Numbers	Tally Marks	Number of times
1	I I	7
2	I	6
3		5
4	I I I I	4
5	I	11
6	I I	7

(a) The number that appeared the minimum number of times is 4.
(b) The number that appeared the maximum number of times is 5.
(c) The numbers that appeared an equal number of times are 1 and 6.

Increasing order of these integers is - 29 < - 28 < - 27 < - 26 < - 25 < - 24, because we are moving to the right from -30 to -23.

Prachi

For divisible by 3, the sum of the digits should be divisible by 3.
Sum of digits of 53 * 46 = 5 + 3 + 4 + 6=18
\(\therefore\)replace * by 0

(i) Perimeter = AB + AC + BC + BD + DE + CE
= 3+ 3+ 3+ 3+ 3+ 3= 18 cm
(ii) Area of square BCED = Side² = 3² = 9 sq cm

\(\frac { 3 }{ 4 } \) revolution

(a) May
(b) 1800 g
(c) May
(d) 100 g.

We know that, 1 right angle = 90°
\({ 1 }°=\frac { 1 }{ 90 } \) right angle.
\({ 135 }°=\frac { { 135 }° }{ { 90 }° } =\left( \frac { 3 }{ 2 } \right) \) right angle.

The right angles in each part of the given figure are as follow:
\(\angle RTS = 90°\)

Let  represents 20 tins of paint.

(a) Rs 12000
(b) 9 tins
(c) 40 tins.

Here, total number of equal parts in all figures = 9
Shaded portion of figure (i) represents fraction = \(\frac { 8 }{ 9 } \)
Shaded portion of figure (ii) represents fraction = \(\frac { 6 }{ 9 } \)
Shaded portion of figure (iii) represents fraction = \(\frac { 4 }{ 9 } \)
Shaded portion of figure (iii) represents fraction = \(\frac { 3 }{ 9 } \) 
Shaded portion of figure (iii) represents fraction = \(\frac { 6 }{ 9 } \)
∴ Denominators of all fractions are same. So, we arrange them in ascending and descending order according to their numerators.
∴ Ascending order of fractions =\(\frac { 3 }{ 9 } <\frac { 4 }{ 9 } <\frac { 6 }{ 9 } <\frac { 8 }{ 9 } \)  and descending order of fractions =\(\frac { 8 }{ 9 } >\frac { 6 }{ 9 } >\frac { 4 }{ 9 } >\frac { 3 }{ 9 } \)

From the given figure, we have
AB= BC = CD = DA= 5cm
i.e. eaeh side of the given figure is 5 cm.
Now, the sum of the lengths of the four sides
= AB + BC + CD + DA = 5 cm + 5 cm + 5 cm + 5 cm
= (5 + 5 + 5 + 5)cm = 20 cm
∴ Perimeter of the given figure
= Sum of the lengths of four sides
=20cm
Hence, the perimeter of the given figure is 20cm

Yes, it is a polygon, because it is a simple closed curve. Figure made up of line segments only. It is a quadrilateral.

143000 (nearest thousand)

(a) The number of people having surname 'Roy' are 400. Because in the given pictograph, the picture symbol represents 100 people.
(b) Surname 'Patel' appears maximum number of times. Because in the given pictograph, the picture symbol represents 100 people. According to this, surname Patel appears 500 times.
(c) The surname 'Saikia' appears the least number of times. Because in the given pictograph, the picture symbol represents 100 people. According to this, surname 'Saikia' appears 200 times.
(d) The surname 'Rao' and 'Roy' appears an equal number of times.

1,2,3,4,5

25000

The measure of angle (by using the protractor) and its classification is shown as below

We can make many situations of this kind, five situations of them are as follows:
Situation 1. Marry is a maid (servant). She charges Rs. 8 per day to clean a house but gives back Rs. 3 to the house owner for saving. What amount does she carry in her hand from 7 houses?
Situation 2. Ankit's pocket money is Rs. 8 per day. He spents Rs. 3 daily. Find his total saving in 7 days.
Situation 3. What will be the seven times the difference of eight and three?
Situation 4. A clerk works 8 h daily in an office, but he remains absent for 3 h daily. In a week, for how many hours did he work?
Situation 5. Seven children with Rs. 8 each went to market. Each of them bought pencils costing Rs. 3. What is total money left with them?

On pushing inward at anyone vertex of the triangle, we find thai the triangle is not distorted. Whereas doing so with the quadrilateral, we find that it is distorted. Triangle is rigid. Thus, we use triangular shapes in making structures like electric tower as triangular shapes.

10> 9 > 8 > 4> 1 > -2>-3

51975

We know that, on the number line, all numbers to the right of a are positive integers and all numbers to the left of a are negative integers.
Thus, representation of numbers on the number line is as follows:

(a) 8 steps to the left of zero is represented by - 8.
(b) 7 steps to the right of zero is represented by + 7.
(c) 11 steps to the right of zero is represented by + 11.
(d) 6 steps to the left of zero is represented by - 6.

(a)
(b) not possible.

Yes, if the product of two whole numbers is zero, then one or both of them will be zero. Since, we know that the product of any whole number with zero is always zero i.e. a x 0 = 0, where a is any whole number and 0 x 0 = 0. Some examples are as follows:

We know that, a line is a line segment which can extend indefinitely in both directions. Name oflines in all possible ways are as follow:
(i) By taking A, all possible ways are \(\overleftrightarrow { AB } ,\overleftrightarrow { AC } and\overleftrightarrow { AD } \).
(ii) By taking B, all possible ways are \(\overleftrightarrow { BC } ,\overleftrightarrow { BD } and\overleftrightarrow {BA } \).
(iii) By taking C, all possible ways are \(\overleftrightarrow { CD } ,\overleftrightarrow { CA } and\overleftrightarrow {CB } \).
(iv) By taking D, all possible ways are \(\overleftrightarrow { DA } ,\overleftrightarrow { DB } and\overleftrightarrow {DC } \).

(a) We have, 5000, 7500, 85400, 7861
Descending order of given numbers is as follows:
85400> 7861 > 7500 > 5000
(b) We have, 1971,45321,88715,92547
Descending order of given numbers is as follows:
92547> 88715 > 45321 > 1971

We have, 15623, 15073, 15189, 15800
Here, the two leftmost digits 15 i.e. digits at thousand and ten thousands place are same in each numbers. So, we compare the hundreds place digit

∴ The greatest number is 15800 and the smallest number is 15073.