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Correct option is A) 2/3

Correct option is A) 0.000095

Length of cloth required for one shirt

= 2 1/4 m + 1/8 m

= (9/4 + 1/8) m

= (18 + 1)/8 m

= 19/8 m

∴ Length of cloth required for 6 shirts

= 19/8 x 6 m

= (19 x 3)/4 m

= 57/4 m

= 14 1/4 m

(1/2) + (2/2) + (3/2) = (1 + 2 + 3)/2

= 6/2 = 3

Heera have milk = 3/7 litre 

Heera gave milk to Bhavna = 1/4 litre 

∴ Remaining milk to Heera = (3/7) – (1/4)

L.C.M. of 7 and 4 = 28 

∴ (3/7) – (1/4) = (3 x 4 - 1 x 7)/28 

= (12 - 7)/28 = 5/28 litre

True.

Given two fractions are like fractions,

Fractions with same denominators are called like fractions.

So, 16 > 13

Therefore, (16/25) > (13/25)

 [3(1/5)] – (7/10)

Convert mixed fraction into improper fraction,

= [3(1/5)] = (16/5)

= (16/5)-(7/10)

For subtraction of two unlike fractions, first change them to the like fractions.

LCM of 5, 10 = 10

Now, let us change each of the given fraction into an equivalent fraction having 10 as the denominator.

= [(16/5) × (2/2)] = (32/10)

= [(7/10) × (1/1)] = (7/10)

Then,

= (32/10) – (7/10)

= (32-7)/10

= (25/10) … [÷ by 5]

= (5/2)

= [2(1/2)]

(5/6) – (3/4)

For subtraction of two unlike fractions, first change them to the like fractions.

LCM of 6, 4 = 12

Now, let us change each of the given fraction into an equivalent fraction having 12 as the denominator.

= [(5/6) × (2/2)] = (10/12)

= [(3/4) × (3/3)] = (9/12)

Now,

= (10/12)-(9/12)

= [(10 – 9)/12]

= (1/12)

(i) Given (3/8), (5/6), (6/8), (2/4), (1/3)

Now we have to arrange these in ascending order, to arrange these in ascending order we have to make those as equivalent fractions by taking LCM’s.

LCM of 8, 6, 4 and 3 is 24

Equivalent fractions are

(9/24), (20/24), (18/24), (12/24), (8/24)

We know that 8 < 9 < 12 < 18 < 20

Now arranging in ascending order

(8/24) < (9/24) < (12/24) < (18/24) < (20/24)

Hence (1/3) < (3/8) < (2/4) < (6/8) < (5/6)

(ii) Given (4/6), (3/8), (6/12), (5/16)

Now we have to arrange these in ascending order, to arrange these in ascending order we have to make those as equivalent fractions by taking LCM’s.

LCM of 8, 6, 12 and 16 is 48

Equivalent fractions are

(12/48), (15/48), (18/48), (32/48)

We know that 12 < 15 < 18 < 32

Now arranging in ascending order

(12/48) < (15/48) < (18/48) < (32/48)

(6/12) < (5/16) < (3/8) < (4/6)

(5/7) – (2/7)

The subtraction of fraction can be performed in a manner similar to that of addition.

For subtracting two like fractions, the numerators are subtract and the denominator remains the same.

= (5 – 2)/7

= (3/7)

[3(4/5)] + [2(3/10)] + [1(1/15)]

First convert each mixed fraction into improper fraction.

We get,

= [3(4/5)] = (18/5)

= [2(3/10)] = (23/10)

= [1(1/15)] = (16/15)

Then,

(19/5) + (23/10) + (16/15)

LCM of 5, 10, 15 = 30

Now, let us change each of the given fraction into an equivalent fraction having 30 as the denominator.

= [(19/5) × (6/6)] = (114/30)

= [(23/10) × (3/3)] = (69/ 30)

= [(16/15) × (2/2)] = (32/30)

Now,

= (114/30) + (69/30) + (32/30)

= [(114+69+32)/30]

= (215/30)

= [7 (5/30)]

= [7 (1/5)]

(8/9) + (7/12)

For addition of two unlike fractions, first change them to the like fractions.

LCM of 9, 12 = 36

Now, let us change each of the given fraction into an equivalent fraction having 36 as the denominator.

