque. 





1+15=20? 
20080425 

From MUBARAK: 1+15=20? Answered by Penny Nom. 





Base 5 arithmetic 
20080306 

From Jana: Hello, my name is Jana, i have asked a question here previously about how to count in base5. I am happy now because i can convert any number now and it is very easy for me. The only thing i am having trouble with is understanding how to do a maths sum or times base5 numbers. it is just a bit hard for me. So do you think you could explain how to do a sum in base5 and how to do a multiplication sum. Please help...Thankyou Jana!! Answered by Harley Weston. 





An arithmetic expression 
20080305 

From Kasani: evaluate the expression: 2^1[14  4(6)]  (7  3) Answered by Penny Nom. 





10  3 + 2 
20080221 

From Amrit: what 103+2
is it 5 or 9 Answered by Penny Nom. 





The nth term 
20071018 

From shannon: Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term. Answered by Penny Nom. 





Solving arithmetic problems in the right order (BEDMAS) 
20071005 

From Kim: 3+4x2(10 divided by 5)= what? Answered by Penny Nom. 





The nth term 
20070909 

From Conor: Please can you help me with this question on the subject of the Nth term.
3.5, 5, 6.5, 8, 9.5
5.1, 7.2, 9.3, 11.4... Answered by Penny Nom. 





2(83)+2^2 
20070730 

From Nikki: 2(83)+2² Answered by Penny Nom. 





How many terms in this sequence? 
20070611 

From Jesse: How do I find how many terms are in the sequence? 51, 48, 45, ...., 75 Answered by Stephen La Rocque and Penny Nom. 





Arithmetic means and geometric means 
20070404 

From Dani: Hi!
I was just wondering why the arithmetic mean of sets of numbers is larger than the mean proportional of the same numbers?
Thanks!
Dani Answered by Haley Ess. 





Arithmetic Series 
20070218 

From Krista: Question The sum of the first 4 terms of an arithmetic series is 8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms. Answered by Stephen La Rocque. 





5,8,11,14,17 
20070118 

From Mairead: the sequence i was given was 5,8,11,14,17 what is the nth term and what is the 10th term ? Answered by Paul Betts. 





An arithmetic series 
20061128 

From Jillian: Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30. Answered by Penny Nom. 





Arithmetic with base 2 
20061126 

From Yuva: can we do arithmetic ,base 2. If yes, how and if not, why. Answered by Stephen La Rocque. 





The sum of 2000 consecutive integers is 1000 
20061029 

From Matias: if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is? Answered by Penny Nom. 





Squaring numbers 
20061008 

From Timothy: did anyone ever try to teach that the easiest way to find the next square in a group of numbers is to add the next odd number in the sequence. for example: 1 squared is 1, 2 squared is 4,difference of 3.the next odd number is 5 so the next square would be 4 +5 or 9 Answered by Paul Betts and Penny Nom. 





what is 8+(2)(5)/4(1)4(2+3) 
20060908 

From Jordan: what is 8+(2)(5)/4(1)4(2+3) Answered by Paul Betts. 





Adding consecutive numbers 
20060426 

From Lisa: When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Answered by Stephen La Rocque. 





Arithmetic and Geometric Sequences 
20060419 

From Skye: If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence. Answered by Stephen La Rocque. 





Arithmetic Sums 
20060412 

From Angel: (a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28.
(b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation. Answered by Stephen La Rocque. 





(175)/3x2 
20060226 

From A student: can you help me answer this question (175)/3x2 Answered by Penny Nom. 





Arithmetic progressions 
20060131 

From A student: 1)the sum to n terms of a particular series is given by S_{n}=17n3n^{2}
a)find an expression for the n term of the series
b)show that the series is an arithmetic progression
2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference
Answered by Penny Nom. 





For what divisors can you get a remainder of 8? 
20060106 

From Thelma: When dividing a 3 digit number by a 1 digit number, for what divisors can you get a remainder of 8? Answered by Penny Nom. 





(5 + 10) x 2  10 = 
20051205 

From Jessica: (5 + 10) x 2  10 = Answered by Penny Nom. 





An Arithmetic sequence 
20051201 

From Aana:
The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82.
Here's what I did to find d
a+2d=19; 25+2d= 19 ;1925=2d d=6/2=3
This is where I'm stuck. Can you please provide me with some guidance.
Answered by Penny Nom. 





Two groups that have equal sums 
20050930 

From Anita: using the numbers 1, 2, 3, 4, 5, 6, 7,and 8. how do we divide them into two groups so that they have equal sums? Answered by Penny. 





