6/28/2020 Step Up Math 7

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6. Verifythe followingand also name the property that is used.

q q
A well has 20 steps inside it. A frog is sitting at the first step. The water level is at the
a. 16 + (–25) = (–25) + 16 b. 65 + [45 + (–86)] = [65 + 45] + (–86) tenth step.

7. Write a pair of integers such that a. In every move the frog jumps 4 steps down and then jumps 3 steps up. Find the
number of jumps in which he willreach the water level.
a. the sum of the two integers is zero. b. the difference of the two integers is zero.
b. Afterreaching the water level, the frog jumps 4 steps up and 3 steps down in every
c. the difference of the two integers is 7. d. the difference of the two integers is a negative
move. In how many jumps willit return to the originalposition?
integer.
Multiplication of Integers
8. Write a pair of integers whose difference is 10.
9. Subtract 67 from the sum of 78 and –54. We have already learnt to add and subtract integers. Let us learn how to multiplyintegers.
10. From the sum of 45 and 89 subtract the sum of 32 and (–78). Multiplication of Two Positive Integers
A –8 3
11. Is subtraction of integers commutative? Give an example to support your answer.
–2 0 D Multiplicationis repeated addition.
12. In a magic square, each row, column and diagonal have the same sum. Find the
missing numbers denoted by A, B, C, D and E in the given magic square. –3 B C For example,
13. Observe the given number line and write the temperature of the cities marked on it in the table (i) 3 + 3 + 3 + 3 = 4 × 3 = 12 (ii)8 + 8 + 8 = 3 × 8 = 24
given below.
Srinagar Delhi Let us verify4 × 3 using a number line.
3 3 3 3
–30 –20 –10 0 10 20 30

–12–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12
Ladakh Gangtok Shimla Ooty From the above example, we can observe that
TemperatureCity

G H
Positive integer × Positive integer = Positive integer
Ooty
Multiplication of a Positive and a Negative Integer
Gangtok
Delhi Consider the followingexamples,
Shimla (i) (–3) + (–3) = 2 × (–3) = (–6)
Srinagar (ii)(–4) + (–4) + (–4) = 3 × (–4) = (–12)
Ladakh Let us study the verificationof examples (i) and (ii)using a number line.

a. Find the temperature difference between the hottest and the coldest cities. i.e. 2 × (–3) = (–6)

b. What is the temperature difference between Ooty and Gangtok? –3 –3

14. The minimumtemperature recorded in a city on Tuesday was –9°C. The next day the temperature
fellfurther by 4°C. What was the minimumtemperature on Wednesday? –12–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12
15. A submarine is positioned at a distance of 1675 m below the sea level. If it ascends 400 m, what Similarly,3 × (–4) = (–12)
willbe its new position?
–4 –4 –4
16. A car begins from a point and moves in the North direction for 26 km and then takes a U-turn and
moves back along the same road in the South direction for 7 km. What is the total distance travelled
by the car? If the distance in the North direction is represented by a positive integer, what willbe –12–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12
the sign for the distance travelled in the South direction?
From the above examples we can observe that
17. Sarita deposited ` 8000 in her bank account on Monday. On Tuesday she withdrew ` 1500. She
deposited ` 1200 on Wednesday. Find the balance in Sarita’s account on Wednesday. Positive integer × Negative integer = Negative integer

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