Kerala Syllabus Class 7 Mathematics - Unit 5 Decimal Methods - Questions and Answers | Teaching Manual 

Questions and Answers for Class 7 Mathematics - Unit 5 Decimal Methods - Study Notes | Text Books Solution STD 7 - Maths: Unit 5 Decimal Methods - Questions and Answers | ദശാംശരീതികൾ - ചോദ്യോത്തരങ്ങൾ 

ഏഴാം ക്ലാസ്സ്‌  Mathematics - Unit 5 Decimal Methods എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്.

STD 7 - Maths: Unit 5 Decimal Methods - Questions and Answers

♦ Textbook Activities - (Textbook Page 71)
(1) Write the following numbers as fractions.
(i) 45.6 
(ii) 45.06 
(iii) 45.67 
(iv) 4.506 
(v) 456.07
Answer:
(i) 45.6 = ⁴⁵⁶⁄₁₀ 
(ii) 45.06 = ⁴⁵⁰⁶⁄₁₀₀
(iii) 45.67 = ⁴⁵⁶⁷⁄₁₀₀
(iv) 4.506 = ⁴⁵⁰⁶⁄₁₀₀₀
(v) 456.07 = ⁴⁵⁶⁰⁷⁄₁₀₀

♦ Textbook Activities - (Textbook Page 73)
(1) The figure below shows a regular pentagon. Find the perimeter of the pentagon.
Answer:
Perimeter = 2.33 × 5
  = ²³⁵⁄₁₀₀ × 5 = ¹¹⁷⁵⁄₁₀₀ = 11.75 m

(2) A kid needs 1.45 metres of cloth for a shirt. How many metres of cloth is needed for 4 shirts?
Answer:
1.45 × 4 = ¹⁴⁵⁄₁₀₀ × 4 = ⁵⁸⁰⁄₁₀₀ = 5.80 m

(3) A bag holds 4.75 kilograms of rice. How much rice can 8 such bags hold?
Answer:
4.75 × 8 = ⁴⁷⁵⁄₁₀₀ × 8 = ³⁸⁰⁰⁄₁₀₀ = 38.00 kg = 38 kg

(4) A vessel full of oil was used to fill in 6 bottles. Each bottle holds 0.75 litres. How much oil was there in the vessel?
Answer:
0.75 × 6 = ⁷⁵⁄₁₀₀ × 6 = ⁴⁵⁰⁄₁₀₀ = 4.5 litre

♦ Textbook Activities - (Textbook Page 74)
(1) Find the area in square metres of a rectangle of length 6.25 metres and width 4.2 metres. 
Answer:
Area = length × width
        = 6.25 × 4.2 = ⁶²⁵⁄₁₀₀ × ⁴²⁄₁₀ = ²⁶²⁵⁰⁄₁₀₀₀ = 26.250 sq.m

(2) The weight of 1 millilitre of coconut oil is 0.91 gram. What is the weight of 10.5 millilitres of coconut oil? 
Answer:
0.91 × 10.5 = ⁹¹⁄₁₀₀ × ¹⁰⁵⁄₁₀ = ⁹⁵⁵⁵⁄₁₀₀₀ = 9.555
Weight = 9.555 gram

(3) The price of 1 litre of petrol is 110.12 rupees. What is the price of 2.5 litres of petrol?
Answer:
110.12 × 2.5 = ¹¹⁰¹²⁄₁₀₀ × ²⁵⁄₁₀ = ²⁷⁵³⁰⁰⁄₁₀₀₀ = 275.300
Price = 275.30 rupees

♦ Textbook Activities - (Textbook Page 76)
(1) Given that 1234 × 56 = 69104 
(i) Find the answers to the following problems without actual multiplication.
(i) 1.234 × 56
(ii) 12.34 × 5.6
(iii) 123.4 × 0.56
(iv) 1234 × 0.056
Answer:
(i) 69.104
(ii) 69.104
(iii) 69.104
(iv) 69.104
(If we examine the numbers to be multiplied, there are 3 digits in their decimal places. Therefore, the products must also have 3 digits in the decimal place.
i.e, put the 'decimal point' after 3 digits from the right to left)

(ii) Like this, how many products can you find which gives 6.9104?
Answer:
Here are 5 products that gives 6.9104
1234 × .0056 = 6.9104
123.4 × .056 = 6.9104
12.34 × .56 = 6.9104
1.234 × 5.6 = 6.9104
0.1234 × 56 = 6.9104

(2) In the following products, how many of them gives the same product as 1.234 × 5.67?
 (i) 12.34 × 0.567
 (ii)  1.234 × 567
 (iii) 0.1234 × 5.67
 (iv) 1.234 × 56.7
 (v) 123.4 × 0.0567
Answer: In the product 1.234 × 5.67, the digits in the decimal part is 3 + 2 = 5. So the products (i) and (v) give the same product as 1.234 × 5.67.

