Find five rational numbers between - 1 2 and 1 2 .

We convert - 1 2 and 1 2 into its equivalent fraction. Multiply 4 at both numerator and denominator of both numbers. - 4 2 × 4 ⇒ - 4 8 and 4 × 1 2 × 4 ⇒ 4 8 then rational numbers lies between - 1 2 and 1 2 are: - 4 8 < - 3 8 < - 2 8 < - 1 8 < 0 8 < 1 8 < 2 8 < 3 8 < 4 8 Hence, the five rational numbers lies between these two rational numbers i . e - 1 2 < - 3 8 < - 1 4 < - 1 8 < 0 < 1 8 < 1 2

A bus is moving at the speed of 40 2 5 km / h . How far will it travel in 6 2 3 hours? If the bus is still at a distance of 10 2 3 km from the final destination, how far is the final destination from the starting point?

Given, A bus moving with speed = 40 2 5 km / h Time = 6 2 3 hours Away from the final destination = 10 2 3 km Distance = speed × time i.e. Distance = 40 2 5 km / h × 6 2 3 h Distance = 202 5 × 20 3 km Distance = 4040 15 km = 808 18 km Distance = 269 1 3 km Total distance travel by bus = 808 3 km Distance between starting and final point = Total distance cover by bus + Remain distance Distance between starting and final point = 808 3 km + 10 2 3 km Distance between starting and final point = 808 3 + 32 3 km Distance between starting and final point = 808 + 32 3 = 840 3 = 280 km Hence, the result is 280 km .

If 3 5 of a number exceeds its 2 7 by 44 , find the number.

Let number is x . Then, 3 5 of the number = 3 5 x 2 7 of the number = 2 7 x According to the question, 3 x 5 - 2 x 7 = 44 ⇒ ( 3 x ) × 7 - ( 2 x ) × 5 35 = 44 ⇒ 11 x 35 = 44 ⇒ 11 x = 44 × 35 ⇒ x = 44 × 35 11 ⇒ x = 4 × 35 ⇒ x = 140 Hence, the number is 140 .

Which is longer and by how much, perimeter of a square of side 4 2 3 m or perimeter of a rectangle with length 5 1 5 m and breadth 3 2 5 m?

Given, Side of the square = 4 2 3 m Length of the rectangle = 5 1 5 m Breadth of the rectangle = 3 2 5 m We know that, Perimeter of square = 4 a So, perimeter of square = 4 × 4 2 3 m Perimeter of square = 4 × 14 3 m Perimeter of square = 56 3 m Perimeter of rectangle = 2 ( Length + Breadth ) Perimeter of rectangle = 2 ( 5 1 5 + 3 2 5 ) Perimeter of rectangle = 2 ( 26 5 + 17 5 ) Perimeter of rectangle = 2 × 43 5 = 86 5 m Clearly we can see that perimeter of square is larger than rectangle. So, 56 3 - 86 5 = 280 - 258 15 = 22 15 m Hence, the perimeter of square is longer by 22 15 m .

Tell what property allows you to compute 1 3 × 6 × 4 3 as 1 3 × 6 × 4 3 .

Given, 1 3 × 6 × 4 3 is computed as 1 3 × 6 × 4 3 . By using associative property of rational numbers under multiplication, for any rational numbers a , b and c we have, a × b × c = a × b × c Hence, the required property which allows the given computation is associative property.

Is 8 9 the multiplicative inverse of - 1 1 8 ? Why or why not?

Given numbers are 8 9 and - 1 1 8 . - 1 1 8 is equal to - 9 8 . And, - 9 8 × 8 9 = - 1 A multiplicative inverse or reciprocal for a number x , denoted by 1 x , is a number which when multiplied by x yields the multiplicative identity 1 . But, here we observe that the product is not 1 . Hence, 8 9 is not the multiplicative inverse of - 1 1 8 .

Represent - 2 11 , - 5 11 , - 9 11 on the number line.

- 2 11 , - 5 11 , - 9 11 i.e. - 2 11 , - 5 11 , - 9 11 all are likes between - 1 and 0 . Since we have 11 is the denominator, we divide the part between - 1 and 0 into 11 equal pars starting from 0 , the second, fifth and ninth to its left respectively represent - 2 11 , - 5 11 , - 9 11 Hence, the required number line is shown above.

E M B I B E

START UP MATHEMATICS>Chapter 1 - Rational Numbers>REVIEW EXERCISES>Q 9

EASY

8th CBSE

IMPORTANT

Earn 100

Represent the following rational numbers on a number line:

$\frac{1}{3}$

Important Questions on Rational Numbers

EASY

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 1 - Rational Numbers>REVIEW EXERCISES>Q 9

Represent the following rational numbers on a number line:

$\frac{- 7}{2}$

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 1 - Rational Numbers>REVIEW EXERCISES>Q 10

Find five rational numbers between

\frac{- 1}{2}

and

\frac{1}{2}

.

HARD

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 1 - Rational Numbers>THINKING SKILLS>Q 1

A bus is moving at the speed of $40 \frac{2}{5} km / h$ . How far will it travel in $6 \frac{2}{3}$ hours? If the bus is still at a distance of $10 \frac{2}{3} km$ from the final destination, how far is the final destination from the starting point?