Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

Write the following fractions as decimal fractions.

(1) Two and a half
Answer:
2 \(\frac{1}{2}\) = 2.5 = 2.50

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

(2) Two and a quarter
Answer:
2 \(\frac{1}{4}\) = 2.25

(3) Two and three quarters
Answer:
2 \(\frac{3}{4}\) = 2.75

(4) Ten and a half
Answer:
10 \(\frac{1}{2}\) = 10.5 = 10.50

(5) Fourteen and three quarters
Answer:
14 \(\frac{3}{4}\) = 14.75

(6) Sixteen and a quarter
Answer:
16 \(\frac{1}{4}\) = 16.25

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

(7) Twenty-eight and a half
Answer:
28 \(\frac{1}{2}\) = 28.50 = 28.5

Adding decimal fractions

Sir : If the cost of one pencil is two and a half rupees and the cost of a pen is four and half rupees, what is the total cost?

Sumit : Two and a half rupees means two rupees and one half rupee. Similarly, four and a half rupees means four rupees and one-half rupee. 4 rupees and 2 rupees make 6 rupees and two half rupees make one rupee, so both objects together cost 6 + 1 = 7 rupees.

Sir : Correct ! Now, see how this is done using decimals.
The sum of the 0’s in the hundredths place is 0.
0.5 + 0.5 is the same as
\(\frac{5}{10}+\frac{5}{10}=\frac{5+5}{10}=\frac{10}{10}=\frac{1}{1}=1\)
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 1

This 1 is carried over to the units place. There is nothing in the tenths place, so we put a zero there. In the units place, 2 + 4 = 6 plus the carried over 1 makes 7.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

So 2.50 rupees and 4.50 rupees add up to 7 rupees.

We use the decimal system to write whole numbers. We extend the same method to write fractions; therefore, we can add in the same way as we add whole numbers.

I will now show some more additions. Watch carefully.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 2

Sumit : There is no carried over number in the first sum, but there are carried over numbers in the second and third sums.

Rekha : While adding whole numbers, we add units first. Similarly, here, tenths are added first. In the second example, the sum of the tenths place is 13. 13 tenths are 10 tenths + 3 tenths = 1 unit + 3 tenths.

Sumit : That is why, in the sum, 3 stayed in the tenths place and 1 was carried over to the units place. 6 + 5 plus 1 carried over makes 12.

Sir : Your observations are absolutely correct. We write digits one below the other according to their place values while adding whole numbers. We do the same thing here. Remember that while writing down an addition problem and the total, the decimal points should always be written one below the other.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

Study the following additions. (Note that: 10 tenths = 1 unit. 10 hundredths = 1 tenth)

Example (1) Add : 7.09 + 54.93
First, add the digits in the 100ths place. 9 + 3 = 12.
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 3

The 1 from the sum 12 in the hundredths place is carried over to the tenths place and 2 is written in the hundredths place. Adding 1 + 9 gives 10 tenths or 1 unit. This 1 is carried over to the units place. 0 is left in the tenths place. Then, the addition is completed in the usual way.

Example (2) Add : 45.83 + 167.4
4 5 . 8 3 We arrange the numbers so that the places and
+
1 6 7. 4 decimal points come one below the other.
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 4

\(\frac{4}{10}=\frac{4 \times 10}{10 \times 10}=\frac{40}{100}\) Therefore, to make the denominators of the fractions equal, 167.4 is written as 167.40 and then the fractions are added.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

As usual, the digits with the smallest place values are added first and then those with bigger place values are added serially.

