Question Set B

cbse 6th Standard Mathematics Decimals Important Questions And Answers Study Material - QB365

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Questions:

Generic 2

10 x 2 = 20

Fill in the boxes.
(i) 7: \(\Box\) :: 21: 96
(ii) 4g : 1.5 kg :: 16g : \(\Box\) kg
(iii) \(\frac { 13 }{ 96 } =\frac { \Box }{ 672 } \)

Construct a line segment of length \(\bar{PQ}\) = 10 cm. From it cut off \(\bar{PR}\) = 5.2cm. Measure \(\bar{RQ}\).

Given two equivalent ratios of 3: 8.

Write the following ratios in the simplest form.
2 cm to 4 m

Draw a circle with radius 3 cm and a circle with same centre and diameter 6 cm. What will be relation between the two?

If area of a rectangle is 600 m² and length is 30 m, then find its width.

Find the areas of the following figures by counting square.

If the perimeter of a rectangle is 120 cm and the width is 25 cm, then find its length

Write the following numbers in the place value table.
(a) 6.5 (b) 30.5

10.

Write the following as decimals.

	Hundreds (100)	Tens (10)	Ones (1)	Tenths\(\left( \frac { 1 }{ 10 } \right) \)
(i)	4	2	8	1
(ii)	9	2	3	4

Generic 5

7 x 5 = 35

11.

Draw an angle of 70°. Make a copy of it using only a straight edge and compasses.

12.

The ratio of Michelle's story books to Aliena's story books is 7 : 5. When Aleena gives 48 story books to Michelle, she would have 1/3 of the number of story books Michelle has. How many story books must Micheelle return to Aleena so that Aleena would have five times as man star books as Michelle?

13.

Seema has Rs 2000, she bought readymade garments for Rs 987.50, medicines for Rs 210.25, groceries for Rs 530.25. She donated Rs 200 for charity.
(a) How much money is left with her?
(b) Mention the value you depict form this.

14.

In figure each square is of unit length
(a) What is the perimeter of the rectangle ABCD?
(b) What is the area of the rectangle ABCD?

(c) Divide this rectangle into ten parts of equal area by shading squares. (Two parts of equal area are shown here)
(d) Find the perimeter of each part which you have divided. Are they all equal?

15.

The lawn in front of Molly's house is 12 m\(\times\) 8m, whereas the lawn in front of Dolly's house is 15 m \(\times\) 5 m. A bamboo fencing is built around both the lawns. How much fencing is required for both?

16.

See the figure and find the ratio of

(a) number of triangles to the number of circles inside n the rectangle.
(b) number of squares to all the figures inside the rectangle.
(c) number of circles to all the figures inside the rectangle.

17.

Can you now write the following as decimals?

Hundreds (100)	Tens (10)	Ones (1)	Tenths \(\left( \frac { 1 }{ 10 } \right) \)
5	3	8	1
2	7	3	4
3	5	4	6

Generic 3

9 x 3 = 27

18.

Refer to the figure given below and answer the following:

(a) Name any diameter of the circle.
(b) Name any radius of the circle.
(c) Name the chord of the circle.
(d) What is the centre of the given circle?

19.

Draw PO of length 7 cm and find its axis of symmetry.

20.

Anil got Rs 1000 as pocket money. He spent Rs 439.74 in playing games and Rs 246.40 in food. How mush did he save?

21.

Draw a line AB to 6.5 cm length. At the end points A B draw two perpendiculars. Are these lines perpendicular to each other?

22.

The weight of 72 books is 9 kg.
(a) What is the weight of 80 such books?
(b) How many such books could weigh 6 kg?

23.

Express as km using decimals
70 km 5 m

24.

Cost of 7 dozen bananas is Rs. 98. How many bananas can be purchased for Rs.217?

25.

Split the following shapes into rectangles and find their areas (The measures are given in centimetres)

26.

The lid of a rectangular box of side 40 cm by 10 cm is sealed all round with tape. What is the length of tape required?

Multiple Choice Question

22 x 1 = 22

27.

The fare for 5 tickets from Kosi Kalan to Mathura is Rs. 150. The fare for 3 tickets is

(a)

Rs. 90

(b)

Rs. 60

(c)

Rs. 75

(d)

Rs. 45

28.

Which of the folIo wing is false?

(a)

25g : 30g::40 kg:48 kg

(b)

81: 91::24h:27 h

(c)

32 m : 40 m::6 minutes : 12 minutes

(d)

25 km : 60 km :: Rs. 10 : Rs. 24

29.

100 students appeared in annual examination. 60 students passed. The ratio of the number of students who failed to the total number of students is

(a)

5:2

(b)

2:5

(c)

2:3

(d)

3:2

30.

