Page 24 - ICSE Math 7

3. Gaurav’s bank balance was ` 2,000. In a month he deposited ` 300, ` 750 and ` 450 and issued
cheques worth ` 700 and ` 1,250. Find the balance in Gaurav’s account at the end of the month?
4. Imagine that you are a fighter pilot flying a jet aircraft at an altitude of 20,000 feet. You lower
the aircraft by 7,000 feet and then raise it by 5,000 feet. What is the net change in the altitude?
Also find the altitude after the two changes.
5. Raghuraj has 30 marbles. In 5 games he won 3 marbles each and in 7 games he lost 2 marbles
each. Find the marbles Raghuraj has at the end of the games.
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6. To convert temperature from Celsius to Fahrenheit, we multiply °C by and add 32, i.e.,
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°F = °C + 32. Find the Fahrenheit temperature that corresponds to:
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(a) –15°C (b) 40°C (c) –40°C
7. In a Microbiology laboratory, certain tests are done under controlled temperature. The variation
in temperature is by fixed number of degrees per minute. Evaluate each of the following.
(a) The temperature at the beginning of an experiment is 20°C. It increases by 4°C per minute.
What is the temperature at the end of the experiment if it took 15 minutes to complete?
(b) The temperature is made to fall by 3°C per minute. The temperature at the end of an experiment
is –7°C, which took 13 minutes to complete. What was the temperature at the beginning of
the experiment?

AT A GLANCE
¾ The set of integers is given by Z = {…, –3, –2, –1, 0, 1, 2, 3, …}.
• 1, 2, 3, 4, … are called positive integers.
• –1, –2, –3, –4, … are called negative integers.
• Zero is neither positive nor negative integer.
• 0, 1, 2, 3, … are called non-negative integers.
• 0, –1, –2, –3, … are called non-positive integers.
¾ The numerical value of an integer, regardless of its sign, is known as the modulus or absolute
value of the integer and is denoted by | a |.
¾ All integers can be represented on the number line.
¾ Addition: For any integers a and b, we define, –a + (–b) = –(a + b)
Properties
• Closure: a + b is again an integer.
• Commutative: a + b = b + a
• Associative: (a + b) + c = a + (b + c)
• Existence of additive identity: Since a + 0 = a = 0 + a for every integer a, ∴ 0 is the additive
identity.
• Existence of additive inverse: If a + (–a) = 0 = (–a) + a, then –a is called the additive inverse
of a.
¾ Subtraction: If a and b are any integers, we define a – b = n iff a = b + n, also a – b = a + (–b)
Properties
• Closure: a – b is again an integer.
• Commutative and associative properties are not true for subtraction in integers.
¾ Multiplication: For any integers a and b, we define a × b = ab, (–a) × (–b) = ab and
(–a) × (b) = (a) × (–b) = –(a × b)

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