Example (3) 10.46 Rupees
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 5

Example (4) 48.80 m
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 6

Example (5) 7.5 cm
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 7

Decimal Fractions Problem Set 40 Additional Important Questions and Answers

(1) Thirty and a quarter
Answer:
30 \(\frac{1}{4}\) = 30.25

(2) Thirty and a half
Answer:
30 \(\frac{1}{2}\) = 30.50 = 30.5

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40

(3) Thirty and three quarters
Answer:
30 \(\frac{3}{4}\) = 30.75

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Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

Question 1.
Subtract the following :

(1) 25.74 – 13.42
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 1

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

(2) 206.35 – 168.22
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 2

(3) 63.4 – 31.8
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 3

(4) 63.43 – 31.8
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 4

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

(5) 63.4 – 31.83
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 5

(6) 8.23 – 5.45
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 6

(7) 18.23 – 9.45
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 7

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

(8) 78.03 – 41.65
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 8

Question 2.
Vrinda was 1.48 m tall. After a year, her height became 1.53 m. How many centimeters did her height increase in a year?
Answer:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 13

∴ 5 cm height has increased in a year.

Something more

Decimals used for measurement

We need to measure distance, mass (weight) and volume every day. We use suitable units for these measurements. Kilometre, metre and centimeter for distance; litre, millilitre for volume and kilogram and gram for mass are the units that are used most of the time.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

All these units are decimal units. In this method, gram, metre and litre are taken as the basic units for mass, distance and volume respectively. Units larger than these increase 10 times at every step and smaller units become \(\frac{1}{10}\) of the previous unit at each step.

Look at the table of these units given below.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 15

The origin of the terms kilo, hecto… milli is in the Greek or Latin language. Their English equivalents are given in brackets along with the terms.

Decimal Fractions Problem Set 42 Additional Important Questions and Answers

Subtract the following:

(1) 304.17 – 95.28
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 9

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

(2) 72.84 – 36.96
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 10

(3) 9.17 – 5.88
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 11

(4) 100 – 49.99
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 12

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42

(5) Atul has 56.25 and Anup has 65. Whose amount is more? How much?
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 42 14

∴ Anup’s amount is more by ₹ 8.75

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41 Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

Question 1.
Convert the following into decimal fractions and add them.

(1) ‘One and a half metre’ and ‘two and a half metres’
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 1

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

(2) ‘Five and three quarter rupees’ and ‘seven and a quarter rupees’
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 2

(3) ‘Six and a half metres’ and ‘three and three quarter metres’.
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 3

Question 2.
(1) 23.4 + 87.9
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 6

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

(2) 35.74 + 816.6
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 7

(3) 6.95 + 74.88
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 8

(4) 41.03 + 9.98
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 9

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

Question 3.
(1) 51.4 cm + 68.5 cm
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 12

(2) 94.7 m + 1738.45 m
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 13

(3) 5158.75 + `841.25
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 14

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

Subtraction of decimal fractions

Study the subtraction of decimal fractions given below.
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41 1

8 hundredths cannot be subtracted from 1 hundredth, so 1 tenth (or 10 hundredths) from 4 tenths are borrowed. The borrowed 10 hundredths and the original one hundredth make 11 hundredths. 11 hundredths minus 8 hundredths are 3 hundredths. They are written in the hundredths place under the line. The rest of the subtraction is carried out using the same method.

Decimal Fractions Problem Set 41 Additional Important Questions and Answers

Convert the following into decimal fractions and add them.

(1) ‘Fourteen and a half rupees’ and ‘Fifteen and a half rupees’.
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 4

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

(2) ‘Three quarters’ and ‘a half’
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 5

Add the following:

(1) 37.84 + 12.16
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 10

(2) 328.69 + 84.84
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 11

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

Solve the following:

(1) 304.86 m + 70.94 m
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 15

(2) 79.56 cm + 19.65 cm
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 16

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 41

(3) ₹ 64.79 + ₹  49.5
Solution:
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 40 17

Maharashtra Board Class 5 Marathi Solutions Chapter 1 नाच रे मोरा

Balbharti Maharashtra State Board Class 5 Marathi Solutions Sulabhbharati Chapter 1 नाच रे मोरा Notes, Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Marathi Sulabhbharati Solutions Chapter 1 नाच रे मोरा

5th Standard Marathi Digest Chapter 1 नाच रे मोरा Textbook Questions and Answers

1. ऐका. म्हणा.

प्रश्न 1.
ऐका. म्हणा.

नाच रे मोरा, आंब्याच्या वनात
नाच रे मोरा नाच!

