Page 289 - Ganit Kaushal

Based on the above information, answer the following questions:

1. What are the maximum marks a student can get?
2. A student answers 6 questions correctly and 4 questions incorrectly in part A, and answers 4 questions
correctly, 1 question partially correctly, and 1 question incorrectly in part B. What is the student’s total
score?

3. By how many marks did the student fall short of achieving the maximum possible marks?
4. What is the score of another student if he answers all questions in Part A incorrectly but manages to
answer 4 questions correctly and 2 partially correctly in Part B?
5. One other student managed to score a total of 30 marks, with 12 marks coming from Part A. How
many questions did he get partially correct in part B if he answered one question correctly and the
remaining incorrectly?

Summary of the Chapter

• Numbers that are less than zero are written with a ‘–’ sign in front of them (e.g., –2), and are called
negative numbers. They lie to the left of zero on the number line.

• The numbers ..., – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, ... are called integers. The numbers 1, 2, 3, 4, … are
positive integers, and the numbers …, – 4, – 3, – 2, – 1 are negative integers. The number zero (0) is
neither positive nor negative.

• Every number has another number associated with it, which when added to the given numbers gives
zero. This is called the additive inverse of the number. For example, the additive inverse of 9 is –9, and
the additive inverse of –213 is 213.
• Addition can be interpreted as: Starting Number + Movement = Target Number.
• Subtraction can be interpreted as: Target Number – Starting Number = Movement needed.

• In general, we can add two numbers by following Brahmagupta’s Rules for Addition:
(a) If both numbers are positive, add the numbers and the result is a positive number. (e.g., 4 + 3 = 7).
(b) If both numbers are negative, add the numbers (without the signs), and then place a minus sign to
obtain the result (–1 + (–24) = –25).

(c) If one number is positive and the other is negative, subtract the smaller number (without the sign)
from the greater number (without the sign), and place the sign of the greater number to obtain the
result (e.g., –5 + 3 = –2).

(d) A number plus its additive inverse is zero (e.g., 2 + (–2) = 0).
(e) A number plus zero gives back the same number (e.g., –2 + 0 = –2).

• We can subtract two integers by converting the problem into an addition problem and then applying
the rules of addition.
• Subtracting an integer is the same as adding its additive inverse.
• Integers can be compared as follows: …, –3 < –2 < –1 < 0 < +1 < +2 < +3 < ... Smaller numbers are to
the left of larger numbers on the number line.

The Other Side of Zero 287