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Quandaries & Queries
Q & Q
 Gauss' Addition of whole numbers. 2018-04-30 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. Adding two negatives 2018-02-04 From Pinasshakoane:(-23)+(-3)Answered by Penny Nom. Adding fractions 2017-10-27 From Sandy:virinchi distributed 4/7 of cake to his friends 1/3 of it to his family members which part of cake is remaining?Answered by Penny Nom. Multiplication and repeated addition 2016-11-23 From Anandmay:Hello I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic. Like:2 x 3 = 3 x 2. This can be proved by considering a 2-D figure(actually,quadrilateral) having length consisting of 2 boxes of 1-by-1 dimensions and breadth of 3 boxes of the same dimensions. Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes. We now notice that we can fit the 2 types of rectangles formed on each other precisely. So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction). Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction? I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 2-3rd,that is, 2/3+2/3+2/3.Fair enough. But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times. So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful? ThanksAnswered by Penny Nom. find f+g 2016-06-26 From yzabelle:find f+g f(x)=x^2-1 g(x)=square root of x+2Answered by Penny Nom. Fractions of two quantities 2016-01-22 From Melody:Kate ate 1/4 of her orange. Ben ate 2/4 of his banana. Did Kate and Ben eat 3/4 of theit fruit? Explain.Answered by Penny Nom. Complex numbers in standard form 2016-01-15 From Michael:express the following complex numbers in standard form (2+3i)+(5-2i)Answered by Penny Nom. A ladder against a wall 2014-07-09 From thabo:A ladder 6.5m long,leans against a wall so that the top of the ladder is 4.8m from the ground.what is the angle of elevation of the ladder to the top of the wallAnswered by Penny Nom. Adding fractions 2014-01-31 From bianco:2/3+3/4= 9/8-6/8=Answered by Penny Nom. A word problem involving fractions 2014-01-23 From Pamela:John put 1/4 of his flowers in a vase He gave 1/2 to of the flower to his wife He gave 1/5 of the flowers to his daughter He has 8 flowers left How many flowers did John start withAnswered by Penny Nom. Why can't we add or subtract speed? 2013-11-21 From kashish:why we cannot add or subtract "speed" / directly in any given distance , speed , time questions?Answered by Chris Fisher. Adding mixed numbers 2013-11-20 From Kathy:1 3/4 + 1 2/3= ? 5 1/2 - 2 5/6= ?Answered by Penny Nom. Group the addends so that you can add mentally 2013-10-01 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+30Answered by Penny Nom. Ann has a bag of marbles. 2013-07-25 From Carmen:Ann has a bag of marbles. she gave one half to her friend Tina and then one third to her friend Tom. Now left with 15. How many did she had originally?Answered by Robert Dawson and Penny Nom. Cutting three sections of pipe 2013-05-16 From Michael:A plumber cuts three sections of pipe from a 12’ length of ABS pipe, the lengths of the sections are 33 3/8”, 56 5/8” and 39 7/8”. What is left over from the full length, if the saw cut is 1/8” wide?Answered by Penny Nom. Adding two fractions 2012-09-19 From jeanette:Question from jeanette, a parent: can you help me figure this according to BEDMAS I am lost steps please: $\frac{12.75^2}{50} + \frac{13.49^2}{60}$ I hope this is not too confusing for you it is to me...Answered by Harley Weston. Adding more than 2 fractions 2012-09-10 From Anonymous:How do you add or subtract more than 2 integer fractions? OK, here is an example. -5/6 + 7/4 + 13/8 Please tell me the steps. Thanks- grade 9 studentAnswered by Robert Dawson and Penny Nom. Adding speeds 2012-08-26 From Roy:May I ask if it is correct to add the following with units included? Some tell me that the units cannot be included in the addition because we cannot add speed.Answered by Harley Weston. Adding fractions 2012-01-05 From laurie:if shaded parts of a circle are 4/7 and the other is 1/3 what fraction is leftAnswered by Penny Nom. 1 third plus 5 sixths 2011-11-10 From Matt:1 third plus 5 sixths =Answered by Penny Nom. pi/2 + 12/13 2011-05-24 From Jen:If you have (pi/2) and you want to add it to (12/13), how would you go about it?Answered by Chris Fisher. Multiplication and order 2011-01-21 From Janet:IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT?Answered by Robert Dawson. 