ढगांशी वारा झुंजला रे
काळा काळा कापूस पिंजला रे
आता तुझी पाळी
वीज देते टाळी
फुलव पिसारा नाच ।। 1 ।।

झर झर धार झरली रे
झाडांची भिजली इरली रे
पावसात न्हाऊ
काहीतरी गाऊ
करून पुकारा नाच ।। 2 ।।

थेंब थेंब तळ्यात नाचती रे
टप्टप् पानात वाजती रे
पावसाच्या रेघात
खेळ खेळू दोघांत
निळ्या सौंगड्या नाच ।। 3 ।।

पावसाची रिमझिम थांबली रे
तुझी माझी जोडी जमली रे
आभाळात छान छान
सात रंगी कमान
कमानीखाली त्या नाच ।। 4 ।।

– ग. दि. माडगूळकर

Maharashtra Board Class 5 Marathi Solutions Chapter 1 नाच रे मोरा

Marathi Sulabhbharati Class 5 Solutions Chapter 1 नाच रे मोरा Additional Important Questions and Answers

1. खालील प्रश्नांची उत्तरे एक किंवा दोन शब्दांत लिहा.

प्रश्न 1.
खालील प्रश्नांची उत्तरे एक किंवा दोन शब्दांत लिहा.

  1. आपला राष्ट्रीय पक्षी कोणता?
  2. मोर कुठे नाचणार आहे?
  3. वारा कोणाशी झुंजत आहे?
  4. ढगाला कशाची उपमा दिली आहे?
  5. कोण टाळी देते?
  6. धार कशी झरत आहे?
  7. तळ्यात कोण नाचतात?
  8. पानावर टपटप कशाचा आवाज येतो?
  9. सवंगडी कोणत्या रंगाचा आहे?
  10. पावसाची रिमझिम थांबल्यावर आकाशात काय दिसू लागले?

उत्तर:

  1. मोर
  2. आंब्याच्या वनात
  3. ढगांशी
  4. काळ्या कापसाची
  5. वीज
  6. झरझर
  7. थेंब
  8. थेंबांचा
  9. निळ्या
  10. सातरंगी कमान

Maharashtra Board Class 5 Marathi Solutions Chapter 1 नाच रे मोरा

2. एका वाक्यात उत्तरे लिहा.

प्रश्न 1.
प्रस्तुत कवितेत कोणत्या ऋतूचे वर्णन केले आहे?
उत्तर:
प्रस्तुत कवितेत पावसाळ्याचे वर्णन केले आहे.

प्रश्न 2.
प्रस्तुत कविता कोणी लिहिली आहे?
उत्तर:
प्रस्तुत कविता ‘ग. दि. माडगूळकरांनी’ लिहिली आहे.

प्रश्न 3.
कवी मोराला कशाप्रकारे नाचण्यास सांगत आहे?
उत्तर:
कवी मोराला पिसारा फुलवून नाचण्यास सांगत आहे.

प्रश्न 4.
झाडांची इरली कशामुळे भिजली आहे?
उत्तर:
झाडांची इरली झर झर धार झरल्यामुळे भिजली आहे.

प्रश्न 5.
कवी कोणाबरोबर खेळ खेळणार आहे?
उत्तर:
कवी निळ्या सवंगड्यांबरोबर खेळ खेळणार आहे.

प्रश्न 6.
कवी मोराला कशाखाली नाचण्यास सांगत आहेत?
उत्तर:
कवी मोराला आभाळातील सातरंगी कमानीखाली नाचण्यास सांगत आहे.

Maharashtra Board Class 5 Marathi Solutions Chapter 1 नाच रे मोरा

प्रश्न 7.
इंद्रधनुष्यातील सात रंग कोणते?
उत्तर:
तांबडा, नारंगी, पिवळा, हिरवा, निळा, पांढरा, जांभळा हे इंद्रधनुष्यातील सात रंग आहेत.

3. कंसातील शब्दांचा आधार घेऊन रिकाम्या जागा भरा.

