Chapter-9 Rational Numbers

Explanation:

To find five rational numbers between -1 and 0, we can use the following method:

Determine the difference between the two numbers: -1- 0 = -1

Divide the difference by the number of rational numbers we want to find plus 1. In this case, we want to find 5 rational numbers, so we divide -1 by 6:

-1÷6 = -0.1666666667

Add the result from Step 2 to the starting point (0), then continue to add this value to each

subsequent result to find the remaining numbers.

So the five rational numbers between -1 and 0 are:

-0.1666666667= -1/6

-0.3333333333= -1/3

-0.5= -1/2

-0.6666666667= -⅔

 -0.8333333333-5/6

Explanation:

To find five rational mumbers between -2 and -1, we can use the same method as before:

Determine the difference between the two numbers: -2-(-1)=-1

Divide the difference by the number of rational numbers we want to find plus L. In this case, we want to find 5 rational numbers, so we divide 1 by 6:

-1÷6= -0.1666666667

Add the result from Step 2 to the starting point (-2), then continue to add this value to each subsequent result to find the remaining numbers.

So the five rational numbers between 2 and -1 are:

-1.8333333333 

-1.6666666667

-1.5

-1.3333333333

-1.1666666667

Explanation:

To find five rational numbers between 4/5 and -2/3, we can use the same method as before:

Determine the difference between the two numbers: -2/3-(-4/5) = 2/15

Divide the difference by the number of rational numbers we want to find plus 1. In this case, we want to find 5 rational numbers, so we divide 2/15 by 6

2/15÷6=1/45

Add the result from Step 2 to the starting point (-4/5), then continue to add this value to each

subsequent result to find the remaining numbers.

So the five rational numbers between -4/5 and -2/3 are:

-0.8

-0.7666666667

-0.7333333333

-0.7

-0.6666666667

Explanation:

To find five rational numbers between-1/2 and 2/3, we can use the same method as before:

Determine the difference between the two numbers: 2/3 - (-1/2) = 7/6

Divide the difference by the number of rational numbers we want to find plus 1. In this case, we want to find 5 rational numbers, so we divide 7/6 by 6:

7/6÷6=7/36

Add the result from Step 2 to the starting point (-1/2), then continue to add this value to each

subsequent result to find the remaining numbers.

So the five rational numbers between -1/2 and 2/3 are:

-0.5

-0.4166666667

-0.3333333333

-0.25

-0.1666666667

Explanation:

Let's simplify -3/5, -6/10, -9/15,-12/20…… to its non-divisive form.

-3/5

-6/10=-3/5

-9/15=-3/5

-12/20-3/5

Since, each term obtained is a multiple of -3/5 and factors are {1/1,2/2,3/3,4/4...) 

Similarly, further numbers can be obtained by multiplying-3/5 from ( 5/5,6/6,7/7,8/8...)

Now next four terms are:

(-3/5)x(5/5)=(-15/25)

(-3/5) x(6/6)=(-18/30)

(-3/5)x(7/7)=(-21/35)

(-3/5)x(8/8)=(-24/40)

So these are the next four terms that can be derived by multiplying the numerator and denominator of -3/5 from 5,6,7 and 8.

Explanation:

Let's simplify -1/4, -2/8, -3/12 to its non-divisive form:

-1/4

-2/8=-1/4 

-3/12--1/4

Since each term obtained is a multiple of -1/4 and factors are (1/1,2/2,3/3, 4/4,...), we can obtain further numbers by multiplying -1/4 with (5/5,6/6, 7/7,8/8...).

Now the next four terms are:

(-1/4) x (4/4)=-4/16

(-1/4) x (5/5)=-5/20

(-1/4) x (6/6)=-6/24

(-1/4) × (7/7)=-7/28

So these are the next four terms that can be derived by multiplying the numerator and denominator of-1/4 from 4,5,6,and 7.

Explanation:

Let's simplify the given terms to their non-divisive form:

-1/6

2/-12=-1/6

3/-18=-1/6

4/-24=-1/6

Since each term obtained is a multiple of -1/6 and factors are (1/1,2/2,3/3,4/4, ...), we can obtain further numbers by multiplying -1/6 with (5/5,6/6, 7/7,8/8..).