1/a^2 + 1/b^2 2011-01-19 From robert:If (a + b)^2 = 81 and ab = 18, find the value of 1/a^2 + 1/b^2 ?Answered by Penny Nom. Convert to multiplication 2010-10-23 From angelina:how to covert 5+5+5=15 to multiplicationAnswered by Penny Nom. 4.5 PLUS 29 2010-09-07 From kiona:4.5 PLUS 29Answered by Penny Nom. A ladder against a wall 2010-03-25 From amber:the distance from the bottom of the ladder to the building is18 foot less than the length of the ladder.How high up the building is the top of the ladder if that distance is 1 ft less than the length of the ladder?Answered by Penny Nom. A 6m ladder is placed against a wall 2010-03-09 From Trevor:A 6m ladder is placed against a wall making a 56 degree angle with the ground. How far up the wall does the ladder reach?Answered by Harley Weston. A 25 foot ladder reaches a window 20 feet high 2010-02-27 From Tanner:a 25 foot ladder reaches a window 20 feet high. how far is the ladder from the building? how far must the foot of the ladder be moved to lower the top of the ladder by four feet?Answered by Tyler Wood. Least common denominator 2010-02-13 From Priscila:3/8 + 4/5 + 7/3 + 9/10 = ? Thank you for your assistance. PriscilaAnswered by Penny Nom. Combining fractions 2010-02-10 From Nick:Combine the fractions 2m/t + 5/mtAnswered by Penny Nom. Ladder Leaning on a Wall 2009-05-14 From clinton:a ladder rests against a wall 24m high.the foot of the ladder is 7m from the foot of the wall. How do you calculate the length of the ladderAnswered by Robert Dawson. A ladder against a wall 2009-04-08 From Jessica:The angle of elevation of a 15 ft. ladder is 70 degrees, find out how far the base of the ladder if from the wall.Answered by Penny Nom. A five game average of 148 2009-04-01 From Shelly:(128 + 145 + 139 + 157 + x) divided by 5 = 148 matches the situation stated below: A person bowled four games and scored 128, 145, 139, and 157. Find x, the score the person would need to have in the fifth game to average 148 for all five games. How do I solve this and how am I supposed to add x like it says in the equation?Answered by Penny Nom. The length of a ladder 2009-03-30 From Susan:The foot of an extension ladder is 7 ft. from a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive integers. How long is the ladder?Answered by Penny Nom. Adding in base six 2009-03-29 From Lucy:If you are working in base 6, what do you have to add to 4(base 6) to get 10(base 6)????Answered by Penny Nom. Multiplying in different bases 2009-02-25 From Susan:11 base 2 X 22 base 3 + 33 base 4 = _________ base 5Answered by Robert Dawson. Averaging percentages 2009-02-21 From Chris:Ok I'll give you a simple example of what I'm doing. Lets say that on one forum, a memebr has made 52 posts out of the 412 posts made altogether. Then on another forum, the same person has made 10 posts out of the 60 posts altogether. What percentage of the posts has this person made in these 2 fourms combined.Answered by Robert Dawson and Harley Weston. Adding fractions 2008-09-17 From amanpreet:please can you help me to simplify: 2(c-3) / 7 + 3(4c-2)/2Answered by Penny Nom. Three addends that sum to ten 2008-09-13 From Alfred:How many probabilities are there to have 3 addends to get a sum of 10? What is the formula?Answered by Harley Weston. Grouping addends 2008-09-13 From juan:how do you group the addends then find the sum: 2+4+6=Answered by Penny Nom. How far is the ladder from the wall? 2008-07-10 From Al:a ladder is leaning against a wall at a 70 degree angle and the ladder is 20 feet tall...how far away is the ladder from the wallAnswered by Penny Nom. .9 repeating plus .2 repeating 2008-06-10 From megan:How do you express the addition of .9 repeating plus .2 repeating?Answered by Penny Nom. How do you add decimals? 2008-06-05 From nyheashiacurry:how do you add up decimals?Answered by Janice Cotcher. 3 radical 48 +11 radical 75 2008-05-24 From Maria:Add 3 radical 48 +11 radical 75. Write answer in simpliest form.Answered by Penny Nom. Adding rational functions 2008-04-29 From Jonathon:1/(x+3) + 1/(x^2+5x+6) =Answered by Penny Nom. Base 5 arithmetic 2008-03-06 From Jana:Hello, my name is Jana, i have asked a question here previously about how to count in base-5. 