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Which out of the following are expressions with numbers only? (a) y + 3 (b) (7 × 20) – 8z (c) 5 (21 – 7) + 7 × 2 (d) 5 (e) 3x (f) 5 – 5n (g) (7 × 20) – (5 × 10) – 45 + p

Solution (a) y + 3: Contains the letter y. Hence it not an expression with only numbers. (b) (7 ×... View Article

Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.

Solution Listed below are some of the expressions formed by 5, 7 and 8 (5 + 7)- 8 (7 +... View Article

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 41and 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)

Solution The given statements can be done for any three numbers. This property is called the associativity of the addition of numbers.... View Article

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 11.2) AB is a diameter of a circle; C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).

Solutions: From the givne figure we get to know that Diameter = AB = AC + CB = r +... View Article

A cube is three dimensional figure as shown in Figure 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.

Solution: Length of an edge of the cube = l We know that Number of edges in a cube =... View Article

The side of the regular hexagon (Figure is denoted by l. Express the perimeter of the hexagon using l.

Solution: Given that Side of a regular hexagon = l We know that perimeter of a hexagon is... View Article

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

Solution Given that Side of equilateral triangle = l We know that perimeter of a traingle is given by= sum... View Article

(a) Look at the following matchstick pattern of squares (Fig ure. 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 (b) Figure 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.

Solution: (a) From the figure we observe that The matchstick pattern, the number of matchsticks are 4, 7, 10 and... View Article

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?

Given that Let the number of oranges in a small box = x Number of oranges in two small boxes... View Article

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?

Given that Let number of laddus mother gave = l Th number of remaining laddus = 5 Total number of... View Article

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.

Given that Leela is Radha’s younger sister. Leela is 4 years younger to Radha Let us assume Radha’s age to... View Article

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?

Solution Number of dots in a row = 9 Let the number of rows = r Total number of dots... View Article

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

Solution Let flying time in minutes be =t Distance covered in one minute = 1 km Distance covered in t... View Article

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

Solution Let the number of students=s Given that Pencils given to each student = 5 Total number of pencils =... View Article

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.)

Solution Let the number of boxes= b Number of mangoes in a box = 50 Total number of mangoes =... View Article

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)

Solution Let n be the number of rows Given that The number of cadets in a row = 5 Total... View Article

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

(b) A pattern of letter Z as (c) A pattern of letter U as (d) A pattern of letter Vas... View Article

Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?

Given Total weight of vegetables Aakash bought = 10.000 kg Weight of onions = 3 kg 500 g Weight of... View Article

Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?

Given Total distance travelled by Namita = 20 km 50 m Distance travelled by bus = 10 km 200 m... View Article

Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?

Given Length of cloth = 20 m 5 cm Length of cloth to make a curtain = 4 m 50... View Article

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