Simplify the following: 3 5 - 6 10 ÷ - 1 2 + - 2 5

We need to find the value of 3 5 - 6 10 ÷ - 1 2 + - 2 5 First, we will solve the brackets We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ 3 5 - 6 10 ÷ - 1 2 + - 2 5 LCM of 5 , 10 = 10 and 2 , 5 = 10 ⇒ 3 × 2 5 × 2 - 6 × 1 10 × 1 ÷ - 1 × 5 2 × 5 + - 2 × 5 5 × 2 ⇒ 6 10 - 6 10 ÷ - 5 10 + - 10 10 ⇒ 0 ÷ - 5 - 10 10 ⇒ 0 Hence, 0 is the required answer.

Simplify the following: 3 5 - 6 10 ÷ - 1 2 + - 2 5

We need to find the value of 3 5 - 6 10 ÷ - 1 2 + - 2 5 First, we will solve the brackets We know that, to add or subtract fractions first convert them into like fractions and then add or subtract the numerators by keeping the denominator same. ⇒ 3 5 - 6 10 ÷ - 1 2 + - 2 5 LCM of 5 , 10 = 10 and 2 , 5 = 10 ⇒ 3 × 2 5 × 2 - 6 × 1 10 × 1 ÷ - 1 × 5 2 × 5 + - 2 × 5 5 × 2 ⇒ 6 10 - 6 10 ÷ - 5 10 + - 10 10 ⇒ 0 ÷ - 5 - 10 10 ⇒ 0 Hence, 0 is the required answer.

What should be added to - 1 6 to obtain the nearest natural number?

Natural numbers are a part of the number system, including all the positive numbers from 1 to infinity. Now, we are asked that what should be added to - 1 6 to obtain the nearest natural number. The nearest natural number to - 1 6 is 1 . Let us assume the number to be x ⇒ x - 1 6 = 1 ⇒ x = 1 + 1 6 LCM of 1 , 6 = 6 ⇒ x = 1 6 + 1 = 1 × 1 6 × 1 + 1 × 6 1 × 6 ⇒ x = 1 + 6 6 ⇒ x = 7 6 That means the required answer is 7 6 .

From of a rope 13 m long, two pieces of length 13 5 m and 33 10 m are cut off. What is the length of the remaining rope?

Given, Total length of rope = 13 m Length of first piece = 13 5 m Length of second piece = 33 10 m Length of the remaining rope = Total length of the rope - Sum of the lengths of two pieces = 13 - 13 5 + 33 10 m = 13 - 13 5 × 10 10 + 33 10 × 5 5 m = 13 - 130 50 + 165 50 m = 13 - 130 + 165 50 m = 13 1 - 295 50 m = 13 1 × 50 50 - 295 50 × 1 1 m = 650 50 - 295 50 m = 650 - 295 50 m = 355 71 50 10 m = 71 10 = 7 1 10 m Hence, the length of the remaining rope is 7 1 10 m .

A drum full of rice weighs 241 6 kg . If the empty drum weighs 55 4 kg , find the weight of rice in the drum.

Given, Weight of a full drum of rice = 241 6 kg Weight of empty drum = 55 4 kg Weight of rice in the drum = Weight of a full drum of rice - Weight of empty drum = 241 6 - 55 4 kg L.C.M. of 6 and 4 = 12 Now, by converting into equivalent rational numbers with the same denominator, we get, = 241 6 × 2 2 - 55 4 × 3 3 kg = 482 12 - 165 12 kg = 317 12 kg = 26 5 12 kg ∴ Weight of rice in the drum is 26 5 12 kg .

A basket contains three types of fruits weighing 58 3 kg in all. If 73 6 kg of these be apples, 17 6 kg be mangoes and rest pears, then what is the weight of pears in the basket?

Given, Total weight of three types of fruits = 58 3 kg Weight of apples = 73 6 kg Weight of mangoes = 17 6 kg We have to find the weight of the pears in the basket, Weight of pears in the basket = Total weight of fruits - Sum of the weights of apples and mangoes = 58 3 - 73 6 + 17 6 kg = 58 3 - 73 + 17 6 kg = 58 3 - 90 6 kg = 58 3 × 2 2 - 90 6 × 1 1 kg = 116 6 - 90 6 kg = 26 6 kg = 13 3 = 4 1 3 kg ∴ Weight of the pears in the basket is 4 1 3 kg .

E M B I B E

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 5

EASY

7th ICSE

IMPORTANT

Earn 100

Simplify the following:

$(\frac{3}{5} - \frac{6}{10}) \div (\frac{- 1}{2} + \frac{- 2}{5})$

Important Questions on Rational numbers

EASY

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 6

What should be added to

\frac{- 1}{6}

to obtain the nearest natural number?

EASY

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 7

What must be subtracted from

\frac{- 1}{2}

to obtain the nearest integer?

HARD

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 1

From of a rope $13 m$ long, two pieces of length $\frac{13}{5} m and \frac{33}{10} m$ are cut off. What is the length of the remaining rope?

HARD

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 2

A drum full of rice weighs $\frac{241}{6} kg$ . If the empty drum weighs $\frac{55}{4} kg$ , find the weight of rice in the drum.

HARD

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 3

A basket contains three types of fruits weighing $\frac{58}{3} kg$ in all. If $\frac{73}{6} kg$ of these be apples, $\frac{17}{6} kg$ be mangoes and rest pears, then what is the weight of pears in the basket?

HARD

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 4

At city M, temperature was $- 7 \frac{1}{2} ° C$ on Monday and then it dropped by $2 \frac{1}{3} ° C$ on Tuesday. What was the temperature on Tuesday? On Wednesday, it rose by $4 \frac{2}{5} ° C$ . What was the temperature on Wednesday?

HARD

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 5

In a movie, $\frac{1}{2}$ of the audience were men and $\frac{1}{2}$ of the remaining were women. If $\frac{1}{5}$ of the women were school girls and the total audience were $600$ in number, then how many were school girls?

HARD

7th ICSE

IMPORTANT

Cambridge connection Mathematics>Chapter 4 - Rational numbers>Let's Practice>Q 6

A plane is flying at the height of $5000 \frac{2}{3} m$ above the sea level. At a particular point, it is exactly above a submarine floating $1200 \frac{3}{4} m$ below the sea level. What is the vertical distance between them?