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\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

D. Fill in the blanks.

1. If x, y and z are integers, then (x + .......... ) + z = .......... + (y + .......... )
2. (–a) + b = b + Additive inverse of .................
3. [12 × ( – 7)] × 5 = ................. × [(– 7) × ................. ]
4. When –16 is divided by ................. the quotient is 4.

5. ................. × (–23) = – 920
E. Answer the following questions.

1. Evaluate the following.
(a) (–4) × (–5) × (–6) × (–2) × (–1) (b) [(–4) × (–12)] ÷ (–16)
(c) (–14) + (–8) ÷ (–2) × (–3) (d) 16 − [16 − 16 − (16 − 16 − 16)]
(e) 26 × (–50) + (–50) × (–36)

2. If * is an operation such that for integers a and b, we have a * b = a × a + b × b – a × b, then find:
(a) (–3) * 2 (b) 3 * (–1)
3. Write a pair of integers whose product is – 15 and whose difference is 8.

4. A caterpillar crawls up 5 cm on a 60 cm vertical rod every second and then falls down 2 cm over
the next second. How many seconds will it take to climb the rod?
5. The temperature of a hot iron rod is 320°C. Every minute the temperature drops by 6°C. What will
be the temperature of the iron rod after 10 minutes?
6. Ruhi evaluated the expression –27 ÷ (–3) and came up with the answer –9. What did Ruhi do
wrong?
7. The population of honey bees in a particular region decreases by 140 bees over a week. At the
same rate, what is the change in the population of honey bees each day in that particular week?
COMPETENCY BASED QUESTION
8. Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date
three days after tomorrow? COMPETENCY BASED QUESTION

9. Water is a very important resource, we use water for almost every activity like drinking, washing,
cooking, cleaning, etc. Out of the population of 1.4 billion people, 35 million people lack access to
safe water, and 678 million people lack access to safe toilets. The groundwater level drops down
continuously because of the frequent pumping of water from the ground. The water level in a well
is 20 m below ground level in summer. During the rainy season, rainwater collected in different
water tanks was drained into the well, and the water level rose 5 m above the previous level. The
wall of the well is 1 m 20 cm high, and a pulley is fixed at a height of 80 cm. Raghu wants to draw
water from the well. What is the minimum length of the rope that he can use?
How can we conserve water? Write any 4 ways to save water.

Brain Sizzlers

Five friends are standing in a line waiting for the opening of a show. They are in line according to
their arrival. Sonam arrived 4 minutes after Sumit. Roma took his place in line at 10:03 p.m. She
was 2 minutes behind Ruhi and 7 minutes ahead of Sonam. The first person arrived at 9:55 p.m.
Imran showed up 6 minutes after the first person. List the time of each person’s arrival. Whose
arrival information helped you to determine the arrival time of each?

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