BEDMAS 
20050901 

From A student: I am a student and am wondering about the answer to this question.
56/2(31)
is the answer 7?
Answered by Harley Weston. 





Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 
20050718 

From Ladis: Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6. Answered by Chris Fisher. 





An arithmetic progression 
20041224 

From A student: the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50 Answered by Penny Nom. 





Bedmas 
20041030 

From Gina: I am just curious whether Bedmas would be used in the following question as it is not in the typical Bedmas format.
Multiply 12 x 24
Add 26
Divide by 2
Subtract 7
Would we go about doing it in the sequence it is given or in Bedmas ? Answered by Penny Nom. 





1+3+5+...+(2n+1) 
20040910 

From Emma: Prove that 1+3+5+...+(2n+1)= (n+1)^{2} Answered by Penny Nom. 





Half way between 
20040908 

From Ben: Find the number halfway between the number shown
751,843 Answered by Penny Nom. 





The sum of some positive integers 
20040607 

From A student: Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7. Answered by Penny Nom. 





The sum of 4,0,4..., 156 
20040428 

From Christina: find the requested sum of the arithmetic sequence
4,0,4..., 156 Answered by Penny Nom. 





(3x50)+20/5=? 
20040403 

From A student: what is the answer to:
(3x50)+20/5=? Answered by Penny Nom. 





Arithmetic in bases other than 10 
20031022 

From Kim: how do you add, subtract, multiply and devide in base 3, base 5, etc? Answered by Penny Nom. 





1 + 1 = 10 
20030917 

From David: could you please explain to me how 1+1=10 thanks Answered by Penny Nom. 





Converting from base 10 to base 5 
20030910 

From Susy:
My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5. His first question of: 24(10) he has calculated to be 4x5 + 4x1 = 44 (5) The next question however is the tricky one.Ư We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it. 25 (10) = _________________ 100 (5) Can you help us figure out how we reach the answer. Answered by Claude Tardif and Penny Nom. 





38 minus 10 plus 12 divided by 4 times 16 
20030423 

From James: please help me work this math problem 38 minus 10 plus 12 divided by 4 times 16 Answered by Harley Weston. 





Chopping trees 
20030419 

From Tamara:
The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Answered by Penny Nom. 





How many hits? 
20030406 

From Jack:
My name is Jack. I'm a uncle. Student is in the 5th grade email is above. If a baseball player at sping training had a good season with the following: one seventh of his hits were doubles. 12.5% of his hits were home runs. But didn't have any triples. How many hits did he have? Can you give me an explanation of you solved the problem. Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





The sum of the first 1000 even integers 
20030206 

From Jill: What is the sum of the first 1000 even integers? Answered by Paul Betts. 





Arithmitic sequence 
20030201 

From A student: I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why. Answered by Claude Tardif. 





1+2+3+...+500 
20030131 

From Brian: What is the sum of the numbers from 1 to 500 inclusive? Answered by Paul Betts. 





5x(2)32/8 
20030113 

From A student: I'm having problems solving this question: 5x(2)32/8 Answered by Penny Nom. 





Integer arithmetic 
20021205 

From A student: Would you please help me with a question?
I am just learning about integers. Can you show me in a way I might understand....My teacher can tell me what is required to do the math, but it just doesn't make sence to me.
(+4)  (3) =+7
Why is the answer not +1 Answered by Diane Hanson. 





Chisanbop 
20021107 

From Paul: I'm trying to find the book/books that explain this system? I have one small book that explains the very beginning of the system, but covers only about 10 to 20%. I'v tried several book sellers and have had no luck. Answered by Diane Hanson. 





Sums of evens 
20020914 

From Rosa: How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + .... Answered by Leeanne Boehm and Harley Weston. 





7+8+9+...+1000 
20020911 

From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom. 





3810+12divided by4multiplied by 16 
20020830 

From Brenda: my math question is as follows: 3810+12divided by4multiplied by 16=? Answered by Penny Nom. 





Order of operations 
20020718 

From Danna: I would like to know how to solve this type of problem; I already have the answer. Problem: 2 [5 (4 + 6)  2] = 96 Also, what do you call this type of problem? Thanks a lot. Answered by Penny Nom. 





8/13*26/27 
20020501 

From Arias: 8/13*26/27= Answered by Penny Nom. 





Arithmetic progressions 
20020424 

From David: I have been searching everywhere for the formula to mathamatical progression. Answered by Penny Nom. 