प्रश्न 1.
कंसातील शब्दांचा आधार घेऊन रिकाम्या जागा भरा.
(रिमझिम, कमान, कापूस, धार, सौंगड्या, जोडी, इरली, तळ्यात, पानात)

  1. काळा काळा ……………….. पिंजला रे.
  2. झर झर …………………. झरली रे.
  3. झाडांची भिजली ……………….. रे.
  4. थेंब थेंब ……………………. नाचती रे.
  5. टप्टप् …………………. वाजती रे.
  6. निळ्या ……………………. नाच.
  7. पावसाची …………….. थांबली रे.
  8. तुझी माझी ………………….जमली रे.
  9. आभाळात छान छान सात रंगी …………………….. .

उत्तरः

  1. कापूस
  2. धार
  3. इरली
  4. तळ्यात
  5. पानात
  6. सौंगड्या
  7. रिमझिम
  8. जोडी
  9. कमान

Maharashtra Board Class 5 Marathi Solutions Chapter 1 नाच रे मोरा

4. खालील कवितेच्या ओळी पूर्ण करा.

प्रश्न 1.
1. ढगांशी वारा झुंजला रे
…………………. पिंजला रे
2. थेंब थेंब तळ्यात नाचती रे
……………………….. वाजती रे
3. पावसाची रिमझिम थांबली रे
…………………………… जमली रे
4. आभाळात छान छान
…………… कमानीखाली त्या नाच।
उत्तर:
1. काळा काळा कापूस
2. टपटप पानात
3. तुझी माझी जोडी
4. छान छान सात रंगी कमान

5. खालील प्रश्नांची थोडक्यात उत्तरे लिहा.

प्रश्न 1.
कवीने पावसाळ्यातील वातावरणाचे वर्णन कसे केले आहे?
उत्तर:
आकाशात काळे काळे ढग जमा झाले आहेत. वारा सुटला आहे. वीज चमकत आहे. झर झर पावसाची धार पडत आहे. झाडांची इरली भिजली आहे. पावसाचे थेंब तळ्यात नाचत आहेत. पावसाच्या थेंबांचा पानांवर पडून टप्टप् असा आवाज येत आहे. आकाशात सात रंगी इंद्रधनुष्य दिसत आहे. अशाप्रकारे कवीने पावसाळ्यातील वातावरणाचे वर्णन केले आहे.

Maharashtra Board Class 5 Marathi Solutions Chapter 1 नाच रे मोरा

प्रश्न 2.
प्रस्तुत कवितेत आभाळाचे वर्णन कसे केले आहे?
उत्तर:
पाऊस सुरू होण्यापूर्वी आभाळात काळा काळा कापूस पिंजावा तसे काळे ढग जमा झाले आहेत व वीज कडाडते आहे. तसेच पावसाची रिमझिम थांबल्यावर आभाळात सात रंगी इंद्रधनुष्य दिसत आहे. अशाप्रकारे कवितेत आभाळाचे वर्णन केले आहे.

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Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36 Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36

Write the following mixed fractions in decimal form and read them aloud.

\(\text { (1) } 3 \frac{9}{10}\)
Answer:
3.9, Three-point nine.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36

\(\text { (2) } 1 \frac{4}{10}\)
Answer:
1.4, One point four.

\(\text { (3) } 5 \frac{3}{10}\)
Answer:
5.3, Five-point three.

\(\text { (4) } \frac{8}{10}\)
Answer:
0.8, Zero points eight.

\(\text { (5) } \frac{7}{10}\)
Answer:
0.5, Zero points five.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36

Hundredths

If \(\frac{1}{10}\) is divided into 10 equal parts, each part becomes \(\frac{1}{100}\) or one hundredth. Therefore, note that 1 tenth =10 hundredths, or 0.1=0.10. By multiplying \(\frac{1}{100}\) by 10 we get \(\frac{10}{100}\) = \(\frac{1}{10}\). Therefore, it is possible to create a hundredths place next to the tenths place. After creating a hundredths place we can write \(\frac{14}{100}\) as 0.14.

