Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 1 Numbers Ex 1.7 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers Ex 1.7

Miscellaneous Practice Problems

Question 1.

If \(\frac{3}{4}\) of a box of apples weighs 3kg and 225 gm, how much does a full box of apples weigh?

Answer:

Let the total weight of a box of apple = x kg.

Weight of \(\frac{3}{4}\) of a box apples = 3 kg 225 gm.

= 3.225kg

\(\frac{3}{4}\) × x = 3225

x = \(\frac{3.225 \times 4}{3}\) kg

= 1.075 × 4kg = 4.3kg

= 4 kg 300 gm

Weight of the box of apples = 4 kg 300 gm.

Question 2.

Mangalam buys a water jug of capacity 3\(\frac{4}{5}\) litre. If she buys another jug which is 2\(\frac{2}{3}\) times as large as the smaller jug, how many litre can the larger one hold?

Answer:

Capacity of the small waterug = 3\(\frac{4}{5}\) litres.

Capacity of the big jug = \(2 \frac{2}{3}\) times the small one.

= \(2 \frac{2}{3} \times 3 \frac{4}{5}=\frac{8}{3} \times \frac{19}{5}=\frac{152}{15}\)

= \(\frac{2}{15}\) litres

Capacity of the large jug = \(\frac{2}{15}\) litres.

Question 3.

Ravi multiplied \(\frac { 25 }{ 8 }\) and \(\frac { 16 }{ 5 }\) to obtain \(\frac { 400 }{ 120 }\). He says that the simplest form of this product is \(\frac { 10 }{ 3 }\) and Chandru says the answer in the simplest form is \(3 \frac{1}{3}\). Who is correct? (or) Are they both correct? Explain.

Answer:

∴ The product is \(\frac{400}{120}\) and its simplest form improper fraction is \(\frac{10}{3}\)

And mixed fraction is \(3 \frac{1}{3}\)

∴ Both are correct

Question 4.

Find the length of a room whose area is \(\frac{153}{10}\) sq.m and whose breadth is \(2 \frac{11}{20}\)m.

Answer:

Length of the room × Breadth = Area of the room

Breadth of the room = \(2 \frac{11}{20}\) m

Area of the room = \(\frac{153}{10}\) sq.m

Length x \(2\frac{11}{20}\) = \(\frac{153}{10}\)

Length of the room = 6 m

Question 5.

There is a large square portrait of a leader that covers an area of 4489 cm^{2}. 1f each side has a 2 cm liner, what would be its area?

Answer:

Area of the square = 4489 cm^{2}

(side)2 = 4489 cm^{2}

(side)2 = 67 × 67

side = 67^{2}

Length of a side = 67

Length of a side with liner = 67 + 2 + 2 cm

= 71 cm

Area of the larger square = 71 × 71 cm^{2}

= 5041 cm^{2}

Area of the liner = Area of big square – Area of small square

= (5041 – 4489) cm^{2}

= 552 cm^{2}

Question 6.

A greeting card has an area 90 cm^{2}. Between what two whole numbers is the length of its side?

Answer:

Area of the greeting card = 90 cm^{2}

(side)^{2} = 90 cm^{2}

(side)^{2} = 2 × 5 × 3 × 3 = 2 × 5 × 3^{2}

Side = 3\(\sqrt{2 \times 5}\)

side = 3√10 cm

side = 3 × 3.2cm

side = 9.6 cm

∴ Side lies between the whole numbers 9 and 10.

Question 7.

225 square shaped mosaic tiles, each of area 1 square decimetre exactly cover a square shaped verandah. How long is each side of the square shaped verandah?

Answer:

Area of one tile = 1 sq.decimeter

Area of 225 tiles = 225 sq.decimeter

225 square tiles exactly covers the square shaped verandah.

∴ Area of 225 tiles = Area of the verandah

Area of the verandah = 225 sq.decimeter

side × side = 15 × 15 sq.decimeter

side = 15 decimeters

Length of each side of verandah = 15 decimeters.

Question 8.

If \(\sqrt[3]{1906624} \times \sqrt{x}\) = 31oo, find x.

Answer:

Question 9.

If 2^{m – 1} + 2^{m + 1} = 640, then find ‘m’.

Answer:

Given 2^{m – 1} + 2^{m + 1} = 640

2^{m – 1} + 2^{m + 1} = 128 + 512

2^{m – 1} + 2^{m + 1} – 2^{7} + 2^{9}

m – 1 = 7

m = 7 + 1

m = 8

[consecutive powers of 2]

Powers of 2:

2, 4, 8, 16, 32, 64, 128, 256, 512,….

Question 10.

Give the answer in scientific notation:

A human heart beats at an average of 80 beats per minute. How many times does it beat in

i) an hour?

ii) a day?

iii) a year?

iv) 100 years?