(3) Find the greatest and least products from the following :
(i) 0.11 × 0.11
(ii) 1.1 × 1.1
(iii) 1.01 × 1.01
(iv) 0.101 × 1.1
(v) 10.1 × 0.101
Answer:
(i) 0.0121
(ii) 1.21
(iii) 1.0201
(iv) 0.1111
(v) 1.0201
The greatest is 1.21 (1.1 x 1.1)
The least is 0.0121 (0.11 x 0.11)
Explanation
The value of a number is the sum of its place values. Here, the number having greatest place value is = 1.21 
 = 1 x 1 + 2 x ⅒ + 1 x ¹⁄₁₀₀
The least number = 0.0121
 = 0 x 1 + 0 x ⅒ + 1 x ¹⁄₁₀₀ + 2 x ¹⁄₁₀₀₀ + 1 x ¹⁄₁₀₀₀₀
♦ Textbook Activities - (Textbook Page 78)
(1) The perimeter of an equilateral triangle is 12.9 centimetres. What is the length of each side?
Answer:
Length of each side = 12.9 ÷ 3 = 12.9 x ⅓
   = ¹²⁹⁄₁₀ x  ⅓ = ¹²⁹⁄₃₀ = ⁴³ ˣ ³⁄₁₀ ₓ ₃ = ⁴³⁄₁₀ = 4.3 cm

(2) 16.5 kilograms of rice was divided equally among 5 people. How many kilogram did each get?
Answer:
16.5 ÷ 5 = 16.5 x ⅕
             =  ¹⁶⁵⁄₁₀ x ⅕ = ¹⁶⁵⁄₅₀ = ³³ ˣ ⁵⁄₁₀ ₓ ₅ = ³³⁄₁₀ = 3.3
Each one of them will get 3.3kg of rice.

(3) A large vessel contains 25.2 litres of coconut oil. It was used to fill 6 small vessels of the same size. How much does each small vessel contain?
Answer:
25.5 ÷ 6 = 25.2 x ⅙
             = ²⁵²⁄₁₀ x ⅙ = ²⁵²⁄₆₀ = ⁴² ˣ ⁶⁄₁₀ ₓ ₆ = ⁴²⁄₁₀ = 4.2
Each small vessel contains 4.2 litres

(4)  33.6 kilograms of rice was divided equally among 8 people. Sujatha divided what she got into three equal parts and gave one part to Razia. How much did Razia get?
Answer:
Sujatha got ⅛ part of 33.6
ie, 33.6 ÷ 8 = 33.6 x ⅛
                  = ³³⁶⁄₁₀ x ⅛ = ³³⁶⁄₈₀ = ⁴² ˣ ⁸⁄₁₀ ₓ ₈ = ⁴²⁄₁₀ = 4.2 kg
Razia got ⅓ part of 4.4 kg
ie, 4.2 ÷ 3 = 4.2 x ⅓
                = ⁴²⁄₁₀ x ⅓ = ⁴²⁄₃₀ = ¹⁴ ˣ ³⁄₁₀ ₓ ₃ = ¹⁴⁄₁₀ = 1.4 kg

(5) We have 7407 ÷ 6 = 1234.5. Use this result to find answers to the following questions without actual division :
(i) 740.7 ÷ 6  
(ii)  74.07 ÷ 6 
(iii) 7.407 ÷ 6 
(iv) 0.7407 ÷ 6 
(v) 0.07407 ÷ 6
Answer:
(i) 740.7 ÷ 6 = 123.45 (2 decimal places) 
(ii)  74.07 ÷ 6 = 12.345 (3 decimal places) 
(iii) 7.407 ÷ 6 = 1.2345 (4 decimal places) 
(iv) 0.7407 ÷ 6 = 0.12345 (5 decimal places)  
(v) 0.07407 ÷ 6 = 0.012345 (6 decimal places) 

♦ Textbook Activities - (Textbook Page 80)
(1) Find the decimal forms of the following fractions.
(i) ⅗
(ii) ⅘
(iii) ¹⁄₂₀
(iv) ⅞
Answer:
(i) ⅗ = ³ ˣ ²⁄₅ ₓ ₂ = ⁶⁄₁₀ = 0.6
(ii) ⅘ = ⁴ ˣ ²⁄₅ ₓ ₂ = ⁸⁄₁₀ = 0.8
(iii) ¹⁄₂₀ = ¹ ˣ ⁵⁄₂₀ ₓ ₅ = ⁵⁄₁₀₀ = 0.05
(iv) ⅞ = ⁷ ˣ ¹²⁵⁄₈ ₓ ₁₂₅ = ⁸⁷⁵⁄₁₀₀₀ = 0.875

(2) 3 litres of milk is used to fill in 8 bottles of the same size. How many litres does each bottle hold?
Answer: ⅜ = ³ ˣ ¹²⁵⁄₈ ₓ ₁₂₅ = ³⁷⁵⁄₁₀₀₀ = 0.375 litre

(3) A rope 17 metres long is cut into 25 equal pieces. What is the length of each piece in metres?
Answer: ¹⁷⁄₂₅ = ¹⁷ ˣ ⁴⁄₂₅ ₓ ₄ = ⁶⁸⁄₁₀₀ = 0.68 metre

