WORKSHEET ON RATIONAL NUMBERS

Worksheet on rational numbers :

Rational numbers worksheet is much useful to the students who would like to practice problems on adding, subtracting, multiplying and dividing rational numbers.

Worksheet on rational numbers - Problems

1.  Add : (-2/3) + (-1/3)

2.  Add : (+2/5) + (+1/5)

3.  Add : (-4/5) + (+7/5)

4.  Add : (+5/9) + (-8/9)

5.  Subtract "2.5" from "3.5" using a number line.

6.  Subtract "1.5" from "4.5" using a number line.

7.  Subtract -1.5 from 2.5.

8.  Multiply -16 and -1/8.

9.  Multiply 2 and -1/4.

10.  Divide 2/3 by -7/6

11.  Divide 9/5 by 3

12.  Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?

13. During the day, the temperature increases by 4.5 degrees. At night, the temperature decreases by 7.5 degrees. What is the overall change in temperature?

14.  During the hottest week of the summer, the water level of the Muskrat River was 5/6 foot below normal. The following week, the level was 1/3 foot below normal. What is the overall change in the water level ?

15.  Gina hiked down a canyon and stopped each time she descended 1/2 mile to rest. She hiked a total of 4 sections. What is her overall change in elevation ?

16.  A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent ?

Worksheet on rational numbers - Solution

Problem 1 :

Solution :

Step 1 :

Find the absolute values.

|-2/3|  =  2/3 and  |-1/3|  =  1/3

Step 2 :

Find the sum of the absolute values :

2/3 + 1/3  =  (2+1) / 3

2/3 + 1/3  =  3/3

2/3 + 1/3  =  1

Step 3 :

Use the sign of the rational numbers to write the sum.

(-2/3) + (-1/3)  =  -1

Problem 2 :

Solution :

Step 1 :

Find the absolute values.

|+2/5|  =  2/5 and  |+1/5|  =  1/5

Step 2 :

Find the sum of the absolute values :

2/5 + 1/5  =  (2+1)/5

2/5 + 1/5  =  3/5

Step 3 :

Use the sign of the rational numbers to write the sum.

(+2/5) + (+1/5)  =  +3/5

Problem 3 :

Solution :

Step 1 :

Find the absolute difference of the rational numbers without the actual signs.

|4/5 - 7/5|  =  |-3/5|  =  3/5

Step 2 :

In the given two rational numbers 4/5 and 7/5, the sign of the bigger number is positive. So, we have to take positive sign to the answer.

Hence, (-4/5) + (+7/5)  =  +3/5

Problem 4 :

Solution :

Step 1 :

Find the absolute difference of the rational numbers without the actual signs.

|5/9 - 8/9|  =  |-3/9|  =  3/9  =  1/3

Step 2 :

In the given rational numbers 5 and 8, the sign of the bigger number is negative. So, we have to take negative sign to the answer.

Hence, (+5/9) + (-8/9)  =  -1/3

Problem 5 :

Subtract "2.5" from "3.5" using a number line.

Solution :

Since we subtract a positive rational number 2.5 from 3.5, we have to move 2.5 units in the negative direction from 3.5 on the number line as given in the picture below.

After having moved 2.5 units in the negative direction, we are in the position of "1"

Hence, 3.5 - (+2.5)  =  1

Problem 6 :

Subtract "1.5" from "4.5" using a number line.

Solution :

Since we subtract a positive rational number 1.5 from 4.5, we have to move 1.5 units in the negative direction from 4.5 on the number line as given in the picture below.

After having moved 1.5 units in the negative direction, we are in the position of "3"

Hence, 4.5 - (+1.5)  =  3

Problem 7 :

Subtract -1.5 from 2.5.

Solution :

Step 1 :

Since we subtract the negative rational number -1.5 from 2.5, we have to move 1.5 units from 2.5 in the positive direction on the number line.

It has been illustrated in the picture given below.

Step 2 :

After having moved 1.5 units in the positive direction from 2.5, we are in the position of "4"

Hence, 2.5 - (-1.5)  =  4

Problem 8 :

Multiply -16 and -1/8.

Solution :

Step 1 :

In the two rational numbers -16 and -1/8, the signs are same.

Step 2 :

Find the product of 16 and 1/8

16 x 1/8  =  16/8  =  16/8  =  2

Step 3 :

Since we multiply two rational numbers with the same sign, the result is always positive.

Hence, -16 x (-1/8)  =  2.

Problem 9 :

Multiply 2 and -1/4.