[(8/9) × (4/4)] = (32/36)

[(7/12) × (3/3)] = (21/36)

Now, add the like fractions,

= (32/36) + (21/36)

= (32+21)/36

= (53/36)

= [1(17/36)]

(a) 1/2 > 1/5

(b) 2/4 = 3/6

(c) 3/5 < 2/3

(d) 3/4 > 2/8

(e) 3/5 < 6/5

(f) 7/9 >3/9

i. \(\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=\frac{3+2+1}{6}=\frac{6}{6}=1\)

ii. \(\frac{4}{10}+\frac{1}{10}+\frac{3}{10}+\frac{2}{10}=\frac{4+1+3+2}{10}=\frac{10}{10}=1\)

iii. \(\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}=1\)

(i) Given (7/9) and (8/13)

Taking LCM for 9 and 13 we get,

9 × 13 = 117

Now we convert the given fractions into its equivalent fractions, then it becomes

(7 × 13)/ (9 × 13) and (8 × 9)/ (13 × 9)

Therefore (91/117) > (72/117)

Hence (7/9) > (8/13)

(ii) Given (11/9) and (5/9)

As the denominator is equal, they forms equivalent fractions.

But we know that 11 > 5

Hence (11/9) > (5/9)

(iii) Given (37/41) and (19/30)

Taking LCM for 41 and 30 we get,

30 × 41 = 1230

Now we convert the given fractions into its equivalent fractions, then it becomes

(37 × 30)/ (41 × 30) and (19 × 41)/ (30 × 31)

Therefore (1110/1230) > (779/1230)

Hence (37/41) > (19/30)

(iv) Given (17/15) and (119/105)

Taking LCM for 15 and 105 we get, 5 × 3 × 7 = 105

Now we convert the given fractions into its equivalent fractions, then it becomes

(17 × 7)/ (15 × 7) and (119/105)

Therefore (119/105) = (119/105)

Hence (17/15) = (119/105)

(a) 1/6 < 1/3

(b) 3/4 > 2/6

(c) 2/3 > 2/4

(d) 6/6 = 3/3

(e) 5/6 < 5/5

(4/5), (7/10), (11/15), (17/20)

LCM of 5, 10, 15, 20 = 5 × 2 × 3 × 2 = 60

Now, let us change each of the given fraction into an equivalent fraction having 60 as the denominator.

[(4/5) × (12/12)] = (48/60)

[(7/10) × (6/6)] = (42/60)

[(11/15) × (4/4)] = (44/60)

[(17/20) × (3/3)] = (52/60)

Clearly,

(42/60) < (44/60) < (48/60) < (52/60)

Hence,

(7/10) < (11/15) < (4/5) < (17/20)

Hence, the given fractions in ascending order are (7/10), (11/15), (4/5) , (17/20)

(5/9)+(3/9)

For adding two like fractions, the numerators are added and the denominator remains the same.

= (5+3)/9

= (8/9)

To find out the difference, we must subtract.

\(\frac{5}{12}-\frac{3}{12}=\frac{5-3}{12}=\frac{2}{12}.\)

Thus, Raju got \(\frac{2}{12}\) extra.

From the question,

Reenu got (2/7) part of an apple

Sonal got (4/5) part of an apple

First we have to compare the given fraction (2/7) and (4/5) to know who got the larger part of the apple.

Then,

By cross multiplication, we have

2 × 5 = 10 and 4 × 7 = 28

But,

10 < 28

∴ (2/7) < (4/5)

So, Sonal got the larger part of the apple

Now,

= (4/5)-(2/7)

= [(28-10)/35]

= [18/35]

∴ Sonal got (18/35) part of the apple larger than Reenu.

(i) 250/400 = \(\frac{5\times 50}{8\times 50}\) = 5/8

Two more fractions are 25/40, 30/48 

(ii) 180/200 = \(\frac{9\times20}{10\times20}\) = 9/10

Two more fractions are 18/20, 27/30

(iii) 660/990 = \(\frac{2\times 330}{3\times330}\) = 2/3

Two more fractions are 20/30, 200/300

(iv) 180/360 = \(\frac{1\times 180}{2\times180}\) = 1/2

Two more fractions are 20/40, 30/60

20/40, 30/60 = \(\frac{2\times 110}{5\times110}\) = 2/5

(v) 220/550 = \(\frac{2\times 110}{5\times110}\) =  2/5

Two more fractions are 20/40, 40/100

Now these can be matched as

(i) – (d),

(ii) – (e),

(iii) – (a),

(iv) – (c),

(v) – (b)

Fraction used by Ramesh = 10/20 = 1/2

Fraction used by sheelu = 25/50 = 1/2

Fraction used by Jamaal = 40/80 = 1/2

Yes, all of them used equal fraction of pencils, i.e., 1/2.

