☰ Contents · Mathematics

Adding on the number line and adding negative numbers

Lessons 31–32 · 2 lessons · M.A. Mirzaahmedov, A.A. Rahimqoriyev, Sh.N. Ismailov, M.A. To‘xtaxodjayeva. Mathematics Grade 6, 2nd edition. O‘qituvchi NMIU, Tashkent, 2017
32

Adding numbers with negative signs

Textbook, pp. 149–151
GoalKnow and apply the rule for adding numbers with negative signs.
New words
sum of the moduli · modullar yig‘indisinegative sign · manfiy ishoraaddend · qo‘shiluvchicommutative property · o‘rin almashtirish xossasi
Explanation

To add two negative numbers, add their moduli and put a “−” sign in front of the sum: (−3) + (−5) = −(3 + 5) = −8. The sum of two negative numbers is smaller than each addend. We add three or more negative numbers in the same way: (−4) + (−9) + (−2) = −15. The commutative and associative properties of addition also hold for negative numbers. Negative quantities, such as temperature drops or debts, add up in this way.

Worked examples
(−12) + (−7) = −(12 + 7) = −19.
The temperature dropped 4 degrees and then 5 more: (−4) + (−5) = −9. In all it dropped 9 degrees.
Class activity

“Debt book”: groups play “shop debts”: each purchase is written as a negative number (−3,000, −5,000, ...). The team finds the total debt and explains why the answer is negative.

Practice
1
Compute (−6) + (−9).
2
Compute (−25) + (−15).
3
The temperature fell 4 degrees and then 5 more. Write the total change as a number.
4
Why is the sum of two negative numbers always negative?