Sum and difference

Learning Objectives Identify problems that involve finding two numbers given their sum and difference. Understand the relationship between the sum, difference, and the two unknown numbers. Apply a systematic approach to find the larger number when the sum and difference are known. Apply a systematic approach to find the smaller number when the sum and difference are known. Solve word problems by setting up and solving equations based on sum and difference. Check their solutions by verifying the sum and difference of the calculated numbers. Imagine you know how many candies two friends have *together* and how many more one friend has than the other. Can you figure out exactly how many each friend has? 🤔 In this lesson, you'll learn a clever trick to find two unknown nu...

TermDefinitionExample SumThe result of adding two or more numbers together; the total amount.The sum of 10 and 5 is 15 (10 + 5 = 15). DifferenceThe result of subtracting one number from another, showing how much larger one number is than the other.The difference between 10 and 5 is 5 (10 - 5 = 5). Larger NumberIn a pair of two different numbers, the one with the greater value.If the two numbers are 13 and 7, then 13 is the larger number. Smaller NumberIn a pair of two different numbers, the one with the lesser value.If the two numbers are 13 and 7, then 7 is the smaller number. UnknownsThe quantities or numbers that we need to find in a problem.In 'What two numbers add to 20?', the two numbers are the unknowns. Problem Solving StrategyA systematic plan or method used to find the...

Finding the Larger Number $\text{Larger Number} = (\text{Sum} + \text{Difference}) \div 2$ To find the larger of the two numbers, first add the given sum and difference together. Then, divide that result by 2. This works because adding the difference to the sum effectively doubles the larger number. Finding the Smaller Number $\text{Smaller Number} = (\text{Sum} - \text{Difference}) \div 2$ To find the smaller of the two numbers, first subtract the given difference from the sum. Then, divide that result by 2. This works because subtracting the difference from the sum effectively doubles the smaller number. Alternative for Smaller Number (after finding Larger) $\text{Smaller Number} = \text{Sum} - \text{Larger Number}$ Once you have found the larger number using the f...