Answer:

Heart beat per minute = 80 beats

(i) an hour

One hour = 60 minutes

Heart beat in an hour = 60 × 80

= 4800

= 4.8 × 10^{3}

(ii) In a day

One day = 24 hours = 24 × 60 minutes

∴ Heart beat in one day = 24 × 60 × 80 = 24 × 4800 = 115200

= 1.152 × 10^{5}

(iii) a year

One year = 365 days = 365 × 24 hours = 365 × 24 × 60 minutes

∴ Heart beats in a year = 365 × 24 × 60 × 80

= 42048000

= 4.2048 × 10^{7}

(iv) 100 years

Heart beats in one year = 4.2048 × 10^{7}

heart beats in 100 years = 4.2048 × 10^{7} × 100 = 4.2048 × 10^{7} × 10^{2}

= 4.2048 × 10^{9}

Challenging Problems:

Question 11.

In a map, if 1 inch refers to 120 km, then find the distance between two cities B and C which are \(4\frac{1}{6}\) inches and \(3\frac{1}{3}\) inches from the city A which lies between the cities B and C.

Answer:

1 inch = 120 km

Distance between A and B = \(4\frac{1}{6}\)

Distance between A and C = \(3\frac{1}{3}\)

∴ Distance between B and C = \(4 \frac{1}{6}+3 \frac{1}{3}\) inches

1 inch = 120km

∴ \(\frac{45}{6}\) inches = \(\frac{45}{6}\) × 120 km = 900 km

Distance between B and C = 900 km

Question 12.

Give an example and verify each of the following statements.

(i) The collection of all non-zero rational numbers is closed under division.

Answer:

let a = \(\frac{5}{6}\) and b = \(\frac{-4}{3}\) be two non zero rational numbers.

∴ Collection of non-zero rational numbers are closed under division.

(ii) Subtraction is not commutative for rational numbers.

Answer:

let a = \(\frac{1}{2}\) and b = \(-\frac{5}{6}\) be two rational numbers.

a – b ≠ b – a

∴ Subtraction is not commutative for rational numbers.

(iii) Division is not associative for rational numbers.

Answer:

Let a = \(\frac{2}{5}\), b = \(\frac{6}{5}\), c = \(\frac{3}{5}\) be three rational numbers.

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

∴ Division is not associative for rational numbers.

(iv) Distributive property of multiplication over subtraction is true for rational numbers. That is, a (b – c) = ab – ac.

Answer:

Let a = \(\frac{2}{9}\), b = \(\frac{3}{6}\), c = \(\frac{1}{3}\) be three rational numbers.

To prove a × (b – c) = ab – bc

∴ From (1) and (2)

a × (b – c) = ab – bc

∴ Distributivity of multiplication over subtraction is true for rational numbers.

(v) The mean of two rational numbers is rational and lies between them.

Answer:

Let a = \(\frac{2}{11}\) and b = \(\frac{5}{6}\) be two rational numbers

∴ The mean lies between the given rational numbers \(\frac{2}{11}\) and \(\frac{5}{6}\)

Question 13.

If \(\frac { 1 }{ 4 }\) of a ragi adai weighs 120 grams, what will be the weight of \(\frac { 2 }{ 3 }\) of the same ragi adai ?

Answer:

Let the weight of 1 ragi adai = x grams

given \(\frac { 1 }{ 4 }\) of x = 120gm

\(\frac { 1 }{ 4 }\) × x = 120

x = 120 × 4

x = 480gm

∴ \(\frac { 2 }{ 3 }\) of the adai = \(\frac { 2 }{ 3 }\) × 480 gm = 2 × 160 gm = 320gm

\(\frac { 2 }{ 3 }\) of the weight of adai = 320gm

Question 14.

If p + 2q =18 and pq = 40, find \(\frac{2}{p}+\frac{1}{q}\)

Answer:

Given p + 2q = 18 ……… (1)

pq = 40 ……… (2)

Question 15.

Find x if \(5 \frac{x}{5} \times 3 \frac{3}{4}\) = 21.

Answer:

25 + x = 28

x = 28 – 25

x = 3

Question 16.

Answer:

Answer:

Question 17.

A group of 1536 cadets wanted to have a parade forming a square design. Is it possible? If it is not possible, how many more cadets would be required?

Answer:

Number of cadets to form square design

The numbers 2 and 3 are unpaired

∴ It is impossible to have the parade forming square design with 1536 cadets.

39 × 39 = 1521

Also 40 × 40 = 1600

∴ We have to add (1600 – 1536) = 64 to make 1536 a perfect square.

∴ 64 more cadets would be required to form the square design.

Question 18.

Evaluate: \(\sqrt{286225}\) and use it to compute \(\sqrt{2862.25}+\sqrt{28.6225}\)

Answer:

Question 19.

Simplify: (3.769 × 10^{5}) + (4.21 × 10^{5})

Answer:

(3.769 × 10^{5}) + (4.21 × 10^{5}) = 3,76,900 + 4,21,000

= 7,97,000

= 7.979 × 10^{5}

Question 20.

Order the following from the least to the greatest: 16^{25}, 8^{100}, 3^{500}, 4^{400}, 2^{600}

Answer:

16^{25} = (2^{4})^{25} = 2^{100}

8^{100} = (2^{3})^{100} = 2^{300}

4^{400} = (2^{2})^{400} = 2^{800}

2^{600} = 2^{600}

Comparing the powers we have.

2^{100} < 2^{300} < 2^{600} < 2^{800}

∴ The required order: 16^{25}, 8^{100}, 3^{500}, 4^{400}, 2^{600}