\(\frac{14}{100}=\frac{10+4}{100}=\frac{10}{100}+\frac{4}{100}=\frac{1}{10}+\frac{4}{100}\) meaning that when writing \(\frac{14}{100}\) in decimal form, 1 is written in the tenths place and 4 is written in the hundredths place. This fraction is written as 0.14 and is read as ‘zero point one four’. Similarly, 6 \(\frac{57}{100}\) is written as 6.57 and 50 \(\frac{71}{100}\) is written as 50.71.

While writing \(\frac{3}{100}\) in decimal form, we must remember that there is no number in the tenths place and so, we put 0 in that place, which means that \(\frac{3}{100}\) is written as 0.03.

Study how the decimal fractions in the table below are written and read.
Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36 1

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36

Decimal Fractions Problem Set 36 Additional Important Questions and Answers

\(\text { (1) } 4 \frac{6}{10}\)
Answer:
4.6, Four point six. 7

\(\text { (2) } 4 \frac{6}{10}\)
Answer:
2.7, Two point seven.

\(\text { (3) } 4 \frac{6}{10}\)
Answer:
6.2, Six points two.

\(\text { (4) } 4 \frac{6}{10}\)
Answer:
21.1, Twenty-one point one.

Maharashtra Board Class 5 Maths Solutions Chapter 9 Decimal Fractions Problem Set 36

\(\text { (5) } 4 \frac{6}{10}\)
Answer:
17.5, Seventeen points five.

Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 35

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 35 Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 35

Determine whether the pairs of numbers given below are co-prime numbers.
(1) 22, 24
Answer:
Common factors of 22 and 24 are 1 and 2. (Not only 1 common factor) So, 22, 24 are not co-prime numbers.

(2) 14, 21
Answer:
Common factors of 14 and 21 are 1 and 7. So, this pair is not co-prime numbers.

(3) 10, 33
Answer:
Common factors of 10 and 33 is only 1. So, 10 and 33 are co-prime numbers.

(4) 11, 30
Answer:
Common factors of 11 and 30 is only 1. So, 11 and 30 are co-prime numbers.

(5) 5, 7
Answer:
Common factor of 5 and 7 is only 1. So, 5 and 7 are co-prime numbers.

(6) 15, 16
Answer:
Common factors of 15 and 16 is only 1. So, 15 and 16 are co-prime numbers.

(7) 50, 52
Answer:
Common factors of 50 and 52 are 1 and 2. So, 50 and 52 are not co-prime numbers.

(8) 17, 18
Answer:
Common factors of 17 and 18 is only 1. So, 17 and 18 are co-prime numbers.

Activity 1 :

  • Write numbers from 1 to 60.
  • Draw a blue circle around multiples of 2.
  • Draw a red circle around multiples of 4.
  • Do all numbers with a blue circle also have a red circle around them?
  • Do all the numbers with a red circle have a blue circle around them?
  • Are all multiples of 2 also multiples of 4?
  • Are all multiples of 4 also multiples of 2?

Activity 2 :

  • Write numbers from 1 to 60.
  • Draw a triangle around multiples of 2.
  • Draw a circle around multiples of 3.
  • Now find numbers divisible by 6. Can you find a property that they share?

Eratosthenes’ method of finding prime numbers
Eratosthenes was a mathematician who lived in Greece about 250 BC. He discovered a method to find prime numbers. It is called Eratosthenes’ Sieve. Let us see how to find prime numbers between 1 and 100 with this method.

Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 35 1

  • 1 is neither a prime nor a composite number. Put a square [ ] around it
  • 2 is a prime number, so put a circle around it.
  • Next, strike out all the multiples of 2. This tells us that of these 100 numbers more than half of numbers are not prime numbers.
  • The first number after 2 not yet struck off is 3. So, 3 is a prime number.
  • Draw a circle around 3. Strike out all the multiples of 3.
  • The next number after 3 not struck off yet is 5. So, 5 is a prime number.
  • Draw a circle around 5. Put a line through all the multiples of 5.
  • The next number after 5 without a line through it is 7. So, 7 is a prime number.
  • Draw a circle around 7. Put a line through all the multiples of 7.

In this way, every number between 1 and 100 will have either a circle or a line through it. The circled numbers are prime numbers. The numbers with a line through them are composite numbers.

