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Q III)  Solve the given problems

a) Find the sum using short cut method

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14

Answer: 1 + 14 = 15

2 + 13 = 15

3 + 12 = 15

4 + 11 = 15

5 + 10 = 15

6 + 9 = 15

7 + 8 = 15

You stop at 7 because then after wards you are repeating the number eg. 8 + 7, 9 + 6 etc

Now we have 15 repeating 7 times so we get

15 x 7 = 105

b) Draw the layout map of your classroom

c) Match each solid shape to its net

LET MJE EXPLAIN A LITTLE BIT OF CONVERTING SOLID SHAPE TO NET DRAWING. IN THE FIGURE SHOWN ABOVE ON THE LEFT HAND SIDE WE HAVE
CUBOID, CYLINDER AND PYRAMID IN SOLID SHAPE.  NOW WHEN WE CUT THESE SOLID SHAPES AND UNFOLD IT ON PIECE OF PAPER THEN THE
DIAGRAM WE GET IS SHOWN ON RIGHT HAND SIDE OF THE FIGURE. SO THAT IS WHAT WE HAVE DONE MATCHING SOLID SHAPE WITH NET DRAWING.

d) The cost of a movie ticket is Rs. 50.75. Find the cost of 5 such movie tickets

1 movie ticket ====== Rs. 50.75

5 tickets =========== ?

? x 1 = 5 x 50.75

? = 253.75 Rs. Therefore 5 ticket costs Rs. 253.75

e) Find the HCF of 70, 105 and 175

i)

2 | 70

5  | 35

7 | 7

| 1

so you have: 2 x 5 x 7

ii) 3 | 105

5  | 35

7   | 7

|   1

so we have 3 x 5 x 7

iii)    5 | 175

5   | 35

7   |  7

|   1

so we have 5 x 5 x 7

Hence Highest common factor is 5 x 7 = 35

The method shown above for finding HCF is easy for children to grasp.

While calculating HCF or LCM you should have list of prime numbers from 1 to 20, they are:

1,2,3,5,7,11,13, 17, and 19. These numbers can calculate HCF or LCM for numbers from 1 to 400.

In exam I do not think that teachers would ask to calculate HCF for numbers greater then 400.

For numbers from 1 to 100 you need to remember prime numbers 1,2,3, 5 and 7.