Now the next four terms are:

(-1/6) x (5/5)=-5/30

(-1/6) x (6/6)=-6/36

(-1/6) x (7/7)=-7/42

(-1/6) x (8/8)=-8/48

So these are the next four terms that can be derived by multiplying the numerator and denominator of-1/6 from 5,6,7 and 8.

Explanation:

Let's simplify the given terms to their non-divisive form

-2/3

2/-3=-2/3

4/-6=-2/3

6/-9=-2/3

Since each term obtained is a multiple of -2/3 and factors are (1/1,2/2,3/3,4/4...), we can obtain further numbers by multiplying -2/3 with (4/4,5/5,6/6, 7/7...).

Now the next four terms are:

(-2/3)x(4/4)=-8/12

(-2/3)x(5/5)=-10/15

(-2/3)x(6/6)=-12/18

(-2/3)x(7/7)=-14/21

So these are the next four terms that can be derived by multiplying the numerator and denominator of-2/3 from 4,5,6 And 7

Explanation:

Next four terms can be obtained as a multiple of -2/7 

Let's multiply-2/7 by (1/1,2/2, 3/3,4/4...)

(-2/7) × 2/2=-4/14 

(-2/7) x 3/3=-6/21

(-2/7) x (4/4)=-8/28 

(-2/7) x (5/5)=-10/35

Thus the number obtained are as follows:

-4/14,-6/21,8/-28,10/-35.

Explanation:

Next four rational numbers equivalent to 5/-3 can be obtained by multiplying it with (2/2,3/3,4/4, 5/5) or any other integer multiples of them.

So.

5/-3 x 2/2 =10/-6

5/-3 x 3/3=15/-9

5/-3x4/4=20/-12

5/-3x5/5=25/-15

Thus, four rational numbers equivalent to 5/-3 are 10/-6, 15/-9, 20/-12, 25/-15,

Explanation:

Next four terms can be obtained as a multiple of 4/9.

Let's multiply 4/9 by (2/2,3/3, 4/4.5/5...)

(4/9)x(2/2) =8/18

(4/9)x(3/3) =12/27

(4/9)x(4/4) = 16/36 

(4/9)x(5/5) =20/45

Thus, the four rational numbers equivalent to 4/9 are 8/18, 12/27, 16/36, and 20/45.

Explanation:

> To represent the rational number 3/4 on a number line:

> We first need to divide the line segment between 0 and 1 into four equal parts.

>Then we can locate the point that corresponds to the number 3/4, which is three-fourths of the way from 0 to 1.

The point that represents 3/4 is located at a distance of 3/4 units from 0, and it is marked with an arrow

Explanation:

To represent-5/8 on a number line, we need to follow the below steps:

> Draw a horizontal line and mark the point 0 on it.

> Decide on a suitable scale for the number line, for example, we can use 1 unit for each

division.

> To represent negative numbers, we need to mark the negative direction. For that, draw an arrow to the left of 0.

> Divide the line into & equal parts and mark cach division as 1/8, 2/8, 3/8….. 7/8. 

>Since the number is negative, we need to move to the left from  on the number line.

We start from 0 and move 5 units to the left (because the numerator is 5). 

> The point where we end up is the representation of -5/8 on the number line.

The number line representation of -5/8 would look like this:

Explanation:

To represent -7/4 on the number line:

> Draw a horizontal line to represent the number line.

> Mark a point as zero in the middle of the line.

> Divide the line into equal parts by drawing ticks on both sides of zero. 

> Label the ticks as -1,-2,.-3,-4 on the left side and 1,2,3,4 on the right side.

>Locate -7/4 on the line by finding the point between -2 and -3 that is 3/4 of the way from -2 to -3

> To find this point, first mark -2 and -3 on the line.

> Then divide the distance between -2 and -3 into 4 equal parts. 

> Count three of these parts from -2 towards -3 to get the point that represents -7/4.

> Label this point as -7/4 on the line.

The final representation of 7/4 on the number line is a point to the left of -2 but to the right of -3 closer -2.

Explanation:

To represent 7/8 on a number line, we can follow these steps:

> Draw a horizontal line and mark a point at its center to represent zero.