(3/7) of a week

The above question can be written as,

= (3/7) of 7 days

We have:

= (3/7) of (7/1)

This can be written as,

= (7/1) × (3/7)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (7 × 3)/ (1 × 7)

On simplifying we get,

= (1×3)/ (1×1)

= 3 days

(7/8) of a day

The above question can be written as,

= (7/8) of 24 hours

We have:

= (7/8) of (24/1)

This can be written as,

= (24/1) × (7/8)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (24 × 7)/ (1 × 8)

On simplifying we get,

= (3×7)/ (1×1)

= 21 hours

(9/20) of a meter

The above question can be written as,

= (9/20) of 100 cm

We have:

= (9/20) of (100/1)

This can be written as,

= (100/1) × (9/20)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (100 × 9)/ (1 × 20)

On simplifying we get,

= (5×9)/ (1×1)

= 45 cm

(7/20) of a kg

The above question can be written as,

= (7/20) of 1000 grams

We have:

= (7/20) of (1000/1)

This can be written as,

= (1000/1) × (7/20)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (1000 × 7)/ (1 × 20)

On simplifying we get,

= (50×7)/ (1×1)

= 350 grams

(5/6) of an year

The above question can be written as,

= (5/6) of 12 months

We have:

= (5/6) of (12/1)

This can be written as,

= (12/1) × (5/6)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (12 × 5)/ (1 × 6)

On simplifying we get,

= (2×5)/ (1×1)

= 10 months

(1/6) of an hour

The above question can be written as,

= (1/6) of 60 min

We have:

= (1/6) of (60/1)

This can be written as,

= (60/1) × (1/6)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (60 × 1)/ (6 × 1)

On simplifying we get,

= (10×1)/ (1×1)

= 10 min

(6/7) of 35 liters

We have:

= (6/7) of (35/1)

This can be written as,

= (35/1) × (6/7)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (35 × 6)/ (1 × 7)

On simplifying we get,

= (5×6)/ (1×1)

= 30 liters

(4/9) of 54 meters

We have:

= (4/9) of (54/1)

This can be written as,

= (54/1) × (4/9)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (54 × 4)/ (1 × 9)

On simplifying we get,

= (6×4)/ (1×1)

= 24 meters

(5/11) of ₹ 220

We have:

= (5/11) of (220/1)

This can be written as,

= (220/1) × (5/11)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (220 × 5)/ (1 × 11)

On simplifying we get,

= (20×5)/ (1×1)

= ₹ 100

(3/20) of 1020

We have:

= (3/20) of (1020/1)

This can be written as,

= (1020/1) × (3/20)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (1020 × 3)/ (1 × 20)

On simplifying we get,

= (51×3)/ (1×1)

= 153

(7/50) of 1000

We have:

= (7/50) of (1000/1)

This can be written as,

= (1000/1) × (7/50)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (1000 × 7)/ (1 × 50)

On simplifying we get,

= (20×7)/ (1×1)

= 140

(5/9) of 45

We have:

= (5/9) of (45/1)

This can be written as,

= (45/1) × (5/9)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (45 × 5)/ (1 × 9)

On simplifying we get,

= (5×5)/ (1×1)

= 25

(3/4) of 32

We have:

= (3/4) of (32/1)

This can be written as,

= (32/1) × (3/4)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (32 × 3)/ (1 × 4)

On simplifying we get,

= (8×3)/ (1×1)

= 24

(1/3) of 24

We have:

= (1/3) of (24/1)

This can be written as,

= (24/1) × (1/3)

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

= (24 × 1)/ (1 × 3)

= (24/3)

= 8

[1(4/7)] × [1(13/22)] × [1(1/15)]

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

By Converting mixed fraction into improper fraction we get,

= (11/7) × (35/22) × (16/15)

= (11×35×16)/ (7×22×15)

On simplifying we get,

= (1×5×16) / (1×2×15)

Again simplifying we get,

= (1×1×8)/ (1×1×3)

= (8/3)

= [2(2/3)]

(8/9) ÷ (16)

We have,

= (8/9) ÷ (16/1)

= (8/9) × (1/16)

(Because reciprocal of (16/1) is (1/16)

= (8 × 1) / (9 × 16)

= (1 × 1) / (9 × 2)

= (1/18)

(i) (5/8)

Solution:-

Reciprocal of (5/8) is (8/5) [∵ ((5/8) × (8/5)) = 1]

(ii) 7

Solution:-

Reciprocal of 7 is (1/7) [∵ ((7/1) × (1/7)) = 1]

(iii) (1/12)

Solution:-

Reciprocal of (1/12) is (12/1) [∵ ((1/12) × (12/1)) = 1]