Take It! 
20020403 

From Bryan: You are playing Take It! for $180,00 with a total stranger. There are 180 identical balls in a big vase. Each player in his turn, reaches into the vase and pulls out 1,5,or8 balls. These balls are discarded. The player who takes the last ball from the vase wins the $180,000. A flip of the coin determines that you will go first. Are you glad? How many will you take out on the first move, and how will you proceed to win the prize? Answered by Claude Tardif. 





Making 24 
20020117 

From Renee: My 4th grade daughter and I need to find a simple math sentence using 5, 5, 3, & 7 to equal 24. You can add, subtract, divide or multiple. Answered by Penny Nom. 





Papy's Computer 
20020111 

From MaryAnne: My secondgrade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8. Answered by Harley Weston. 





Painting walls 
20011212 

From Rizwan: 3 sixth graders painted 4 walls in 3.5hrs. At that rate, how many walls would they paint in 7 hrs. Answered by Penny Nom. 





Recalling the basic facts 
20011212 

From A parent: My son is in 4th grade and is a very bright student. He is in the gifted program and makes straight A's on his report card and has through out school so far. My question is how can I teach him to memorize his basic math facts? He does well in math, but when he is placed in a times situation for completing math fact sheets he freezes up. He can not recall the basic facts when questioned at any other time either. He will calculate the answer in his head, like 6 + 3, but he can't just come out with the answer quickly. How can I help him? Answered by Claude Tardif. 





Negative times negative is positive 
20011026 

From Mary: I have a question about adding and multiplying positive and negative numbers. When we add two negative numbers the answer is negative BUT when we multiply two negative numbers the answer is positive. I don't understand. Why? Answered by Penny Nom. 





Arithmetic sequences 
20010910 

From Rachel: I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting 9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given. Answered by Penny Nom. 





Geometric and arithmetic sequences 
20010126 

From Garry: what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Answered by Leeanne Boehm and Penny Nom. 





Order of operations 
20001126 

From Margaret Pratt: My daughter has a math question and I am afraid I am of no help. Can you help? 2x5/2+15= She arrives at 8 as the answer and has been told this is incorrect. Any help you can give would be appreciated. Answered by Penny Nom. 





Arithmetic in base 5 
20000920 

From Lesley Emerson: my daughter is 9 and has been aske to solve the following in base 5 3+2 4+10 . . . Answered by Penny Nom. 





Order of operations 
20000919 

From Nicole: the problem is, 4x818 divided by 6= do you solve this by doing 4x8=32 then by dividing 18by 6= 3, then subtracting 3 from 32 = 29? If not what is the order of operation? Answered by Penny Nom. 





7     77 
20000913 

From Peter: Does anyone know how to solve the following: 7 _ _ _ _ 77 ? I have to find the missing values. Answered by Chris Fisher and Walter Whiteley. 





How many 17's and 19's total 1000? 
20000907 

From Jonathan: My question is: what 2 numbers would multiply 17 and 19 for a total of 1000. The numbers should not contain any decimal. Answered by Penny Nom. 





The sum of the squares of 13 consecutive positive integers 
20000825 

From Wallace: Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square. Answered by Harley Weston. 





Find the next term 
20000812 

From Ashley: 8,27,64 I need the next three numbers & I can't figure it out. I have worked on this all day. Answered by Penny Nom. 





Why does division start from the left? 
20000524 

From Salil Dave: Addition, subtraction and multiplications start with right most digit and proceed left, but division starts from leftmost digits and goes right ... why? Answered by Harley Weston. 





The number of seats in an auditorium 
20000516 

From David Evaska: There are 10 students in the first row of seats in an auditorium 12 in the second 14 in the third and 2 additional in each seat. The total number of rows is 40. I know the answer is 1960 can you please show me the formula step by step. Answered by Penny Nom. 





Finding a formula 
20000505 

From Erica Hildebrandt: If a farmer has a field and his plots are laid out in the following grid where each # represents a plot: 4  5  12  13  20  3  6  11  14  19  2  7  10  15  18  1  8  9  16  17  Of course the plot numbers aren't meaningful as I have described above. In fact they may not be numbers at all. The only constants I have are the total number of rows and columns. Using the total number of rows and columns and my current position row and column, how can I write a formula that tells me column 3 row 3 = 10, column 4 row 2 = 14, etc. I can see the pattern but can't quite get the formula. I believe I will need 2 different formulas one for even and one for odd rows. Answered by Paul Betts and Penny Nom. 





Adding fractions 
20000423 

From A grade 6 student: In adding fractions, how do I rewrite the fractions so that the denominators are equal? The problem is 3/4 + 1/6 = The other problem is 11/18 + 4/9 = Answered by Penny Nom. 





