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Browse Elementary Addition
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    What is 1+1?

Adding Positives and Negatives [12/01/1998]
I'm having trouble solving problems like these: -31+(-46)=b, a=16+(- 36), and 74+(-63)=d.

Adding Positive to Negative Numbers [06/01/1999]
How do positive numbers get added to negative numbers?

Adding Shortcut [05/05/2003]
Explain how 10 helps you find the sum of 9 and 8.

Adding stickers [12/2/1994]
Jacob earned two stickers for the mad minute. Laura earned two stickers for mad minute. Melissa earned two stickers also. How many stickers did they earn all together?

Adding Two-Digit Numbers Using Money [09/13/2001]
I don't understand how to add 2-digit numbers like 24 + 56 + ?

Addition and Subtraction Patterns [09/22/2000]
In my fourth grade class we found patterns in addition problems, but when we tried this with subtraction it did not work...

Addition of 1 and 99999999.999999 [5/1/1995]
A student asks how to add 1 to a long list of nines.

Addition Shortcut [05/27/1997]
Besides just adding everything up, is there another way to solve (2+4+ 6+8+...+34)/(3+6+9+12+...+54)?

Addition with Variables [4/16/1996]
I was wondering if you could help me with: 3a+a ?

Additive Identity and Other Properties [01/03/1999]
Can you explain the identity of zero and the commutative and multiplicative properties? Why are they special?

Almost a Magic Square [12/16/1996]
Given a set of 16 numbers, place them in a 4 by 4 square so that the sum of the members of each row or column equals 44.

Associative and Commutative Properties [08/20/2001]
Please tell me if this problem is associative or commutative and explain the difference.

Baseball Wins [9/10/1996]
A baseball team played 18 games and won 4 more games than it lost. How many games did it win?

A + B = B + A ? [7/24/1996]
Is A + B = B + A true or not true?

Brackets [01/29/2001]
Please explain how brackets [] work.

Can You Multiply Three Numbers Simultaneously? [03/15/2004]
If I have the problem 24 + 342 + 506 I can line the numbers up and add them at the same time. Can I do this with the problem 24 x 342 x 506? If I can, how do you do it? If I can't, why not?

Carrying and Borrowing [01/14/1998]
My son has a problem understanding addition and subtraction when he has to do regrouping, what I call carrying and borrowing...

Casting out Nines: How Is 9 the Same As 0? Why Bother? [09/25/2009]
Doctor Peterson makes a case for this old technique in the calculator age -- and makes a connection between digital roots and remainders in base ten division.

Casting Out Nines to Check Arithmetic [08/26/1999]
Can you explain how to use the 'casting out 9's' technique in a way that a 6th grader can understand?

Chisanbop: Advanced Counting on Fingers [3/18/1996]
I saw on TV years ago kids in 1st grade doing advanced math by counting by using their fingers as a kind of abacus...

Coin Combinations Quickened by Process of Elimination [11/04/2013]
A student seeks a method for efficiently attacking a puzzle that involves partitioning sums of coins. Doctor Greenie suggests he reverse his thinking and work backwards.

The Commutative Property Around Us [11/24/1998]
Which operations are commutative... to put on your coat and to pick up your boots...

Comparing Sums of Odd and Even Integers [03/31/2004]
Which is greater, the sum of all of the even numbers that are less than 100, or the sum of all of the odd numbers that are less than 100? It takes too long to add them all up!

Confusion over Interpretation of PEMDAS [03/24/2005]
Students take PEMDAS letter by letter, tending to do all multiplication before any division, rather than working from left to right. Here's a suggestion on how to help avoid that confusion.

Consecutive Odd Integers [08/28/1997]
I need to know three consecutive odd integers that equal 150.

Counting Money [06/28/1997]
How can I learn to count money better?

Distributive Property over Addition vs. Multiplication [12/11/2002]
Why can't you use the distributive property when the integers in the parenthesis are being multiplied?

Eight Circles, Sum is 13 [09/25/2002]
Arrange the numbers 1,2,3,4,5,6,7,8 in a given pattern so that the sum of the numbers in any line equals 13.

Evaluating Parentheses, Brackets, Braces and Grouping Symbols [01/20/2007]
How do I evaluate or simplify an expression with lots of grouping symbols, like (18/2){[(9 x 9 - 1)/ 2] - [5 x 20 - (7 x 9 - 2)]}?

Even More on Order of Operations [10/26/2017]
How can 8/4(3-1) have two answers? Doctor Peterson unpacks the ambiguities that have made the order of operations a persistent lightning rod for controversy — and misunderstanding.

Explaining Order of Operations [09/06/2001]
How would you explain the order of operations to a 5th or 6th grader who has not yet studied the subject?

Fractions and School Enrollments [02/26/2003]
The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School is exactly the enrollment of the Language School. The sum of 1/5, 1/6, 1/7, and 1/8 of the enrollment of the Business School is exactly that of the Design School. What are the enrollments of these three schools, assuming no school has more than 1000 pupils?

How we solve problems [11/21/1994]
How do you know all these problems, do you use a computer or calculator? Do you know 364,786,598+56=364,786,654?

Identity Element [10/12/2001]
What is an "identity element"?

Incorrect Application of PEMDAS and Order of Operations [09/14/2006]
My students think PEMDAS means that all addition should be done before any subtraction is done. How can I show and convince them that they need to do both operations at the same time working from left to right?

Kindergarten Math - Addition [12/21/1996]
How can I continue to enhance my daughter's math skills without making her feel overwhelmed?

Learning Addition and Multiplication with Algebra [3/16/1996]
How do you know what the (a) is in algebra? I saw this on a picture: a(1/a) = 1/a(a) = 1...

Left Associativity [05/27/1999]
Is the 'left to right' rule in mathematics a law or is it just used for consistency?

Lining Up Decimal Points [03/03/2003]
Why do we line up decimal points for addition and subtraction but not for division and multiplication?

Mental Math: Making Tens [09/16/2003]
What is the 'make a ten' strategy in mental math?

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