 > Draw an arrow to the right to represent positive numbers and another arrow to the left to

represent negative numbers.

> Divide the line into eight equal parts.

> Starting from the zero point, mark the seventh part towards the positive duection, i,e.,

towards the arrow pointing right.

> Label the point as ⅞.

Explanation:

To check if two fractions represent the same rational number, we can simplify them and then compare

> (-7/21) can be simplified to (-1/3) by dividing the numerator and denominator by 7. 

> (39) can be simplified to (1/3) by dividing the numerator and denominator by 3.

Then,

-7/21=3/9

-1/3 =1/3

-1/3 ≠ 1/3

So, (-7/21) and (3/9) do not represent the same rational number since their simplified forms are different.

Explanation:

To check whether (-16/20) and (20-25) represent the same rational number, we can simplify both of them to lowest terms and see if they are equal:

(-16/20) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4. We get

(-16/20)=(-4/5)

(20-25) can be simplified by dividing both the numerator and denominator by their greatest

common factor, which is 5. We get:

(20/-25)=(-4/5)

Therefore,(1-16/20) and (20/-25) represent the same rational number, which is (-4/5).

Explanation:

To check whether (-2/-3) and (2/3) represent the same rational number, we can simplify both of them to lowest terms and see if they are equal:

(-2/-3) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1. We get:

(-2/-3)=2/3

Therefore, (-2/-3) and (2/3) represent the same rational number

Explanation:

To check whether (-3/5) and (-12/20) represent the same rational number, we can simplify both of them to lowest terms and see if they are equal:

(-3/5) cannot be simplified any further as the numerator and denominator do not have any common factors other than 1.

(-12/20) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4. We get:

(-12/20)=(-3/5)

Therefore, (-3/5) and (-12/20) represent the same rational number, which is (-3/5).

Explanation:

To check whether (8/-5) and (-24/15) represent the same rational number, we can simplify both of them to lowest terms and see if they are equal:

(8-5) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1. We get

(8/-5)=(-8/5)

(-24/15) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3. We get

(-24/15)=(-8/5)

Therefore, (8/-5) and (-24/15) represent the same rational number, which is (-8/5).

Explanation:

To check whether (1/3) and (19) represent the same rational number, we can simplify both of them to lowest terms and see if they are equal:

(1/3) cannot be simplified further as I and 3 do not have any common factors other than 1.

(-1/9) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1. We get

(-1/9)=(-1)/(3x3)

Therefore, (1/3) and (-1/9) do not represent the same rational number as they are not equal after simplification to lowest terms.

22. (-5/-9) and (5/-9)

Explanation:

To check whether (-51-9) and (5/9) represent the same rational number, we can simplify both of them to lowest terms and see if they are equal

(-5/9) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1. We get:

(5/-9)=-5/9

(5/-9) can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1. We get

(5/9)=5/9

Therefore, (-5/-9) and (5/-9) do not represent the same rational number.

Explanation:

To simplify -8/6,

we can divide both the numerator and denominator by their HCF, which is 2.

(-8÷ 2)/(6÷ 2)= -4/3

Therefore, -8/6 simplified to 4/3

Explanation:

To simplify -44/72.

we can divide both the numerater and denominator by their HCF, which is 4.

(-44÷ 4)/(72-4)=-11/18

Therefore, -44/72 simplified to -11/18

Explanation:

To simplify-8/10, we can divide both the numerator and denominator by their HCF, which is 2.

(-8÷ 2)/(10÷ 2)=-4/5

Therefore, -8/10 simplified to -4/5

Explanation:

To compare 2/3 and 5/2, we will convert them into like fractions by finding their LCM of the

denominators which is 6.

2/3 =4/6

5/2=15/6

Now, we can see that 15/6 is greater than 4/6. Therefore, 5/2 is greater than 2/3.

So, 5/2>2/3.

Explanation:

To compare -5/6 and -4/3, we will convert them into like fractions by finding their LCM of the denominators which is 6

-5/6=-5/6

Now by multiplying numerator and denominator of -4/3) by 2 we get.

-4/3=-8/6

Now, we can see that -5/6 is greater than -8/6. 