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 base-5 numbers. it is just a bit hard for me. So do you think you could explain how to do a sum in base-5 and how to do a multiplication sum. Please help...Thankyou Jana!!Answered by Harley Weston. Sum and difference of cubes 2008-01-30 From Amanda:It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2]-[1/x+2]. Please help!!!Answered by Penny Nom. Adding fractions 2007-12-31 From Lisa:As an educator in Adult Education, I am preparing a young man for a US Government test. The equation I have trouble with is explaining the following equation. It asks: If it takes A 3 days to dig a certain ditch, whereas b can dig it in 6 days, and C in 12, how long would it take all three to do the job? I know the equation is 1/3 + 1/6 + 1/12 and it equals = 7/12 but I don't understand how it equals 7/12. This simple math eludes me. So the question is not the final answer of 1 and 5/7 of days but where one comes up with the 7/12?Answered by Penny Nom and Claude Tardif. Percentage increase in profit 2007-12-04 From Dee:If I had a certain % increase in profits for the entire year, why can't I add the profits I made for the first 1/2 of the year to the profit I made in the second 1/2 of the year to get the total year end profit percentage? Or how can I compare the increase/decrease for each 1/2 of the year to the total % increase/decrease?Answered by Penny Nom. Addends 2007-11-27 From jessica:what is a addends my son needs to write a number sentence that has two addends that are the sameAnswered by Stephen La Rocque. Number sentences 2007-09-15 From jen:list the addition number sentences that can be written using two sets of cards with the numbers 5 6 and 7. which number sentences have the same addends but show a different order?,,,,,,,,,,,,,,Ithis is for my son in 3rd grade and for the life of us we can't figure it out,,thanks for this elementary helpAnswered by Harley Weston. Adding algebraic fractions 2007-08-14 From John:Ive completely forgot anything to do with the subject mentioned, so my question is straight to the point.. I need to know how to do the following problem (Preferably do not give me an answer though) (k/3k-8) - (4/k+2)Answered by Penny Nom. Fractions of fractions 2007-07-18 From Bridget:Sam and Mary each owned one-half stock in a printing company. Sam sold 2/3 of his stock to Mary. What fractional part of the printing business does Mary now own?Answered by Penny Nom. Period of a sum of trig functions 2007-06-17 From Aakash:the period of the function f(x)=cos3x+sin4x+tan4xAnswered by Stephen La Rocque. How high does the ladder reach? 2007-06-11 From Madi:A ladder 8 ft long resting on a house makes a 60 degree angle with the ground. how far up the house does it reach?Answered by Stephen La Rocque. Linear systems 2006-09-21 From Alexander:Hello, i have a math assignment due tonight at midnight and i need some help please It is using the addition method to solve linear systemsAnswered by Penny. 1/x + 1/y 2006-08-11 From Sonya:what is 1/x+1/y = ? is it equal to 1/x+y or what?Answered by Penny Nom. Rate of ladder falling 2006-04-30 From Harsh:A ladder 4 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 30 cm/s, how quickly is the top of the ladder sliding down the wall when the bottom of the ladder is 2 m from the wall?Answered by Stephen La Rocque. Adding polynomials and counting the terms 2006-04-28 From Kris:Suppose that two polynomials, each containing 3 terms, are added. Is it possible for the sum to contain more than 3 terms? fewer than 3 terms? exactly 3 terms? Explain.Answered by Leeanne Boehm and Steve La Rocque. Ladder and wall 2006-04-27 From Lori:A 12-foot ladder is leaning across a fence and is touching a higher wall located 3 feet behind the fence. The ladder makes an angle of 60 degrees with the ground. Find the distance from the base of the ladder to the bottom of the fence.Answered by Stephen La Rocque. Adding consecutive numbers 2006-04-26 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. Adding with mixed fractions 2006-03-30 From Becca:can anyone help with how we change to get the same denominator with adding whole number. example:8+7 3/8 6 1/2 + 2 5/6 Answered by Stephen La Rocque. Adding fractions 2006-03-26 From Barbara:I know that to subtract 1/4 from 2/3 I must find a common denom. Now the 2/3 becomes 8/12.....i understand the 12, but where does the 8 come from?Answered by Penny Nom. A 25 foot ladder is leaning against a building. 