There are 20 teachers in a school of 500 students. The ratio of the number of teachers to the number of students is

(a)

1:20

(b)

1:50

(c)

1:25

(d)

25:1

31.

In a family, there are 8 males and 4 females. The ratio of the number of females to the number of males is

(a)

1:2

(b)

1:4

(c)

1:8

(d)

2:1

32.

The cost of a pen is Rs.10. The cost of a pencil is Rs. 2. How many times of the cost of a pencil is the cost of a pen?

(a)

5 times

(b)

2 times

(c)

10 times

(d)

None of these.

33.

5g=

(a)

0.005 kg

(b)

0.05 kg

(c)

0.5 kg

(d)

none of these

34.

The expression for 'x is divided by 2 and the result is added to 1 ' is

(a)

1+\(\frac { x }{ 2 } \)

(b)

1-\(\frac { x }{ 2 } \)

(c)

2+x

(d)

2-x

35.

The rule, which gives the number of matchsticks required to make the matchstick pattern A, is

(a)

3 n

(b)

(c)

5 n

(d)

6 n.

36.

Which of the following letters has horizontal line of symmetry?

(a)

(b)

(c)

(d)

37.

The perimeter of a rectangular piece of cardboard is 6 m. Its breadth is 1m. Find its length.

(a)

1 m

(b)

2 m

(c)

3 m

(d)

6 m

38.

The area of a square of side 1 cm is

(a)

1 cm²

(b)

4 cm²

(c)

9 cm²

(d)

16 cm²

39.

The area of a rectangle of length 2 cm and breadth 1 cm is

(a)

1 cm²

(b)

2 cm²

(c)

4 cm²

(d)

8 cm²

40.

How many lines of symmetry does the figure have?

(a)

(b)

(c)

(d)

41.

The perimeter of a regular hexagon of side 1m is

(a)

3 m

(b)

2 m

(c)

4 m

(d)

6 m

42.

Perimeter of a rectangle =

(a)

Length x Breadth

(b)

Length + Breadth

(c)

2 x (Length + Breadth)

(d)

2 x (Length x Breadth)

43.

If 7 : 30 :: x :15, then the value of x is

(a)

\(\frac{7}{2}\)

(b)

\(\frac{2}{7}\)

(c)

(d)

44.

The ratio of 6 books to 30 books is

(a)

5 : 1

(b)

2 : 3

(c)

1 : 5

(d)

2: 5

45.

In the given figure, point B lies

(a)

interior

(b)

exterior

(c)

both (a) and (b)

(d)

None of these

46.

Two lines are perpendicular, if they intersect each other at

(a)

acute angle

(b)

right angle

(c)

obtuse angle

(d)

None of these

47.

The perimeter of a triangle whose sides are 1.2cm, 3.4 cm and 1.7 cm, is

(a)

6.3 cm

(b)

6.2 m

(c)

6.5 cm

(d)

6.4 cm

48.

Savitri has a sum of Rs x. She spent Rs 1000 on grocery, Rs 500 on clothes and Rs 400 on education and received Rs 200 as a gift. How much money (in Rs ) is left with her?

(a)

x -1700

(b)

x -1900

(c)

x + 200

(d)

x-2100

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Answers Key:

Generic 2

10 x 2 = 20

(i) 32
(ii) 6 kg
(iii) 91

\(\bar{RQ}\) = 4.8 cm.

\(3:8=\frac{3}{8}=\frac{3\times2}{8\times2}=\frac{6}{16},3:8=\frac{3}{8}=\frac{3\times3}{8\times3}=\frac{9}{24}\)
Hence, two equivalent ratios of 3: 8 are 6: 16 and 9: 24.

2 cm to 4 cm \(=\frac{2}{400}=1:200[\because\ 1\ m=100 cm]\)

Coincide

20 m

Given, figure is covered by 5 full squares.
∴. Area = 5 \(\times\) 1 sq unit = 5 sq units

35 cm

Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have,

Number	Tens(10)	Ones(1)	Tenths\(\left( \frac { 1 }{ 10 } \right) \)
6.5	0	6	5
30.5	3	0	5

10.

Given number can be written as follows:
(i) 4 hundreds + 2 tens + 8 ones + 1 tenth = 4 \(\times\) 100 + 2 \(\times\)10 + 8 \(\times\) 1 \(\times\) \(\frac { 1 }{ 10 } \)
= 400 + 20 + 8 + 0.1 = 428.1
(ii) 9 hundreds +2 tens +3 ones +4 tenths = 9 \(\times\) 100 + 2 \(\times\) 10 + 3 \(\times\) 1+ 4 \(\times\) \(\frac { 1 }{ 10 } \)
= 900 + 20 + 3 + 0.4 = 923.4

Generic 5

7 x 5 = 35

11.

