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Q. 5.     To find sum of three numbers 14,  27  and  13, we can have two ways:

             (a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total  sum 54 or

             (b) We may add 27 and 13 to get 40 and then add 14 to get the sum  54. Thus,(14+27)+13=14+(27+13)

                    This can be done for any three numbers. This property is known as the associativity of addition of numbers. Express this property which we have already studied in the chapter on Whole Numbers, in a general way, by using variables a, b and c.

According to the given condition,                              

Q. 4.     The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure (Fig 11.12)AB  is a diameter of the circle; C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).

                

Length of diameter is double the length of the radius. Thus,d = 2r

Q. 3.     A cube is a three-dimensional figure as shown in Fig 11.11. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.  

            

Length of one edge of cube = l Number of edges in a cube  = 12 So,  total length = 

Q. 2.     The side of a regular hexagon (Fig 11.10) is denoted by l. Express the perimeter of the hexagon using l. (Hint: A regular hexagon has all its six sides  equal in length.)

                

The side of a hexagon is l. Therefore, the perimeter of the hexagon 

Q. 1.     The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.

The side of an equilateral triangle is . Therefore, the perimeter of the equilateral triangle 

Q. 11.    (b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

                    

                    

(a) 3 matchsticks (b) 5 matchsticks (c) 7 matchsticks (d) 9 matchsticks If we remove 1 matchstick from each then it forms a table of 2 i.e.,  2,4,6,8............ So, required equation  = 2x+1 , x= number of triangles  

Q. 11.     (a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks

                       

                     in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

(a) 4 matchsticks (b) 7 matchsticks (c) 10 matchsticks (d) 13 matchsticks If we remove 1 matchstick from each then it forms a table of 3 i.e.,3,6,9,12,..... So, required equation  = 3x+1 , x= number of squares          

Q. 10.     Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x. what is the number of oranges in the larger box?

Number of oranges in one box = x Number of box = 2 So, the total number of oranges = 2x Remaining number of oranges = 10 Thus, the number of oranges = 2x+10

Q. 9.     Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?

Number of laddus given = l Number of laddus remaining = 5 Thus,tota number of laddus  = (l+5)

Q. 8.     Leela is Radha's younger sister. Leela is 4 years younger than Radha. Can you write Leela's age in terms of Radha's age? Take Radha's age to be x  years

Radha's age = x years Thus, age of Leela = (x-4) years

Q. 7.     Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Number of rows = r Number of dots in each row  = 9 dots Thus, the total number of dots = 9r When the number of rows is 8, then the total number of dots are  dots. When the number of rows is 10, then the total number of dots are  dots.

Q. 6.     A bird flies 1  kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes.)

Time taken by bird = t minutes Speed of bird  = 1 km per minute Thus, distance covered by bird                                                 

Q. 5.     The teacher distributes 5  pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)

pencils per student = 5  number of students = s Thus, the total pencils needed = 5s

Q. 4.     If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)

mangoes in a box = 50 Number of boxes = b Thus, the total number of mangoes = 50b

Q. 3.     Cadets are marching in a parade. There are 5  cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows.)

cadets in a row = 5 number of rows = n Thus, the total  number of cadets = 5n  

Q. 2.     We already know the rule for the pattern of letters L,C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?

Letter "T" and "v" has pattern 2n because 2 matchsticks are used in these two letters.

Q. 1.     Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.

             (a) A pattern of letter T as .

             (b) A pattern of letter Z as .

             (c) A pattern of letter U as  .

             (d) A pattern of letter V as .

             (e) A pattern of letter E as .

             (f) A pattern of letter S as .

             (g) A pattern of letter A as .

             (a) A pattern of letter T as ( because 2 matchsticks are used )              (b) A pattern of letter Z as  ( because 3 matchsticks are used )              (c) A pattern of letter U as  ( because 3 matchsticks are used )              (d) A pattern of letter V as ( because 2 matchsticks are used )              (e) A pattern of letter E as ( because 5 matchsticks are used )        ...
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