2006-03-24 From Ali:A 25 foot ladder is leaning against a building. The base of the ladder is 7 feet from the building. How high up the building does the ladder reach? Answered by Stephen La Rocque. Daddy Warbucks' cash 2006-02-22 From Grace:Daddy Warbucks always carries a specific number of $100 and$500 bills for impulse purchases and $1 bills for tips. If he has 500 bills in his briefcase and they total$50,000, how many bills of each denomination does he carry?Answered by Stephen La Rocque. GCF, LCM, primes and the ladder method 2006-01-07 From Linda:How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.???Answered by Penny Nom. Adding 10 and multiples of tens to one and two digit numbers 2005-12-13 From Meghan:I am teaching in a grade 2/3 class and I am struggling with trying to find a simple way of explaining to the students how to add 10 and multiples of tens to one and two digit numbers.Answered by Diane Hanson. Adding improper fractions 2005-11-25 From Paula:I would like a simple step by step explanation on how to add improper fractions.Answered by Penny Nom. How to add three addends 2005-09-28 From Patricia:explaination of how to add three addends if you use a double to add or if you use a sum of 10 8+3+2= 6+4+0= 3+3+6= 2+5+4= Answered by Baul Betts and Penny Nom. The language of subtraction 2005-09-26 From Chris:When you have an addition problem you have two addends that equal a sum. Therefore . . . I know the answer to a subtraction problem is the difference - what is the name of the numbers that make up a subtraction problem?Answered by Diane Hanson and Harley Weston. Adding positive and negative numbers 2005-09-03 From Billy:46 + -24 = -38 + -22 = 19 - 20 = Answered by Penny Nom. Adding consecutive integers 2005-05-13 From Yas:i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5Answered by Penny Nom. The least common denominator 2004-11-03 From A student:Write the LCD for each pair of fractions. 13. 1/3,1/5 14. 2/7,1/4 15. 3/4,3/5Answered by Penny Nom. Subtracting fractions 2004-05-11 From Filipe: Question: _5_ - __7__ 6ab 8aAnswered by Penny Nom. A/30 + B/105 = (7A + 2B)/x 2004-02-05 From Jim:If A/30 + B/105 = (7A + 2B)/x and A, B, and x are integers greater than 1, what must x equal? Answered by Penny Nom. Adding percentages 2003-12-19 From Paula:How do you add percentages e.g 90% + 80% + 60% + 54% + 25% = ? Answered by Penny Nom. Adding fractions 2003-11-16 From Ken:My name is Ken and I am taking my GED course for my High School and have not been in a class for 35 years. I am doing this for re-training. I am at the part about fractions. Here is an example that I am having trouble with. 1 3/7 + 4 2/3 + 11/21 They have no common denominators. Could you PLEASE help me. If you could send me a step by step explanation it would be greatly appreciated.Answered by Penny Nom. A 16 foot ladder 2003-09-04 From Kelly:Two buildings are separated by a three-foot alleyway. Fatima wants to use a 16 foot ladder to reach a window in the wall of one of these buildings. If she places the foot of the ladder against the base of the other building, how far up the wall will the top of the ladder reach??Answered by Penny Nom. 7+8+9+...+1000 2002-09-11 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. Common Denominator 2002-08-26 From Slobodanka:What is a Common Denominator?Answered by Penny Nom. Adding algebraic fractions 2002-03-20 From Dolores:I get totally confused with this problem. I get confused with the getting the lowest terms. 4/x-5 + -2/x -10/x^2-5x Answered by Penny Nom. F = -3 + 3 2002-03-19 From Jessica:F= -3 + 3 WHAT IS F?????Answered by Penny Nom. Adding algebraic fractions 2002-01-23 From Francine: Hello, I've come up with an answer for the following problem but it's not the same as the book's answer. However, the book has a lot of mistakes in it and I don't know if I'm doing it properly or not. Your help would be soooo appreciated. It's driving me crazy.The problem is:  2 + 3 + 4 --------- + --------- + ---------- (x-1)^3 (x-1)^2 (x-1)  [(x-1)^3 is (x-1) to power of 3 etc.] Answered by Penny Nom. Adding vectors 2002-01-12 From Lena:how do you add vectors together? If you are given the length and angles of both vectors and are asked to add/subtract them, how do you do it? I know you are supposed to do the head to tail method, but whenever i try it i get the wrong