Q. 5. To find sum of three numbers and we can have two ways:
(a) We may first add and to get and then add to it to get the total sum or
(b) We may add and to get and then add to get the sum Thus,
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.
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) is a diameter of the circle; is its centre.) Express the diameter of the circle in terms of its radius
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 Find the formula for the total length of the edges of a cube.
Q. 2. The side of a regular hexagon (Fig 11.10) is denoted by Express the perimeter of the hexagon using (Hint: A regular hexagon has all its six sides equal in length.)
Q. 1. The side of an equilateral triangle is shown by . Express the perimeter of the equilateral triangle using
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.
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.)
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 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?
Q. 9. Mother has made laddus. She gives some laddus to guests and family members; still laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Q. 8. Leela is Radha's younger sister. Leela is years younger than Radha. Can you write Leela's age in terms of Radha's age? Take Radha's age to be 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 rows? How many dots are there if there are rows? If there are rows?
Q. 6. A bird flies kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use for flying time in minutes.)
Q. 5. The teacher distributes pencils per student. Can you tell how many pencils are needed, given the number of students? (Use for the number of students.)
Q. 4. If there are mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use for the number of boxes.)
Q. 3. Cadets are marching in a parade. There are 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.)
Q. 2. We already know the rule for the pattern of letters and . Some of the letters from Q.1 (given above) give us the same rule as that given by Which are these? Why does this happen?
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 .