One more method to find prime numbers

Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 35 2

See how numbers from 1 to 36 have been arranged in six columns in the table alongside.

Continue in the same way and write numbers up to 102 in these six columns.

You will see that, in the columns for 2, 3, 4, and 6, all the numbers are composite numbers except for the prime numbers 2 and 3. This means that all the remaining prime numbers will be in the columns for 1 and 5. Now isn’t it easier to find them? So, go ahead, find the prime numbers!

Something more

  • Prime numbers with a difference of two are called twin prime numbers. Some twin prime number pairs are 3 and 5, 5 and 7, 29 and 31 and 71 and 73. 5347421 and 5347423 are also a pair of twin prime numbers.
  • There are eight pairs of twin prime numbers between 1 and 100. Find them.
  • Euclid the mathematician lived in Greece about 300 BC. He proved that if prime numbers, 2, 3, 5, 7, ……., are written in serial order, the list will never end, meaning that the number of prime numbers is infinite.

Multiples and Factors Problem Set 35 Additional Important Questions and Answers

Determine whether the pairs of numbers given below are co-prime numbers.

(1) (12,18)
Answer:
Common factors of 12 and 18 are 1, 2, 3, 6. Hence 12 and 18 are not co-prime numbers.

(2) (26, 39)
Answer:
Common factors of 26 and 39 are 1 and 13. Hence, 26 and 39 are not co-prime numbers.

(3) (23, 29)
Answer:
Common factor of 23 and 29 is only 1. Hence, 23 and 29 are co-prime numbers.

(4) (28, 32)
Answer:
Common factors of 28 and 32 are 1, 2, 4 (not only 1). Hence, 28, 32 are not co-prime numbers.

Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 34

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 34 Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 34

Question 1.
Write all the prime numbers between 1 and 20.
Answer:
2, 3, 5, 7, 11, 13, 17, 19.

Question 2.
Write all the composite numbers between 21 and 50.
Answer:
Composite numbers between 21 and 50 are 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49.

Question 3.
Circle the prime numbers in the list given below. 22, 37, 43, 48, 53, 60, 91, 57, 59, 77, 79, 97, 100
Answer:
Maharashtra Board Class 5 Maths Solutions Chapter 8 Multiples and Factors Problem Set 34 1

Question 4.
Which of the prime numbers are even numbers?
Answer:
Only even prime number is 2. (the Rest of the even numbers are composites.)

Co-prime numbers

Dada : Tell me all the factors of 12 and 18.

Anju : I’ll tell the factors of 12: 1, 2, 3, 4, 6, 12.

Manju : I’ll give the factors of 18: 1, 2, 3, 6, 9, 18.

Dada : Now find the common factors of 12 and 18.

Anju : Common factors ?

Dada : 1, 2, 3 and 6 are in both groups, which means that they are common factors. Now tell me the factors of 10 and 21.

Sanju : Factors of 10 : 1, 2, 5, 10.

Manju : Factors of 21: 1, 3, 7, 21.

Dada : Which of the factors in these two groups are common?

Sanju : 1 is the only common factor.

Dada : Numbers which have only 1 as a common factor are called co-prime numbers, so 10 and 21 are co-prime numbers. The common factors of 12 and 18 are 1, 2, 3 and 6; which means that the common factors are more than one. Therefore, 12 and 18 are not co-prime numbers. Now tell me whether 8 and 10 are co-prime numbers.

Manju : The factors of 8 are 1, 2, 4 and 8 and the factors of 10 are 1, 2, 5 and 10. These numbers have two factors, 1 and 2, in common, so 8 and 10 are not co-prime numbers.

Multiples and Factors Problem Set 32 Additional Important Questions and Answers

Question 1.
21 to 50
Answer:
23, 29, 31, 37, 41, 43, 47

Question 2.
Which of the number is neither prime nor composite?
Answer:
1

Question 13.
Between nearest which two prime numbers the prime number 43 lies?
Answer:
43 lies between prime numbers 41 and 47.

Question 14.
Which of the prime numbers are odd numbers?
Answer:
All prime numbers are odd except 2.