answer. I need help setting it up. example: A is 2.7cm, and 60 degrees, B is 1.6cm and 135 degrees, find the magnitude and amplitude Answered by Penny Nom. Odd plus even is odd 2001-10-14 From James:Why is the sum of an odd number and an even number always odd?Answered by Peny Nom. Adding and subtracting rational expressions 2001-05-03 From Donna:Adding and subtracting Rational expressions. I am in grade 10 and I am a student here is an example of the questions: 1/(x+1) - 1/(x-1) = ? Answered by Penny Nom. Adding functions 2001-02-19 From Jackie:f(x) = x2 + 1; g(x) = x2 - 1 find a) ((f+g) of h)) (x) b) ((f-g) of h)) (x) c) ((f of h) - (g of h)) (x) Answered by Penny Nom. What is wrong with these probelms? 2001-02-09 From Cindy:Hi, I am a planning on becomming a teacher and i am asked to find out what is wrong with these probelms and how i would go about showing a student what is wrong with them!! Error in patterns: 13/35=1/5; 27/73=2/3; 16/64=1/4 4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11 2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10 Answered by Leeanne Boehm and Penny Nom. Order of operations 2000-11-26 From Margaret Pratt:My daughter has a math question and I am afraid I am of no help. Can you help? 2x5/2+1-5= 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. Word addition 2000-07-05 From Harman Chaudhry:What is the value of DISHES if SEE + THE + WAITER + WASHES = DISHES. In addition, I know there is a name for these types of problems--what are they actually called?Answered by Chris Fisher. Why does division start from the left? 2000-05-24 From Salil Dave:Addition, subtraction and multiplications start with right most digit and proceed left, but division starts from left-most digits and goes right ... why? Answered by Harley Weston. Adding fractions 2000-04-23 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. Making fruit salad 2000-03-29 From A grade 5 student:Miss.Muffet males a fruit salad by adding 31/2 pounds of grapes and 4 1/4 pounds of apples to every 2 1/4 pounds of melon. How many pounds of grapes does she use in 50 pounds of fruit salad? Answered by Claude Tardif. Addition 2000-01-11 From Deanna:what is the answer for 20+5+32-3+98Answered by Penny Nom. The shortest ladder 1999-06-26 From Nicholas:A vertical wall, 2.7m high, runs parallel to the wall of a house and is at a horizontal distance of 6.4m from the house. An extending ladder is placed to rest on the top B of the wall with one end C against the house and the other end, A, resting on horizontal ground. The points A, B, and C are in a vertical plane at right angles to the wall and the ladder makes an angle@, where 0<@Answered by Harley Weston. A ladder problem 1999-04-22 From Michael Blade:There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question- the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions?Answered by Penny Nom. A number between 1998-11-25 From Jimmy Nikola:A number is less than 3,425 + 8,630 and greater than 7,614 + 4,429. What could the number be? This question is on page 93, question number 23. in Silver Burdett Ginn Math book, which is a 3rd grade math book.Answered by Jack LeSage. Adding Fractions 1998-10-15 From Lindsay:please help me!!!!Answered by Harley Weston. A Sum or Product of Fractions 1998-10-06 From Emily Robb:Find a pair of fractions that when they are multiplyed and added the sum /product is the sameAnswered by Penny Nom. Adding Fractions 1998-10-03 From Pam Bailey:Can you help me simplfy this? (1/2a + 1/3b) - (1/4a - 1/5b) + (1/6a - 1/7) thanxAnswered by Harley Weston. Using your fingers 1998-04-21 From Ian Sutherland:My 7-year-old son, in Grade 2, constantly uses his fingers to count.  I know for now this is a useful crutch but at what point should he stop? Answered by Diane Hanson. calcul des hh,mn,sec 2008-01-19 From gillot:bonjour, mon fils à des additions et soustractions d'horaire et je n'arrive pas à trouver la règle pour lui espliquer comment il faut faire il y a t il une formule pour les additions et soustractions merci par avance pour vos réponsesAnswered by Claude Tardif. A=B+C+D+F+G+H+J 2007-11-27 From Boubendir:voila ma question et comme savoir les nombres additioné en etulisant le resultat A=B+C+D+F+G+H+J au debut ons a les B,C,D,F,G,H,J on connaissent leur valeur comment retrouver valeur on etulisant leur resultatAnswered by Claude Tardif.