List of top Mathematics Questions on Properties Of Division Of Integers

In a class test (+3) marks are given for every correct answer and (–2) marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores –5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?

Fill in the blanks:
(a) 369 ÷ _____ = 369
(b) (–75) ÷ _____ = –1
(c) (–206) ÷ _____ = 1
(d) – 87 ÷ _____ = 87
(e) _____ ÷ 1 = – 87
(f) _____ ÷ 48 = –1
(g) 20 ÷ _____ = –2
(h) _____ ÷ (4) = –3

The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

Some pictures (a) to (c) are given below. Tell which of them show:
\((a)\)

\((b)\)

\((c)\)

(i) 3 × \(\frac{1}{5}\) =\(\frac{3}{5}\)
(ii) 2 × \(\frac{1}{3}\) =\(\frac{2}{3}\)
(iii) 3 × \(\frac{3}{4}\) = \(\frac{21}{4}\)

Which of the drawings (a) to (d) show : 
\((a)\)

\((b)\)

\((c)\)

\((d)\)

(i) 2 × \(\frac{1}{5}\)
(ii) 2 × \(\frac{1}{2}\)
(iii) 3 × \(\frac{2}{3}\)
(iv) 3 × \(\frac{1}{4}\)

An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m.

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = – 4, c = 2 (b) a = (–10), b = 1, c = 1