Using expressions to understand relationships | Linear inequalities | Algebra I | Khan Academy

TL;DR

If a, b, and c are integers greater than 0, a is divisible by c, and (a + b)/c is an integer, then b must be a multiple of c.

Transcript

Let's say that we have three integers, a, b, and c, and we know that all of these integers are greater than 0. So they're integers, and they are greater than 0. And we also know that the expression a plus b over c, that this is also an integer. The entire expression, if you were to evaluate it, is also an integer. And then finally, we know that a i... Read More

Key Insights

• 😃 All integers a, b, and c are greater than 0.
• 😑 The expression (a + b)/c is guaranteed to be an integer.
• 😀 If a is divisible by c, then a/c must be an integer.
• 😃 If (a + b)/c is an integer, both a/c and b/c must be integers.
• 🪜 Adding an integer to another integer results in an integer.

Questions & Answers

Q: What are the given constraints for the integers a, b, and c?

The integers a, b, and c are all greater than 0.

Q: What is the requirement for the expression (a + b)/c to be an integer?

For (a + b)/c to be an integer, a must be divisible by c.

Q: Does b have to be a multiple of c?

Yes, b has to be a multiple of c given the constraints of a, b, and c.

Q: How can we rewrite the expression a + b/c?

The expression a + b/c can be rewritten as a/c + b/c, which is equivalent to the original expression.

Summary & Key Takeaways

• Three integers, a, b, and c, are greater than 0.

• (a + b)/c is an integer.

• a is divisible by c.