(4) 19 kilograms of rice was equally divided among 20 people. How much kilograms did each get?
Answer: ¹⁹⁄₂₀ = ¹⁹ ˣ ⁵⁄₂₀ ₓ ₅ = ⁹⁵⁄₁₀₀ = 0.95 kg
♦ Textbook Activities - (Textbook Page 81)
(1) A ribbon 14.5 centimetres long is cut into two equal pieces. What is the length of each piece in centimetres?
Answer:
14.5 ÷ 2 = 14.5 x ½ = ¹⁴⁵⁄₁₀ x ½ = ¹⁴⁵⁄₂₀
Dividing 145 and 20 by 5, we get, 
²⁹⁄₄ = 7¼ = 7 + ¼ = 7 + 0.25 = 7.25
(Decimal form of ¼ = ¹ ˣ ²⁵⁄₄ ₓ ₂₅ = ²⁵⁄₁₀₀ = 0.25)
Length of one piece = 7.25 cm

(2) What is the length of a side of a square of perimeter 20.5 metres?
Answer:
20.5 ÷ 4 = 20.5 x ¼ = ²⁰⁵⁄₁₀ x ¼ = ²⁰⁵⁄₄₀ = ⁴¹⁄₈ = 5⅛ = 5 + ⅛
                               = 5 + 0.125 = 5.125
(⅛ = ¹ ˣ ¹²⁵⁄₈ ₓ ₁₂₅ = ¹²⁵⁄₁₀₀₀ = 0.125)

(3) The price of 6 pens is 40.50 rupees. What is the price of one pen?
Answer:
40.50 ÷ 6 = 40.50 x ⅙ = ⁴⁰⁵⁰⁄₁₀₀ x ⅙ = ⁴⁰⁵⁰⁄₆₀₀
(Divide 4050 and 600 by 50 to get ⁸¹⁄₁₂ ; and then divide 81 and 12 is by 3, to get ²⁷⁄₄. Otherwise, divide both 4050 and 600 by 150.)
²⁷⁄₄ = 6¾ = 6 + ¾
Decimal form of ¾ = ³ ˣ ²⁵⁄₄ ₓ ₂₅ = ⁷⁵⁄₁₀₀ = 0.75
So, 6 + ¾ = 6 + .75 = 6.75
Price of one pen = 6.75 rupees

♦ Textbook Activities - (Textbook Page 82)
(1) A vessel contains 4.05 litres of coconut oil. It is to be used to fill 0.45 litre bottles. How many bottles are needed?
Answer:
Method: 1
4.5 = ⁴⁰⁵⁄₁₀₀, 0.5 = ⁴⁵⁄₁₀₀
⁴⁵⁄₁₀₀ part of the number of bottles is ⁴⁰⁵⁄₁₀₀
That is, the number of bottles = ¹⁰⁰⁄₄₅ times of ⁴⁰⁵⁄₁₀₀
       = ⁴⁰⁵⁄₁₀₀ x ¹⁰⁰⁄₄₅ = ⁴⁰⁵⁄₄₅ = 9
So, we need 9 bottles
Method: 2
4.05 ÷ 0.45 = ⁴⁰⁵⁄₁₀₀ ÷ ⁴⁵⁄₁₀₀ = ⁴⁰⁵⁄₁₀₀ x ¹⁰⁰⁄₄₅ = ⁴⁰⁵⁄₄₅ = 9

(2) An iron rod 17.5 metres long is cut into pieces of length 2.5 metres each. How many pieces are there?
Answer: 
Method: 1
17.5 = ¹⁷⁵⁄₁₀, 2.5 = ²⁵⁄₁₀
²⁵⁄₁₀ times the number of pieces is ¹⁷⁵⁄₁₀
Therefore, ¹⁰⁄₂₅ part of ¹⁷⁵⁄₁₀ is the number of pieces.
¹⁷⁵⁄₁₀ x ¹⁰⁄₂₅ = ¹⁷⁵⁄₂₅ = 7
Method: 2
17.5 ÷ 2.5 = ¹⁷⁵⁄₁₀ ÷ ²⁵⁄₁₀ = ¹⁷⁵⁄₁₀ x ¹⁰⁄₂₅ = ¹⁷⁵⁄₂₅ = 7

(3) 6.5 kilograms of chilli powder was packed in  0.25 kilogram packets. How many packets are there?
Answer:
Method: 1
6.5 = ⁶⁵⁄₁₀, 0.25 = ²⁵⁄₁₀₀
²⁵⁄₁₀₀ part of the number of packets is ⁶⁵⁄₁₀
¹⁰⁰⁄₂₅ times of ⁶⁵⁄₁₀ is the number of packets 
⁶⁵⁄₁₀ x ¹⁰⁰⁄₂₅ = ⁶⁵⁰⁄₂₅ = 26 packets
Method: 2
6.5 ÷ 0.25 = ⁶⁵⁄₁₀ ÷ ²⁵⁄₁₀₀ = ⁶⁵⁄₁₀ x ¹⁰⁰⁄₂₅ = ⁶⁵⁰⁄₂₅ = 26 packets