= 12

(iv) [12(3/5)]

Solution:-

Convert mixed fraction into improper fraction,

= (63/5)

Reciprocal of (63/5) is (5/63) [∵ ((63/5) × (5/63)) = 1]

[3(1/16)] × [7(3/7)] × [1(25/39)]

By the rule Multiplication of fraction,

Product of fraction = (product of numerator)/ (product of denominator)

Then,

By Converting mixed fraction into improper fraction we get,

= (49/16) × (52/7) × (64/39)

= (49×52×64)/ (16×7×39)

On simplifying we get,

= (7×4×4) / (1×1×3)

= (112)/ (3)

= [37(1/3)]

[3(3/5)] ÷ (4/5)

Convert mixed fraction into improper fraction,

= [3(3/5)] = (18/5)

We have,

= (18/5) ÷ (4/5)

= (18/5) × (5/4)

(Because reciprocal of (4/5) is (5/4)

= (18 × 5) / (5 × 4)

= (9 × 1) / (1 × 2)

= (9/2)

= [4(1/2)

(i) Given (3/8) by (5/9)

From the rule of division of fraction we know that (a/b) ÷ (c/d) = (a/b) × (d/c)

(3/8)/ (5/9) = (3/8) × (9/5)

= (3 × 9) / (8 × 5)

= (27/40)

(ii) Given 3 (1/4) by (2/3)

Converting 3 (1/4) to improper we get (13/4)

From the rule of division of fraction we know that (a/b) ÷ (c/d) = (a/b) × (d/c)

(13/4)/ (2/3) = (13/4) × (3/2)

= (13 × 3) / (4 × 2)

= (39/8)

= 4 (2/7)

(iii) Given (7/8) by 4 (1/2)

Converting 4 (1/2) to improper we get (9/2)

From the rule of division of fraction we know that (a/b) ÷ (c/d) = (a/b) × (d/c)

(7/8)/ (9/2) = (7/8) × (2/9)

= (7 × 2) / (8 × 9)

= (14/72)

= (7/36)

(iv) Given 6 (1/4) by 2 (3/5)

Converting 6 (1/4) and 2 (3/5) to improper we get (25/4) and (13/5)

From the rule of division of fraction we know that (a/b) ÷ (c/d) = (a/b) × (d/c)

(25/4)/ (13/5) = (25/4) × (5/13)

= (25 × 5) / (4 × 13)

= (75/52)

= 2 (21/52)

(a) 7/10 - .... = 3/10

..... = 7/10 - 3/10 = (7 - 3)/10 

= 4/10 = 2/5

(b) ... - 3/21 = 5/21

.... = 5/21 + 3/21 = (5 + 3)/21 

= 8/21

(c) .... - 3/6 = 3/6

.... = 3/6 + 3/6 = (3 + 3)/6 

= 6/6 = 1

(d) .... + 5/27 = 12/27

..... = 12/27 - 5/27 

= (12 - 5)/27 = 727

45 by [1(4/5)]

The above question can be written as,

= 45 ÷ [1(4/5)]

Convert mixed fraction into improper fraction,

= [1(4/5)] = (9/5)

We have,

= (45/1) × (5/9)

(Because reciprocal of (9/5) is (5/9)

= (45 × 5) / (1 × 9)

= (5 × 5) / (1 × 1)

= 25

(i) Given (3/8) by 4

= (3/8)/4

= (3/8 × 4)

= (3/32)

(ii) Given (9/16) by 6

= (9/16)/6

= (9/ 16 × 6)

= (9/ 96)

= (3/32)

(iii) Given 9 by (3/16)

= 9/ (3/16)

= (9 × 16)/3

= 16 × 3

= 48

(iv) Given 10 by (100/3)

= 10/ (100/3)

= (10 × 3)/100

= (3/10)

7 – [ 4 (2/3)]

Convert mixed fraction into improper fraction, and then find the difference.

= [4(2/3)] = (14/3)

= 7-(14/3)

= (21-14)/3

= (7/3)

= [2 (1/3)]

[ 3(3/10)] – [1(7/15)]

Convert mixed fraction into improper fraction, and then find the difference.

= [3(3/10)] = (33/10)

= [1(7/15)] = (22/15)

We get,

= (33/10) – (22/15)

LCM of 10, 15 = 30

Now, let us change each of the given fraction into an equivalent fraction having 10 as the denominator.

= [(33/10) × (3/3)] = (99/30)

= [(22/15) × (2/2)] = (44/30)

Then,

= (99/30) – (44/30)

= (99 -44)/30

= (55/30)

= (11/6)

= [1(5/6)]