HALFWAY BETWEEN THE TWO GIVEN RATIONAL NUMBERS

Problem 1 :

Find ten rational numbers between -2/5 and 1/2

Solution :

Since we are finding 10 rational numbers, let us use the second method.

Problem 2 :

Find five rational numbers between 2/3 and 4/5

Solution :

Since we are finding 5 rational numbers, let us use the second method.

Problem 3 :

Find five rational numbers between -3/2 and 5/3

Problem 4 :

Find five rational numbers between 1/4 and 1/2

Solution :

a = 1/4 and b = 1/2

Let c be the halfway between a and b.

a = 1/4 and b = 3/8

Let d be the halfway between a and b.

a = 1/4 and b = 5/16

Let e be the halfway between a and b.

Problem 5 :

Find each weighted average.

a. The coordinate 2 has a weight of 1, and the coordinate 8 has a weight of 2.

b. The coordinate 3 has a weight of 1, the coordinate 5 has a weight of 3, and the coordinate 9 has a weight of 2.

Solution :

a)

Weighted average = sum of weighted values / sum of weights

Here the weights are 1 and 2.

= [2(1) + 8(2)] / (1 + 2)

= (2 + 16)/3

= 18/3

= 6

b)

Weighted average = sum of weighted values / sum of weights

Here the weights are 3, 1 and 2.

= [3(1) + 5(3) + 9(2)] / (3 + 1 + 2)

= (3 + 15 + 18)/6

= 36/6

= 6

Problem 6 :

Identify the segment bisector of XY. Then find the length of XY.

Solution :

From the figure shown,

XM = MY

3x + 1 = 8x - 24

3x - 8x = -24 - 1

-5x = -25

x = 25/5

x = 5

Length of XY = 3x + 1 + 8x - 24

= 11x - 23

Applying the value of x, we get

= 11(5) - 23

= 55 - 23

= 32 units.

Problem 7 :

Identify the segment bisector of XY. Then find the length of XY.

Solution :

From the figure shown,

XM = MY

5x + 8 = 9x + 12

5x - 9x = 12 - 8

-4x = 4

x = -1

Length of XY = 5x + 8 + 9x + 12

= 14x + 20

Applying the value of x, we get

= 14(-1) + 20

= -14 + 20

= 6 units.

Problem 8 :

identify the segment bisector of line segment JK. Then find length of JM.

Solution :

From the given figure, JM = MK

7x + 5 = 8x

7x - 8x = -5

-x = -5

x = 5

Applying the value of x in JM, we get

JM = 7x + 5

= 7(5) + 5

= 35 + 5

= 40 units.

Problem 9 :

identify the segment bisector of line segment JK. Then find length of JM.

From the given figure, JM = MK

3x + 15 = 8x + 25

3x - 8x = 25 -15

-5x = -10

x = 10/5

x = 2

Applying the value of x in JM, we get

JM = 3x + 15

= 3(2) + 15

= 6 + 15

= 21 units.

Related Pages

• Find halfway between two rational numbers worksheet
• Rational numbers between two rational numbers