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c) 5

First we have to convert the mixed fraction into improper fraction 3¾ = 15/4

Then, 15/4 ÷ ¾

= (15/4)/ (¾)

= (15/4) × (4/3)

= (15 × 4)/ (4 ×3)

= (5 × 1)/ (1 ×1)

= 5

False.

Consider the given decimal number, 3.725

In the thousandths place has number 5.

Then, hundredths has number 2 it will be increased by 1 number to correct two decimal places.

Therefore, the decimal 3.725 is equal to 3.73 correct to two decimal places.

False.

So, (25/19) + (6/19)

= (25 + 6)/19

= 31/19

Fractions with same denominators are called like fractions.

True.

25/8 can be further simplified by dividing both numerator and denominator by 8.

65/8 or 8 1/8 (because 8.125 = 8125/1000)

Decimal 16.25 is equal to the fraction 16¼ or 65/4.

Decimals can be converted into fractions by removing their decimal points and writing 10,100, etc in the denominators, depending upon the number of decimal places in the decimals.

16.25 = 1625/100

Divide both numerator and denominator by 25.

= 65/4

= 16¼

Fraction 7/25 is equal to the decimal number 0.28.

Multiply numerator and denominator by 4 to get denominator 100.

(7/25) = (7 × 4)/(25 × 4)

=28/100

We know that, fractions with denominators 10,100, etc. can be written in a form, using a decimal point, called decimal numbers or decimals.

= 0.28

1/10th part of 80 is 18.

The value of 50 coins of 50 paisa = ₹25.

We know that, ₹1 = 100 paisa

So, 50 coins of 50 paisa = 50 × 50

= 2500 paisa.

Then,

= 2500/100

= ₹ 25

(17/9) + (41/9) = 58/9.

Fractions with same denominators are called like fractions.

Sum of two like fractions = (17 + 41)/9

= 58/9

(67/14) – (24/14) = 43/14.

Fractions with same denominators are called like fractions.

Difference of two fractions = (67 – 24)/14

= 43/14

The fraction 17/34 in simplest form is ½.

The given fraction 17/34, is further simplified by dividing both numerator and denominator by 17.

= ½

(i) 10.8

(ii) 8.5

(iii) 5/13

(iv) 0.2 gm

(A) 19/17

If denominators of the given fraction are same we can add both fractions.

So, (4/17) + (15/17)

= (4 + 15)/17

= 19/17

(B) 5/6

We know that, numerators of all given friction is same then smaller denominator is the greatest fraction.

5/9 < 5/8 < 5/7 < 5/6

Therefore, among four options, (B) 5/6 has small denominator. So, it is the greatest fraction.

8.76 – 2.68 = 6.08.

Method I: Conversion of both numbers 13/17 and 0.82 into decimals 13/17 = 0.76 and 0.82

Method II: Conversion of both numbers 13/17 and 0.82 into fractions

0.82 = 82/100 = 41/50 and 13/17

∴ Method of converting numbers into decimals is easier because we can easily compare the numbers in this method but in other method we will also convert the fractions into like fractions to compare the numbers.

(b) 13/21, 2/3, 6/7

LCM of 21, 3, 7 = 21

Now, let us change each of the given fraction into an equivalent fraction having 21 as the denominator.

[(13/21) × (1/1)] = (13/21)

[(2/3) × (7/7)] = (14/21)

[(6/7) × (3/3)] = (18/21)

Clearly,

(13/21) < (14/21) < (18/21)

Hence,

(13/21) < (2/3) < (6/7)

Hence, the given fractions in ascending order are (13/21), (2/3), (6/7)

17/2 + 3½ = 12.

First we have to convert mixed fraction into improper fraction = 3½ = 7/2

Fractions with same denominators are called like fractions.

Sum of two like fractions = (17/2) + (7/2)

= (17 + 7)/2

= 24/2

= 12

(i) 200 g = 200/1000 kg = 2/10 kg = 0.2 kg

(ii) 3470 g = 3470/1000 kg = 3.47 kg

Correct option is  C) 20/25

(C) 3/8

We know that, denominator of all given friction is same then smaller numerator is the smallest fraction.