To draw an angle of measure 70°, we use the following steps of construction:
Step I Draw \(\bar{AB}\) of any length. Place the centre of the protractor at A and the zero edge along \(\bar{AB}\) .
Step II Start with zero near B. Mark point C at 70°.
Step III Join AC. Then, \(\angle\)BAC is an angle of measure 70°.

Now, to draw a copy of 70°, by using straight edge and compasses, we use the following steps of construction:
Step IV Draw a line I and choose a point P on it.

Step V Place the pointer at A and draw an arc to cut the rays of \(\angle\)A at M and N.

Step VI Use the same compasses setting to draw an arc with P as centre, cutting I at Q.

Step VII Set your compasses to the length of MN.

Step VIII Without disturbing the compasses. Place the compasses pointer at Q and draw an arc at R to cut the arc drawn in Step VI.

Step IX Join PR, this give us \(\angle\) RPQ. It has the same measure as LBAC. Hence, \(\angle\)RPQ is required copy of an angle of measure 70°.

12.

168

13.

(a) Total money that Seem a has = Rs 2000.
Cost of readymade garments = Rs 987.50
Cost of medicines = Rs 210.25
Cost of groceries = + Rs 530.25
__________
Total cost = Rs 1728.00
___________
Money donate for charity = Rs 200
=Rs 1728.00
Total money spent = + Rs 200
____________
Rs 1928
____________
Money she had = Rs 2000
Spent money = - Rs 1928
_________
Balance = Rs 072
_________
So, Rs 72 are left with her.
(b) Humanity, helpfulness.

14.

Given, each side of square is of unit length. Figure contains length of 10 squares and width of 6 squares.
Now, length of rectangle, AD = (BC)
= Sum of length of a side of 10 squares
=1+1+1+1+1+1+1+1+1+1
=10\(\times\)1 =10 units
and breadth of rectangle, AB = (DC)
= Width of 6 squares = 6 \(\times\)1 = 6 units
(a) The perimeter of the rectangle ABCD
= AB+ BC+ CD+DA
= 6+10+ 6+10
= 32 units
(b) The area of the rectangle ABCD = Length \(\times\)Breadth
= AD\(\times\)AB=10\(\times\)6
= 60 units
(c) The total area of rectangle = 60 units

Now, we have to divide the rectangle into 10 equal parts i..e \(\frac{60}{10}=6\) square uni.t.s I.e. we have to take a group of 6-6 square blocks, which is shown in the figure
(d) Now, we find the perimeter of part l.

We know that perimeter of a figure is the total length of its boundary.
∴ Perimeter of part I
= 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1= 12 units
Similarly, we can find the perimeters of remaining 9 parts, all the parts have same perimeter i.e. 12 units.
Yes, all the parts have same perimeter.

15.

Given, size of lawn in front of Molly's house
=12m\(\times\)8m
Perimeter = 2 (12 + 8) m= 40 m ... (i)
Now, size of lawn in front of Dolly's house
=15m\(\times\)5m
Perimeter = 2 (15+ 5) m = 40 m ... (ii)
From Eqs. (i) and (ii), we get = 40+ 40= 80 m
Hence, total length of bamboo fencing is 80 m.

16.

In the given figure,
Number of triangles = 3; Number of squares = 2
Number of circles = 2
\(\therefore\) Total number of figures = 3 + 2 + 2 = 7
(a) Required ratio of number of triangles to the number of circles \(=\frac{Number\ of\ triangles}{Number\ of\ circles}=\frac{3}{2}=3:2\)
(b) Required ratio of number of squares to all the figure \(=\frac{Number\ of\ squares}{Total\ number\ of\ figures}=\frac{2}{7}=2:7\)
(c) Required ratio of number of circles to all the figure \(=\frac{Number\ of\ circles}{Total\ number\ of\ figures}=\frac{2}{7}=2:7\)

17.

