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Sum of Digits - Concept
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
One difficult type of Algebra problem are word problems asking about the sum of digits in a two digit number. Solving systems of equations by substitution is one of the most common ways to solve sum of digits problems. Other types of word problems using systems of equations include mixture problems, money word problems, work word problems and rate word problems.
When you're working with word problems some are easier than others and the trick is that sometimes what looks like an easy word problem is actually pretty challenging. What we're going to be looking at are the types of word problems where it says the sum of the digits of the number is 35 or something, when you reverse the digits you get blah blah blah. Okay so when you're working with these kinds or problems it's important to think about what you know about digits. And it sounds like stuff you learned in like second grade which is true but now we're applying it to Algebra so it gets more challenging.
Here's what I mean the number 68 really mean 6 times 10 that's your tens digit plus 8 times 1, that's your ones digit. We call that the tens digit and the ones digit for a reason, that's going to become really important when you're switching the digits like for example if I were to take 68 and switch the digits to get 86 that would be 8 times 10 plus 6 times 1. Keep that in mind when you're going through to solve these problems that involve the sum of the digits, switch the digits blah blah.
One thing I want to leave you with before you guys start these problems is thinking about how to write an equation. You're going to have some expression that represents your original number and that's going to be equal to another expression that represents your flips digits, flipped, can I say flipped or switched whatever you want to think about, flipped digits and then chances are it's going to say "the original number is equal to 54 more than the flips digit." So you're going to have to add or subtract some quantity to one of these expressions.
Before you guys try I'm about to let you go, make sure you keep this idea in mind about tens digits and ones when you're approaching these problems. They look like they're pretty easy but they're actually pretty challenging, let's work through them step by step when you guys watch the coming up Brightstorm videos.
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Sample Problems (3)
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Sum of Digits
Problem 1 4,298 views
The sum of the digits of a 2-digit number is 12. When the digits are reversed, the new number is 54 more than the original number.What is the original number?
Sum of Digits
Problem 2 2,995 views
The sum of the digits of a certain 2-digit number is 6. When you reverse the digits, you decrese the number by 54.Find the number.
Sum of Digits
Problem 3 133 views