Understanding variables representing integers on number line | 7th grade | Khan Academy

TL;DR

Learn how to order expressions with negative numbers by understanding their values and using subtraction.

Transcript

• Let's get some practice understanding the variables and the negative numbers that they might represent or the positive numbers. So we're told to order the following expressions by their values from least to greatest. And they've given us these three expressions q minus n, n, and n minus q and then they plot n and q on the number line. So just to ... Read More

Key Insights

• 🟰 Q minus n is positive when q is greater than n, regardless of the signs of q and n.
• #️⃣ Subtracting a negative number from a positive number results in a positive value greater than the original.
• 🛩️ Subtracting a positive number from a will make the value smaller.

Questions & Answers

Q: How do you determine whether an expression with q and n is positive or negative?

If q is greater than n, the expression will be positive regardless of the signs of q and n. If q is positive and n is negative, subtracting a negative number from a positive number will result in a positive value.

Q: How do you estimate the values of n and q in the second example?

By looking at the number line, q is approximately 0.8 and n is approximately -1.8. Subtracting a negative number from a positive number will make it less than the original value.

Q: Why is a minus 0.5 the least in the second example?

Subtracting a positive number from a will result in a smaller value. 0.5 is positive, so the expression a minus 0.5 is the least.

Q: Can you explain why a minus b is the greatest in the second example?

Since a minus b means subtracting a negative number from a, the result will be greater than a. When subtracting a negative number, it is equivalent to adding a positive number.

Summary & Key Takeaways

• Given three expressions: q minus n, n, and n minus q.

• q minus n is positive and greater than q.

• n is a negative number between -1 and -2, approximately -1.8.

• n minus q is the most negative, followed by n, and q minus n is the greatest.