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Integers

Sana and Fatima participated in an apple race. The race was conducted
in 6 parts. In the first part, Sana won by 10 seconds. In the second
part she lost by 1 minute, then won by 20 seconds in the third part
and lost by 25 seconds in the fourth part, she lost by 37 seconds in
the fifth part and won by 12 seconds in the last part. Who won the
race finally?

Integers

Height of a place A is 1800 m above sea level. Another place B is 700 m below sea level. What is the difference between the levels of these two places?

Integers

Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:
u × v = u
x × w = w
u + x = w
(a) v
(b) w
(c) x
Explain your reasoning using the properties of integers

Integers

If ∆ is an operation such that for integers a and b we have
a ∆ b = a × b – 2 × a × b + b × b (–a) × b + b × b
then find (i) 4 ∆ ( – 3)
(ii) ( – 7) ∆ ( – 1)
Also show that 4 ∆ ( – 3) ≠ (– 3) ∆ 4
and ( – 7) ∆ ( – 1) ≠ ( – 1) ∆ (– 7)

Integers

If * is an operation such that for integers a and b we have a * b = a × b + (a × a + b × b)

then find (i) ( – 3) * (– 5) (ii) ( – 6) * 2

Integers

.Evaluate the following, using distributive property.
(i) – 39 × 99 (ii) (– 85) × 43 + 43 × ( – 15)
(iii) 53 × ( – 9) – ( – 109) × 53 (iv) 68 × (–17) + ( –68) × 3

Integers

You are at an elevation 380 m above sea level as you start a motor
ride. During the ride, your elevation changes by the following metres:
540 m, –268 m, 116 m, –152 m, 490 m, –844 m, 94 m. What is your
elevation relative to the sea level at the end of the ride?

Integers

What’s the Error? Reeta evaluated –4 + d for d = –6 and gave an answer of 2. What might Reeta have done wrong?

Integers

What’s the Error? Ramu evaluated the expression –7 – (–3) and came
up with the answer –10. What did Ramu do wrong?

Integers

(a) Write a positive integer and a negative integer whose sum is a
negative integer.
(b) Write a positive integer and a negative integer whose sum is a
positive integer.
(c) Write a positive integer and a negative integer whose difference is
a negative integer.
(d) Write a positive integer and a negative integer whose difference is
a positive integer.
(e) Write two integers which are smaller than – 5 but their difference
is – 5.
(f) Write two integers which are greater than – 10 but their sum is
smaller than – 10.
(g) Write two integers which are greater than – 4 but their difference
is smaller than – 4.
(h) Write two integers which are smaller than – 6 but their difference
is greater than – 6.
(i) Write two negative integers whose difference is 7.
(j) Write two integers such that one is smaller than –11, and other
is greater than –11 but their difference is –11.
(k) Write two integers whose product is smaller than both the
integers.
(l) Write two integers whose product is greater than both the
integers.