Find the value of 31 1 6 × 31 5 6 by using Ekaadhiken Purven Sutra.

To find the value of 31 1 6 × 31 5 6 by using Ekaadhiken Purven Sutra: Now, 31 1 6 × 31 5 6 = 31 × 31 + 1 / 1 6 × 5 6 ⇒ 31 1 6 × 31 5 6 = 31 × 32 / 5 36 ⇒ 31 1 6 × 31 5 6 = 992 5 36 .

Multiply 3 7 ÷ 21 and write the solution in mixed fraction.

Given, 3 7 ÷ 21 Take the reciprocal of the divisor → 1 21 Multiply the dividend and the reciprocal of the divisor. That is, 3 7 × 1 21 = 3 1 147 49 = 1 49 Therefore, the required answer is 1 49 .

Vikas can cover a distance of 20 2 3 km in 7 3 4 hours on foot. How many km per hour does he walk?

Given, The distance covered by Vikas in 7 3 4 hours = 20 2 3 km Conversion of mixed fraction to improper fraction is given by Denominator × Quotient + Remainder Denominator Therefore, 20 2 3 = 62 3 and 7 3 4 = 31 4 So, the distance covered by him in 1 hour = 20 2 3 ÷ 7 3 4 km = 62 3 ÷ 31 4 km = 62 3 × 4 31 km = 2 × 4 3 km = 8 3 km Conversion of improper fraction into mixed fraction is given by Quotient Remainder Denominator . If we divide 8 ÷ 3 , we get Quotient = 2 Remainder = 2 Therefore, 8 3 km = 2 2 3 km Therefore, the distance covered by Vikas per hour is 2 2 3 km .

Given, 9 7 ÷ 3 Take the reciprocal of the divisor → 1 3 Multiply the dividend and the reciprocal of the divisor. That is, 9 7 × 1 3 = 9 3 21 7 = 3 7 Therefore, the required answer is 3 7 .

Given, 2 5 ÷ 2 Take the reciprocal of the divisor → 1 2 Multiply the dividend and the reciprocal of the divisor. That is, 2 5 × 1 2 = 2 1 10 5 = 1 5 Therefore, the required answer is 1 5 .

18 boxes of nails weigh equally and their total weight is 49 1 2 kg . How much does each box weigh?

Given: Weight of 18 boxes of nails = 49 1 2 kg Conversion of mixed fraction to improper fraction is given by Denominator × Quotient + Remainder Denominator Therefore, 49 1 2 = 99 2 So, Weight of 1 box = 99 2 ÷ 18 kg = 99 2 × 1 18 kg [∵ Reciprocal of 18 = 1 18 ] = 99 × 1 2 × 18 kg = 11 × 1 2 × 2 kg = 11 4 kg Conversion of improper fraction into mixed fraction is given by Quotient Remainder Denominator . If we divide 11 ÷ 4 , we get Quotient = 2 Remainder = 3 Therefore, 11 4 = 2 3 4 Therefore, the weight of each box is 2 3 4 kg .

Preeti bought 8 1 2 kg of sugar for ₹ 242 1 4 . Find the price of sugar per kilogram.

Given, The cost of 8 1 2 kg of sugar is ₹ 242 1 4 . Conversion of mixed fraction to improper fraction is given by Denominator × Quotient + Remainder Denominator Therefore, 8 1 2 = 17 2 and 242 1 4 = 969 4 That is, the cost of 17 2 kg of sugar = ₹ 969 4 So, the cost of 1 kg of sugar is, = 969 4 ÷ 17 2 = 969 4 × 2 17 = 57 2 Conversion of improper fraction into mixed fraction is given by Quotient Remainder Denominator . If we divide 57 ÷ 2 , we get Quotient = 28 Remainder = 1 ⇒ 57 2 = 28 1 2 Therefore, the cost of sugar is ₹ 28 1 2 per kilogram.

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Divide:
$\frac{5}{6} \div \frac{5}{6} =$

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Important Questions on Fractions and Decimals

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

Three numbers are in the ratio

\frac{3}{4} : \frac{5}{8} : \frac{7}{12}

. If the difference between the greatest and the smallest number is

48

, then the value of the greater number will be:

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

A fraction is such that the numerator is five less than the denominator. Also four times the numerator is one more than the denominator. The fraction is:

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

A man covers

\frac{5}{12}

of a total journey by train,

\frac{7}{18}

of the journey by bus and the remaining

7 km

on foot. His total journey is:

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

Which one of the following fractions will have minimum change in its value if

3

is added to both the numerator and the denominator of all the fractions?

MEDIUM

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

$\frac{(a - b)^{3} + (b - c)^{3} + (c - a)^{3}}{3 (a - b) (b - c) (c - a)} = ?$

What is the value of above expression?

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

A school group charters three identical buses and occupies

\frac{4}{5}

of the seats. After

\frac{1}{4}

of the passengers leave, the remaining passengers use only two of the buses. The fraction of the seats on the two buses that are now occupied is

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

Find the value of

31 \frac{1}{6} \times 31 \frac{5}{6}

by using Ekaadhiken Purven Sutra.

EASY

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

By mistake, the reciprocal of a positive fraction got typed in place of itself, and thereby its value got reduced by

\frac{175}{4} %

. What was the value of the fraction?

MEDIUM

Mathematics>Arithmetic>Fractions and Decimals>Division of Fractions

A cake is distributed among 5 friends. Four of them get $\frac{1}{8}, \frac{1}{6}, \frac{5}{12}$ and $\frac{1}{12}$ , and as shares. What part of the cake will be got by the fifth friend?