SUM / DIFF / MULTIPLE
Sum, difference and multiple problems, solved in three steps.
Enter a sum with a difference, a sum with a multiple, or a difference with a multiple, and get both numbers back with step-by-step working. A staple primary-school olympiad topic with random practice, all computed locally in your browser.
结果会显示在这里
Everything runs locally in your browser
The three formulas at a glance
| Type | Given | Larger | Smaller |
|---|---|---|---|
| Sum and difference | sum S, difference D | (S + D) / 2 | (S - D) / 2 |
| Sum and multiple | sum S, multiple n | S / (n + 1) x n | S / (n + 1) |
| Difference and multiple | difference D, multiple n | D / (n - 1) x n | D / (n - 1) |
The one idea behind all three: call the smaller number 1 part. Sum-and-multiple and difference-and-multiple both start by finding what one part is, then multiply; sum-and-difference just folds the difference into the sum to get twice the larger number.
What is this?
Sum, difference and multiple problems are the most basic primary-school olympiad type, and all of them boil down to treating two numbers as so many parts. For sum-and-difference you know the total and the gap, and folding the gap into the total gives twice the larger number, so larger = (sum + difference) / 2. For sum-and-multiple and difference-and-multiple, treat the smaller number as one part: the sum is n+1 parts and the difference is n-1 parts, so find one part and multiply. Random practice questions are provided below.
FAQ
How is this different from the chicken-and-rabbit problem?
The chicken-and-rabbit problem uses the assumption method: assume everything is a chicken, then work backwards from the leg difference. Sum, difference and multiple problems instead model the two numbers as parts and parts, solved directly with the three formula families. The given conditions and the reasoning both differ, so first work out which type you are looking at.
Why do I sometimes get decimals back?
If whole numbers are expected but the figures do not divide evenly, you get decimals: a sum of 60 with a difference of 18 is fine (39 and 21), but a sum of 60 with a difference of 17 gives 38.5 and 21.5. That usually means a figure was copied wrong, so go back and check the original question.
Can the multiple be a decimal?
No. The multiple must be greater than 1, otherwise the supposed larger number would be smaller than the other, contradicting the premise. The tool requires a multiple above 1; and in difference-and-multiple a multiple of exactly 1 means the two numbers are equal with a difference of zero, which is not a usable condition either.
Does this upload anything?
No. All arithmetic happens inside your current browser with no network requests and no sign-up, which makes it fine for classroom practice or tutoring at home.