







Multiplication and repeated addition 
20161123 

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 2D figure(actually,quadrilateral) having length consisting of 2 boxes of
1by1 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 23rd,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?
Thanks Answered by Penny Nom. 





find f+g 
20160626 

From yzabelle: find f+g
f(x)=x^21
g(x)=square root of x+2 Answered by Penny Nom. 





Fractions of two quantities 
20160122 

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 
20160115 

From Michael: express the following complex numbers in standard form (2+3i)+(52i) Answered by Penny Nom. 





A ladder against a wall 
20140709 

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 wall Answered by Penny Nom. 





Adding fractions 
20140131 

From bianco: 2/3+3/4=
9/86/8= Answered by Penny Nom. 





A word problem involving fractions 
20140123 

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 with Answered by Penny Nom. 





Why can't we add or subtract speed? 
20131121 

From kashish: why we cannot add or subtract "speed" / directly in any given distance , speed , time questions? Answered by Chris Fisher. 





Adding mixed numbers 
20131120 

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 
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. 





Ann has a bag of marbles. 
20130725 

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 
20130516 

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 
20120919 

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 
20120910 

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 student Answered by Robert Dawson and Penny Nom. 





Adding speeds 
20120826 

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 
20120105 

From laurie: if shaded parts of a circle are 4/7 and the other is 1/3 what fraction is left Answered by Penny Nom. 





1 third plus 5 sixths 
20111110 

From Matt: 1 third plus 5 sixths = Answered by Penny Nom. 





pi/2 + 12/13 
20110524 

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 
20110121 

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 
20110119 

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 
20101023 

From angelina: how to covert 5+5+5=15 to multiplication Answered by Penny Nom. 





4.5 PLUS 29 
20100907 

From kiona: 4.5 PLUS 29 Answered by Penny Nom. 





A ladder against a wall 
20100325 

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 
20100309 

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 
20100227 

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 
20100213 

From Priscila: 3/8 + 4/5 + 7/3 + 9/10 = ?
Thank you for your assistance.
Priscila Answered by Penny Nom. 





Combining fractions 
20100210 

From Nick: Combine the fractions
2m/t + 5/mt Answered by Penny Nom. 





Ladder Leaning on a Wall 
20090514 

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 ladder Answered by Robert Dawson. 





A ladder against a wall 
20090408 

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 
20090401 

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 
20090330 

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 
20090329 

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 
20090225 

From Susan: 11 base 2 X 22 base 3 + 33 base 4 = _________ base 5 Answered by Robert Dawson. 





Averaging percentages 
20090221 

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 
20080917 

From amanpreet: please can you help me to simplify:
2(c3) / 7 + 3(4c2)/2 Answered by Penny Nom. 





Three addends that sum to ten 
20080913 

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 
20080913 

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? 
20080710 

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 wall Answered by Penny Nom. 





.9 repeating plus .2 repeating 
20080610 

From megan: How do you express the addition of .9 repeating plus .2 repeating? Answered by Penny Nom. 





How do you add decimals? 
20080605 

From nyheashiacurry: how do you add up decimals? Answered by Janice Cotcher. 





3 radical 48 +11 radical 75 
20080524 

From Maria: Add 3 radical 48 +11 radical 75. Write answer in simpliest form. Answered by Penny Nom. 





Adding rational functions 
20080429 

From Jonathon: 1/(x+3) + 1/(x^2+5x+6) = 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. 





Sum and difference of cubes 
20080130 

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 
20071231 

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 
20071204 

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 
20071127 

From jessica: what is a addends my son needs to write a number sentence that has two addends that are the same Answered by Stephen La Rocque. 





Number sentences 
20070915 

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 help Answered by Harley Weston. 





Adding algebraic fractions 
20070814 

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/3k8)  (4/k+2) Answered by Penny Nom. 





Fractions of fractions 
20070718 

From Bridget: Sam and Mary each owned onehalf 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 
20070617 

From Aakash: the period of the function f(x)=cos3x+sin4x+tan4x Answered by Stephen La Rocque. 





How high does the ladder reach? 
20070611 

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 
20060921 

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 systems Answered by Penny. 





1/x + 1/y 
20060811 

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 
20060430 

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 
20060428 

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 
20060427 

From Lori: A 12foot 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 
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. 





Adding with mixed fractions 
20060330 

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 
20060326 

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. 
20060324 

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 
20060222 

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 
20060107 

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 
20051213 

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 
20051125 

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 
20050928 

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 
20050926 

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 
20050903 

From Billy: 46 + 24 =
38 + 22 =
19  20 = Answered by Penny Nom. 





Adding consecutive integers 
20050513 

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+5 Answered by Penny Nom. 





The least common denominator 
20041103 

From A student: Write the LCD for each pair of fractions.
13. 1/3,1/5
14. 2/7,1/4
15. 3/4,3/5 Answered by Penny Nom. 





Subtracting fractions 
20040511 

From Filipe: Question:
_5_  __7__
6ab 8a Answered by Penny Nom. 





A/30 + B/105 = (7A + 2B)/x 
20040205 

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 
20031219 

From Paula:
How do you add percentages
e.g 90% + 80% + 60% + 54% + 25% = ?
Answered by Penny Nom. 





Adding fractions 
20031116 

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 retraining. 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 
20030904 

From Kelly: Two buildings are separated by a threefoot 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 
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. 





Common Denominator 
20020826 

From Slobodanka: What is a Common Denominator? Answered by Penny Nom. 





Adding algebraic fractions 
20020320 

From Dolores: I get totally confused with this problem. I get confused with the getting the lowest terms. 4/x5 + 2/x 10/x^25x Answered by Penny Nom. 





F = 3 + 3 
20020319 

From Jessica: F= 3 + 3 WHAT IS F????? Answered by Penny Nom. 





Adding algebraic fractions 
20020123 

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
 +  + 
(x1)^3 (x1)^2 (x1)
[(x1)^3 is (x1) to power of 3 etc.] Answered by Penny Nom. 





Adding vectors 
20020112 

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 
20011014 

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 
20010503 

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/(x1) = ? Answered by Penny Nom. 





Adding functions 
20010219 

From Jackie: f(x) = x^{2} + 1; g(x) = x^{2}  1 find a) ((f+g) of h)) (x) b) ((fg) of h)) (x) c) ((f of h)  (g of h)) (x) Answered by Penny Nom. 





What is wrong with these probelms? 
20010209 

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 
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. 





Word addition 
20000705 

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 problemswhat are they actually called? Answered by Chris Fisher. 





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. 





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. 





Making fruit salad 
20000329 

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 
20000111 

From Deanna: what is the answer for 20+5+323+98 Answered by Penny Nom. 





The shortest ladder 
19990626 

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 
19990422 

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 
19981125 

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 
19981015 

From Lindsay: please help me!!!! Answered by Harley Weston. 





A Sum or Product of Fractions 
19981006 

From Emily Robb: Find a pair of fractions that when they are multiplyed and added the sum /product is the same Answered by Penny Nom. 





Adding Fractions 
19981003 

From Pam Bailey: Can you help me simplfy this? (1/2a + 1/3b)  (1/4a  1/5b) + (1/6a  1/7) thanx Answered by Harley Weston. 





Using your fingers 
19980421 

From Ian Sutherland: My 7yearold 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 
20080119 

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 réponses Answered by Claude Tardif. 





A=B+C+D+F+G+H+J 
20071127 

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 resultat Answered by Claude Tardif. 