Therefore. 5/6 is greater than 4/3

So, -5/6 > 4/3.

Explanation:

To compare -3/4 and 24-3, we will convert them into like fractions by finding their LCM of the denominators which is 12.

-3/4=9/12 (multiplying numerator and denominator by 3) 

2/-3=-8/12 (multiplying numerator and denominator by 4 and changing the sign)

Now, we can see that -9/12 is less than -8/12. Therefore, 2-3 is greater than -3/4.

So, 2/-3>-3/4

Explanation:

To compare -1/4 and 1/4, we can see that they have the same denominators, so it is already a like fractions. We can directly compare their numerators.

Since -1/4 is a negative fraction, it is less than 9, and 1/4 is a positive fraction, it is greater than 0.

Therefore, 1/4 is greater than -1/4.

So, 1/4>-1/4

Explanation:

To compare -3(2/7) and -3(4/5), we can first simplify the mixed numbers by converting them into improper fractions.

-3(2/7)= -(37+2)/7=-23/7 

-3(4/5)=-(35+4)/5=-19/5

Now we can see that the denominators are different, so we need to find a common denominator to compare them. The LCM of 7 and 5 is 35, so we can convert both fractions to have a denominator of 35.

-23/7=(-23/7) × (5/5)=-115/35 

-19/5=(-19/5)x (7/7)=-133/35

Now we can see that -133/35 is less thin-115/35. Therefore, -3(4/5) is less than -3(2/7)

So.-3(2/7)>-3(4/5).

Explanation:

To write-3/5, -2/5, and 1/5 in ascending order, we can use the fact that negative fractions are less than 0 and compare the absolute values of the fractions,

|-3/5|= 3/5

|-2/5|=2/5

|-1/5|=1/5

Now we can see that 1/5 <2/5<3/5. Since the fractions are negative, we need to reverse the order to get them in ascending order.

Therefore,-3/5<-2/5 <-1/5 is the ascending order of the given rational numbers.

Explanation:

To write -1/3,-2/9, and -4/3 in ascending order, we can first convert them into like fractions by finding their LCM of the denominators which is 9.

-1/3=-3/9

-2/9=-2/9 

-4/3=-12/9\

Now we can see that -12/9 is the least among the three fractions since it has the smallest numerator.

Therefore, we have:

-12/9 <-3/9 <-2/9

But we need to convert these fractions back to their original form, so we can simplify them:

-12/9=-4/3

-3/9= -1/3 

-2/9=-2/9

Now we have the fractions in ascending order

4/3<-1/3<-2/9

Therefore, 4/3<-1/3<-2/9 is the ascending order of the given rational numbers.

Explanation:

To write -3/7,-3/2, and -3/4 in ascending order, we can find simplify them by finding their least common multiple (ICM) of the denominators which is 28.

-3/7=-12/28 

-3/2=-42/28

-3/4=-21/28

Now we can see that -42/28 is the least among the three fractions since it has the smallest numerator. Therefore, we have:

-42/28<-21/28 <-12/28

But we need to convert these fractions back to their original form, so we can simplify them:

-42/28=-3/2 

-21/28-3/4

-12/28=-3/7

Now we have the fractions in ascending order:

-3/2<-3/4<-3/7\

Therefore, -3/2 <-34 <-377 is the ascending order of the given rational numbers.

Explanation:

Find the least common multiple (LCM) of the denominators, which is 4,

Rewrite the fractions with a common denominator of 4:

(5/4)+(-11/4)-(5/4)+(-114) x (1/1)=(5/4)+(-11/4) x (1/1) x (4/4) = (5/4)+(-44/16)

Add the numerators while keeping the common denominator

(5/4)+(-44/16) (5 x 44 x4)+(-44/16)=(2016)+(-44/16)

Simplify the resulting fraction by adding the minerators:

(20/16)+1-44/16)=(-24/16)

Simplify the fraction by dividing both the numerator and denominator by their greatest common

factor, which is 8:

(-24/16)=(-24/8)+(16/8)=-3/2

Therefore, (5/4)+(-11/4) = -3/2

Explanation:

Find the least common multiple (LCM) of the denominators, which is 15.