Borrowing 
20000417 

From A college student: How would you explain borrowing to an elementary school student? Answered by Penny Nom. 





Starmultiplication 
20000407 

From Greg Potts: I have this question to answer and I don't know where to start. 1*9=0, 9*8=72 and 2*8=9, then 9*9 =? Answered by Penny Nom. 





A negative times a negative 
20000229 

From Michael J. Butler: I have reviewed the answer in relation to the question of why (3)x(2)=6; however, I am still not able to properly explain the reasoning to my son, Jonathan, who is in grade 7. I want him to understand the reason for the rule that the multiplication or division of two negative numbers equals a positive number. Can you help? Answered by Chris Fisher. 





Compatible numbers 
20000127 

From Angie: Use compatible numbers to estimate each product and quotient. 23*1/2 1/3*11 Answered by Penny Nom. 





Order of operations 
20000116 

From Dorothy: I was wondering if you could tell me where I can get some info. on how to solve the following problem. I was given the answer but I don't know how it is solved. 4+2x(6x2)5=23 Answered by Penny Nom. 





Four fours 
19990909 

From Roger: I need help with a math problem my child asked me about I guess in her 7th grade math class they were told to come up with a answer from 110 only using four 4's and she got stuck on the problem that needs to be equal to ten, she asked me and I couldn't help her it's sad so if you could give me the problem and and answer so i could explain it to her I would really appreciate it. Answered by Penny Nom. 





A double negative 
19990901 

From Dennis: If b = 2 what does b = ? As in (a + 8.5)  [(b) + c] a = 1.5, c = 1.7 Answered by Penny Nom. 





Division by a negative 
19990819 

From Sangeeta B.: 56/8 Answered by Penny Nom. 





A Weighty Problem 
19990617 

From A parent: When using a balance scale, weights can be placed on either side of the scale. For example, if a 10 pound weight provides a counter balance to an object and a 7 pound weight, then the object must weigh 3 pounds. What four weights can be used to weigh objects of 1, 2, 3 ... 38, 39, 40 pounds? Answered by Penny Nom. 





Base 2 to Base 10, conversion, convert 
19990508 

From Larry Bader: 10100011_{2} is the same as what number in Base ten? a. 83 b. 128 c. 93 d. 326 e. 163 Answered by Penny Nom. 





Roman Numerals 
19990429 

From Michelle Jenkinson: Someone proposed this question to me and I do not know the answer, so I was wondering if you could help. How, using Roman Numeral, did people add, subtract, multiply, and divide with no zero or negative numbers? Answered by Penny Nom. 





Divisibility by 9 
19990221 

From Razzi: I've been having a hard time trying to solve the following problem and I was wondering if you could help me. For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b). Answered by Chris Fisher and Harley Weston. 





Modular Arithmetic 
19990204 

From Leslie Kupper: I am trying to do a project on modular arithmetic. I was wondering if there were any websites that include a sample lesson plan on modular arithmetic for any grade level. Let me know where and how to find them. Thanks. Answered by Harley Weston. 





Arithmetic Progressions 
19981112 

From Gerry Boser: It has been years since I was in school and I can't remember if there is a formula for the following problem: If you deposit $1.00 on the first day of the month, $2.00 on the second day, $3.00 on the third day . . $31.00 on the last day of the month, how much do you have in the bank? Now will this formula also work if it was, $0.25 (then day two you would deposit 2x $0.25 or $0.50, day three you would deposit 3x $0.25, $0.75. . . ). Will it work with any denomination?? Thank you for your time. I promise I'll write this one down for future reference. . . Answered by Penny Nom. 





Dividing a Class 
19981001 

From Tom Barker: My eighth grade niece called with the following homework problem: A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class? I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated. Answered by Penny Nom. 





Sequences and series 
19980527 

From Michael Le Francois: The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term. The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term. Answered by Penny Nom. 





Clock Arithmetic. 
19980309 

From Joann Dixon: What is clock mathematics? Answered by Patrick Maidorn. 





Integer Problems. 
19970915 

From Eric Kowalsky: I have some intergers I can't solve. Please help me solve them! Please show me how you got the answer. 5(4)[3(6)+(3)4(2(4)7)]+3(8)=
 2[73(4)+52(1)]+3(6+8)=
 4[6(27)5(7+2)]=
 7(4)2[3(4+6)+6(73(4))]
P.S. Thank you very much. Answered by Harley Weston. 