3/8 < 5/8 < 7/8 < 9/8

Therefore, among four options, (C) 3/8 has small numerator. So, it is the smallest fraction.

False.

Fractions with same denominators are called like fractions.

 D)\(\frac{25}{45}\) = \(\frac{125}{175}\) 

(A) 84/75 = \(\frac{262\times3\times7}{3\times5^2} = \frac{2^2\times7}{5^2}\) = \(\frac{4\times7}{25}\) = \(\frac{28}{25}\neq\frac23\)

(B) 375/1000 = \(\frac{3\times5^3}{3\times5^3}=\frac{3}{2^3}=\frac38\)

(C) 7000/1000 = 7/1 = 70/10

(D) 125/225 = \(\frac{5^2}{3^2\times5^2}\) = \(\frac59=\frac{5}9\times\frac55=\frac{25}{45}\) = 125/225

Correct option is   A) \(\frac{2}{3}\)= \(\frac{84}{75}\)

Correct option is  C) 5/8

4.55 + 9.73 = 14.28.

35 mm = 35/10 cm = 3.5 cm

35 mm = 35/(10 x 100) m = 0.035 m

35 mm = 35/(10 x 100 x 1000) km

= 35/1000000

= 0.000035 km

True.

First we have to convert given decimals into like decimals = 13.730

So, 13.730 = 13.730

Therefore, 13.730 = 13.73

6/11 and 6/13 are unlike proper fractions.

The denominators are different, then they are called unlike fractions.

Since, we know that the measurement of a straight angle is 180° and a right angle is 90°.

∴ The required fraction is 90/180 = 1/2.

Let 5/6 = 60/?

Then, we have to find the missing numeral. To get 60 in the numerator, we multiply 5 by 12.

So, we multiply the numerator and denominator by 12.

(5 x 12)/(6 x 12) = 60/72

Hence, 5/6 and 60/72 are equivalent fractions.

The correct option is (C) 11/10.

A number representing a part of a whole is called a fraction.

Example: ¼, ¾, 1/5, 3/6 etc.

(A) 3/8

\(\frac{375}{1000} = \frac{3\times5^3}{2^3\times5^3}\) = \(\frac3{2^3}\) = 3/8

Correct option is  A) 3/8

(B) 9.07

First we have to convert given decimals into like decimals = 15.80

Now, 15.80 – 6.73 = 9.07

(j) 35.07

(ii) 262.327

The required number is 0.8531, which is the largest four digit decimal number less than 1.

A fraction with denominator greater than the numerator is called a proper fraction.

Example: 2/5, 3/8, 10/11 etc. are proper fractions.

For rounding off to tenths place, we look at the hundredths place. Here the digit is 5. 

So, the digit at the tenths place (9) will be increased by 1 (i.e., it will become 9 + 1) 

Hence, rounding off 87.952 to tenths place, we get 88.0 

(Note: Do not write it as 88.)

Correct answer is (b) 0.0025

∵ The digits are already given in the form of like decimals.

Clearly, 12.104 < 12.124 < 12.142 < 12.214 < 12.401

(C) 0.078

First we have to convert given decimals into like decimals = 0.070 + 0.008

So, sum of 0.070 and 0.008 = 0.070 + 0.008

= 0.078

We have to arrange them from the smallest to the greatest number. We arrange them as follows (using the idea of place value and comparing their digits at different places); 2.0226, 2.023, 2.2, 20.42, 22.1

(Note: Using the < sign, these numbers can also be written as 2.0226 < 2.023 < 2.2 < 20.42 < 22.1.)

Correct answer is (d) 15/2.

We have,

3 2/5

= (3 x 5) + 2/5

= (15+2)/5

= 17/5

Now,

17/5

= (17 x 2)/(5 x 2)

= 34/10

= 3.4

The Solution of 6.25 ÷ 5 is  1.25.

Correct answer is (b) 21 cm.

Since 1000 g = 1 kg, therefore, 5809 g = 5809/1000 kg

= 5.809 kg

The two non-zero fractions whose product is 1, are called the Reciprocal of each other.

45 mm = 0.045 m