Given numbers can be written in decimals as follows:
(i) 5 hundreds + 3 tens + 8 ones + 1 tenth
= 5 \(\times\) 100 + 3 \(\times\) 10 + 8 \(\times\) 1+ 1 \(\times\) \(\frac { 1 }{ 10 } \)
= 500 + 30 + 8 + \(\frac { 1 }{ 10 } \) = 538 + 0.1 = 538.1
(ii) 2 hundreds + 7 tens + 3 ones + 4 tenths
= 2 \(\times\) 100 + 7 \(\times\) 10 + 3 \(\times\) 1+ 4 \(\times\) \(\frac { 1 }{ 10 } \)
= 200 + 70 + 3 + \(\frac { 4 }{ 10 } \) = 273 + 0.4 = 273.4
(iii) 3 hundreds + 5 tens + 4 ones + 6 tenths
= 3 \(\times\) 100 + 5 \(\times\) 10 + 4 \(\times\) 1+ 6 \(\times\) \(\frac { 1 }{ 10 } \)
= 300 + 50 + 4 + \(\frac { 6 }{ 10 } \) = 354 + 0.6 = 354.6

Generic 3

9 x 3 = 27

18.

(a) Diameter of circle is \(\bar{AB}\) .
(b) Radius of the circle is \(\bar{OA}\), \(\bar{OB}\) and \(\bar{OC}\) .
(c) The chord of the circle are \(\bar{EF}\) and \(\bar{AB}\) .
(d) Centre of circle is 'O'.

19.

We know that, perpendicular bisector of a line segment is its axis of symmetry.
Step I Draw a line segment \(\bar{PQ}\) = 7 cm.
Step II With P and 0 as centres and radius more than half of \(\bar{PQ}\), draw two arcs which intersect each other at A and B.

Step III Join A and B.
Thus, AB is the axis of symmetry of \(\bar{PQ}\).

20.

Rs 313.86

21.

No, they are parallel to each other.

22.

(a) 10 kg
(b) 48

23.

We know that 1 m \(={1\over 1000}\) km
\(\therefore\) 70 km 5 m = 70 km + 5 m
= 70 km \(+5\times{1 \over 1000}\) km
= 70 km \(+{5\over 1000}\) km
= (70+0.005) km
= 70.005 km.

24.

15.5 dozens

25.

Let the given figure is divided into two rectangles A, B and their lengths and breadths are written on the figure. For rectangle A,
Length = 12 cm
and breadth = 2 cm

∴ Area of the rectangle A = Length \(\times\) Breadth
= 12 cm \(\times\) 2 cm = 24 sq cm
For rectangle B,
Length = 8 cm and breadth = 2cm
:. Area of the rectangle B = Length \(\times\) Breadth
= 8 cm \(\times\) 2 cm16 sq cm
Now, total area of given figure
= Area of rectangle A + Area of rectangle B
= (24+16) sq cm = 40 sq cm
Hence, required area is 40 sq cm.

26.

Given, length of lid of a rectangular box = 40 cm
and breadth of the lid of a rectangular box = 10 cm
Length of the tape required = Perimeter of the lid of the rectangular box
= 2\(\times\) (Length + Breadth)
= 2 \(\times\)(40 cm + 10 cm) = 2 x 50 cm = 100 cmor 1 m
[∵ 1 cm = \(\frac{1}{100}\)m or 100 cm = 1 m]
Hence, the length of tape required is 100 cm or 1 m.

Multiple Choice Question

22 x 1 = 22

27.

\(\frac { 150 }{ 5 } \times 3\) = 90

28.

32 m : 40 m = \(\frac { 32 }{ 40 } =\frac { 32\div 8 }{ 40\div 8 } =\frac { 4 }{ 5 } \)=4:5
6 minutes : 12 minutes = \(\frac { 6 }{ 12 } =\frac { 6\div 6 }{ 12\div 6 } =\frac { 1 }{ 2 } \)
4 : 5 \(\neq\) 1 : 2

29.

100-60=40
40:100 = \(\frac { 40 }{ 100 } =\frac { 40\div 20 }{ 100\div 20 } =\frac { 2 }{ 5 } \)= 2:5

30.

20:500=\(\frac { 20 }{ 500 } =\frac { 1 }{ 25 } \)=1:25

31.

\(\frac { 4 }{ 8 } =\frac { 1 }{ 2 } \)= 1:2

32.

10=5x2

33.

(a)
0.005 kg

34.

(a)
1+\(\frac { x }{ 2 } \)

35.

36.

37.

Length = \(\frac{6}{2}\) - 1 = 2 m

38.

Area = 1 x 1 = 1 cm²

39.

Area = 2 x 1 = 2 cm²

40.

41.

Perimeter = 6 x 1 = 6 m

42.

43.

(a)
\(\frac{7}{2}\)

44.

45.

(a)
interior

46.

(b)
right angle

47.

(a)
6.3 cm

48.

(a)
x -1700

cbse 6th Standard Mathematics Decimals Important Questions And Answers Study Material - QB365 Set B

QB365 Student Learing Managemnet System

Std: 6th Standard CBSE - Mathematics

chapter: Decimals - Important Questions And Answers

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Questions:

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