Rewrite the fractions with a common denominator of 15:

(5/3)+(3/5)=(5/3) x (5/5) + (3/5) x (3/3)=(25/15)+(9/15)

Add the numerators while keeping the common denominator

(25/15)+(9/15)=(25+91/15

Simplify the resulting fraction by adding the mumerators:

(25+9/15=34/15

Simplify the fraction by dividing both the mumerator and denominator by their greatest common factor, which is 1:

34/15

Therefore, (5/3) + (3/5)=34/15.

Explanation:

Find the least common multiple (LCM) of the denominators, which is 30.

Rewrite the fractions with a common denominator of 30.

(-9/10) + (22/15)=(-9/10) x (3/3) + (22/15) x (2/2)=(-27/30) + (44/30)

Add the numerators while keeping the common denominator

(-27/30)+(44/30)=(44-27)/30

Simplify the resulting fraction by adding the numerators:

(44_27)/30=17/30

Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:

17/30

Therefore, (-9/10)+(22/15)=17/30.

Explanation:

Find the least common multiple (LCM) of the denominators, which is 99,

Rewrite the fractions with a common denominator of 99:

3/11+5/9=3/11 x (9/9)+5/9x (11/11)=27/99 + 55/99

Add the numerators while keeping the common denominator:

27/99 +55/99 = (27 +55)/99

Simplify the resulting fraction by adding the numerators:

(27+55)/99=82/99

Simplify the fraction by dividing both the numerator and denominator by their greatest common factor which is 1:

82/99

Therefore, 3/11+5/9=82/99.

Explanation:

Find the least common multiple (LCM) of the denominators, which is 57

Rewrite the fractions with a common denominator of 57:

(-8/19)+(-2/57) = (-8/19) x (3/3)+(-2/57) x (19/19)=(-24/57)+(-2/57)

Add the numerators while keeping the common denominator:

(-24/57)+(-2/57)=(-24-2)/57

Simplify the resulting fraction by adding the numerators:

(-24-2)/57=-26/57

Therefore, (-8/19)+(-2/57) = -26/57.

Explanation:

To add -2/3 and 0, we can rewrite 0 as an equivalent fraction with a denominator of 3:

0= 0/3

-2/3+ 0/3=-2/3+0=-2/3

Therefore, 2/3+0=-2/3.

Explanation:

To subtract these fractions, we need to find a common denominator. The least common multiple of 24 and 36 is 72.

Rewrite each fraction with a denominator of 72:

7/24=(7/24) x (3/3) x (2/2)=42/72

17/36=(17/36) x (2/2) x (2/3) = 34/72

Now we can subtract the fractions

7/24-17/36=42/72-34/72

Simplify by subtracting the numerators

=8/72

Reduce the fraction by dividing both the numerator and denominator by their greatest common factor, which is 8:

=1/9

Therefore, 7/24-17/36=1/9

Explanation:

We can rewrite -6/21 as-2/7

5/63-(-2/7)

To subtract fractions, we need to find a common denominator. The least common multiple of 63 and 7 is 63.

Rewrite each fraction with a denominator of 63.

5/63=5/63 x 1=5/63

-2/7=-2/7 x 99=-18/63

Now we can subtract the fractions

5/63-(-27)=5/63+ 18/63

Simplify by adding the numerators

Therefore, 5/63-(-6/21)=23/63.

Explanation:

To subtract these fractions, we need to find a common denominator. The least common multiple of 13 and 15 is 195.

Rewrite each fraction with a denominator of 195:

-6/13= (-6/13) x (15/15) x (3/3)=-90/195

-7/15=(-7/15) x (13/13) x (3/3)=-91/195

Now we can subtract the fractions:

-6/13-(-7/15)=-90/195+91/195

-7/15=(-7/15)x(13/13)x(3x3)=-91/195

Now we can subtract the fractions:

-6/13-(-7/15)=-90/195+91/195

Simplify by adding the numerators:

=1/195

Therefore, 6/13-(-7/15) = 1/195

Explanation:

To subtract these fractions, we need to find a common denominator. The least common multiple of 8 and 11 is 88.

