Find two numbers when you know only their sum and their difference, and see why the order of the numbers decides the sign.
Preview · progress not saved — Chapter 1 is free
What 'sum' and 'difference' mean, and why the order of the numbers matters.
Rakesh says: "I have thought of two numbers. Their sum is 25, and their difference is 11. Can you tell me the two numbers?"
You don't need a formula. Try pairs of numbers and check them.
Rakesh's puzzle solved step by step, then the twist with difference −11.
Problem. Find two numbers whose sum is 25 and whose difference is 11. Then find two numbers whose sum is 25 and whose difference is −11. (Textbook p. 24)
Two quick patterns that make these puzzles faster.
Fill the missing steps to solve Figure it Out (a).
Figure it Out (a): Sum = 27, Difference = 9.
Try first = 15. For the sum to be 27, the second number is . The difference is 15 − 12 = . That is too small, so make the first number bigger.
Try first = 18. The second number is . Sum = . Difference = . ✓
So the two numbers are 18 and 9.
Five sum-and-difference puzzles from the book, including negatives.
Sum = 4, Difference = 12. What are the numbers? (first, second)
Make your own puzzle for a friend, then solve one.
The book suggests a partner game (p. 25): one person thinks of two integers and gives their sum and difference; the other finds the integers.
Pick two integers, at least one negative.
Show both calculations.
Show your guesses and both checks.