Solution :

Step 1 :

In the two rational numbers 2 and -1/4, the signs are different.

Step 2 :

Find the product of 2 and 1/4

2 x 1/4  =  2/4  =  1/2

Step 3 :

Since we multiply two rational numbers with different signs, the result is always negative.

Hence, 2 x (-1/4)  =  - 1/2.

Let us look at the next problem on "Worksheet on rational numbers".

Problem 10 :

Divide 2/3 by -7/6

Solution :

Step 1 :

Take the reciprocal of the second rational number.

-7/6 ---- reciprocal ----> -6/7

Step 2 :

Multiply the first rational number 2/3 by -6/7

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

Step 3 : Simplify

(2/1) x (-2/7)

Step 4 : Multiply

(2/1) x (-2/7)  =  -4/7    Positive times negative equals      negative

Hence, 2/3 ÷ -7/6  =  -4/7

Let us look at the next problem on "Worksheet on rational numbers".

Problem 11 :

Divide 9/5 by 3

Solution :

Step 1 :

Take the reciprocal of the second rational number.

---- reciprocal ----> 1/3

Step 2 :

Multiply the first rational number 9/5 by 1/3

(9/5) x (1/3)

Step 3 : Simplify

(3/5) x (1/1)

Step 4 : Multiply

(3/5) x (1/1)  =  3/5    Positive times positive equals   positive

Hence, 9/5 ÷ 3  =  3/5

Let us look at the next problem on "Worksheet on rational numbers".

Problem 12 :

Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?

Solution :

Step 1 :

Use positive numbers to represent the distance Malachi hiked.

Step 2 :

Find 2.5 + 1.5.

Let us use the real number line to add 2.5 and 1.5.

Step 3 :

Start at 2.5.

Step 4 :

Move 1.5 units to the right because the second addend is positive.

The result is 4.

Malachi hiked 4 miles.

Let us look at the next problem on "Worksheet on rational numbers".

Problem 13 :

During the day, the temperature increases by 4.5 degrees. At night, the temperature decreases by 7.5 degrees. What is the overall change in temperature?

Solution :

Step 1 :

Use a positive number to represent the increase in temperature and a negative number to represent a decrease in temperature.

Step 2 :

Find 4.5 + (-7.5).

Let us use the real number line to add 4.5 and (-7.5).

Step 3 :

Start at 4.5.

Step 4 :

Move | -7.5 | = 7.5 units to the left because the second addend is negative.

The result is -3.

The temperature decreased by 3 degrees overall.

Let us look at the next problem on "Worksheet on rational numbers".

Problem 14 :

During the hottest week of the summer, the water level of the Muskrat River was 5/6 foot below normal. The following week, the level was 1/3 foot below normal. What is the overall change in the water level ?

Solution :

Subtract to find the difference in water levels. That is, we have to find -1/3 - (-5/6)

Step 1 :

Since we subtract the negative rational number -5/6 from -1/3, we have to move 5/6 units from -1/3 in the positive direction on the number line.

It has been illustrated in the picture given below.

Step 2 :

After having moved 5/6 units in the positive direction from -1/3, we are in the position of "1/2"

Hence, the water level changed 1/2 foot.

Let us look at the next problem on "Worksheet on rational numbers".

Problem 15 :

Gina hiked down a canyon and stopped each time she descended 1/2 mile to rest. She hiked a total of 4 sections. What is her overall change in elevation?

Solution :

Step 1 :

Use a negative number to represent the change in elevation.

Step 2 :

Find 4 x (-1/2).

Step 3 :

Start at 0. Move 1/2 unit to the left 4 times.

The result is -2.

Hence, the overall change is -2 miles.

Check :

Use the rules for multiplying rational numbers.

4 x (-1/2) = - 4/2  A negative times a positive equals a the the the the te kdjhnegative.

4 x (-1/2) = - 2      Simplify

Let us look at the next problem on "Worksheet on rational numbers".

Problem 16 :

A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent ?

Solution :

To find how far she should travel in each descent, we have to divide 100 by 5.

Step 1 :

Take the reciprocal of the divisor 5.

---- reciprocal ----> 1/5

Step 2 :

Multiply 100 by 1/5

(100) x (1/5)

Step 3 : Simplify

(20) x (1/1)

Step 4 : Multiply

(20) x (1/1)  =  20

Hence, she should travel 20 feet in each descent.

After having gone through the stuff given above, we hope that the students would have understood "Worksheet on rational numbers".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6