Rewrite each fraction with a denominator of 88:

-3/8=(-38) x (11/11) x (11/11)=-33/88

7/11 = (7/11) x (8/8) x (11/11) = 56/88

Now we can subtract the fractions

-3/8-7/11=-33/88 - 56/88

Simplify by subtracting the numerators:

=-89/88

Therefore, 3/8-7/11=-89/88.

Explanation:

we need to first convert the mixed number to an improper fraction:

-2(7/9)=-(2 x9+1)/9=-19/9

Now we can rewrite the expression as

-19/9-6

To subtract fractions, we need to find a common denominator. The least common multiple of 9 and 1 is 9.

Rewrite the second fraction with a denominator of 9:

6=6/1 x 9/9=54/9

Now we can subtract the fractions:

-19/9-54/9=-73/9

Therefore, -2(1/9)-6=-73/9,

Explanation:

To find the product of (9/2) and (-7/4), we need to multiply the numerators together and the

denominators together.

(9/2)x(-7/4)=(9x-7)/(2x4)=-63/8

So the product of (9/2) and (-7/4) is-63/8

Explanation:

For the problem (-6/5) x (9/11), we can multiply the numerators and denominators separately as follows:

(-65)x(9/11)=-6x9)/(5x11)

Simplifying the numerator, we get:

=-54/55

Therefore, the product of (-6/5) and (9/11) is-54/5S

Explanation:

To find the product of ( 6/5) and (9/11), we multiply their numerators and denominators separately as follows:

(-6/5) x (9/11)=(-6x9)/(5x11)

Simplifying the numerator, we get:

=-54/55

Therefore, the product of (-6/5) und (9/11) is -54/55.

Explanation:

To find the product of ( 6/5) and (9/11), we multiply their numerators and denominators separately as follows:

(-6/5) x (9/11)=(-6x9)/(5x11)

Simplifying the numerator, we get:

=-54/55

Therefore, the product of (-6/5) und (9/11) is -54/55.

Explanation:

For the problem (3/11) x (2/5), we can multiply the numerators and denominators separately as follows:

(3/11)x(2/5)=(3x2)/(11×5)

Simplifying the numerator, we get:

6/55

Therefore, the product of (3/11) and (2/5) is 6/55.

Explanation:

For the problem (3-5)x(-5/3), we can multiply the numerators and denominators separately a

follows.

(3-5) x (-5/3)=(3x-5)/(-5×3)

Simplifying the numerator and denominator, we get.

-15/-15

Simplifying further by canceling out the common factor of -15 in the numerator and denominator,

we get:

Therefore, the product of (3-5) and (-5/3) is 1.

Explanation:

To divide by a fraction, we can multiply by its reciprocal (flip the fraction upside down). So, we have:

(-4)-(2/3)=(-4)x(3/2)

Now, we can simplify by multiplying the numerator and denominator:

(4)x(3/2)=(-12/2)=-6

Therefore, (-4)+ (2/3) = -6.

Explanation:

To divide a fraction by a whole number, we can convert the whole number into a fraction by putting it over 1. So, we have:

(-4/5)+(-3/1)

Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite the above

expression as

(-4/5) x (-1/3)

To multiply two fractions, we multiply their numerators together and their denominators together. So we have:

((-4)x(-1))/((5)× (3))

Simplifying the numerator and denominator, we get:

4/15

Therefore, (-4/5)+(-3)=4/15.

Explanation:

To divide two fractions, we need to invert the second fraction and multiply it with the first fraction.

Therefore

(-1/8) + (3/4) = (-1/8) × (4/3)

Now we can multiply the numerators and denominatists separately:

(-1/8) x (4/3)=(-1x4)/(x3)

Simplifying the numerator, we get:

24

Reducing the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4, we get:

-1/6

Therefore, (-1/8)+(34)=-1/6,

Explanation:

To divide national numbers, we can multiply the first number by the reciprocal of the second number. Thus, we have:

(3/13)+(-4/65)=(3/13) x (-65/4)

Multiplying the numerators and denominators, we get:

=(3x-65)/(13x4)

Simplifying the numerator, we get:

=-195/52

We can reduce the fraction by dividing both the numerator and denominator by their greatest common factor, which is 13:

-15/4

Therefore, (-7/12)+(-2/13)=-154