# OPERATIONS WITH RATIONAL NUMBERS WORKSHEET

## About "Operations with rational numbers worksheet"

Operations with rational numbers worksheet :

Worksheets on operations with rational numbers is much useful to the students who would like to practice problems on rational numbers.

## Operations with rational numbers worksheet

1.  Simplify : 2/5 + 3/5

2.  Simplify : 7/5 - 3/5

3.  Simplify : 1/8 + 1/3

4.  Simplify : 5/12 + 1/20

5.  Convert the fraction 17/5 into mixed number

6.  Multiply 2/3 and 4/5

7.  Divide 6 by 2/5

8.  Divide 1/5 by  3/7

9.  Lily earned \$54 mowing lawns in two days. She worked 2.5 hours yesterday and 4.25 hours today. If Naomi was paid the same amount for every hour she works, how much did she earn per hour ?

10.  David traveled from A to B in 3 hours at the rate of 50 miles per hour. Then he traveled from B to C in 2 hours at the rate of 60 miles per hour. What is the average speed of David from A to C ?

11.  Each part of a multipart question on a test is worth the same number of points. The whole question is worth 37.5 points. Daniel got 1/2 of the parts of a question correct. How many points did Daniel receive ?

12.  The bill for a pizza was \$14.50. Charles paid for 3/5 of the bill. How much did he pay ?

## Operations with rational numbers worksheet - Solutions

Problem 1 :

Simplify : 2/5 + 3/5

Solution :

Here, for both the fractions, we have the same denominator, we have to take only one denominator and add the numerators.

Then, we get

2/5 + 3/5  =  (2+3) / 5  =  5/5  =  1

Problem 2 :

Simplify : 7/5 - 3/5

Solution :

Here, for both the fractions, we have the same denominator, we have to take only one denominator and subtract the numerators.

Then, we get

7/5 - 3/5  =  (7-3) / 5  =  4/5

Problem 3 :

Simplify : 1/8 + 1/3

Solution :

In the given two fractions, denominators are 8 and 3.

For 8 and 3, there is no common divisor other than 1.

So 8 and 3 are co-prime.

Here we have to apply cross-multiplication method to add the two fractions 1/8 and 1/3 as given below.

Hence, 1/8 + 1/3  =  11/24

Problem 4 :

Simplify : 5/12 + 1/20

Solution :

In the given two fractions, denominators are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

2 & 4

So 12 and 20 are not co-prime.

In the next step, we have to find the L.C.M (Least common multiple) of 12 and 20.

12 =  2² x 3

20 = 2² x 5

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20.

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 = 2² x 3 x 5

= 4 x 3 x 5

= 60

Now we have to make the denominators of both the fractions to be 60 and add the two fractions 5/12 and 1/20 as given below.

Hence, 5/12 + 1/20  =  7/15

Problem 5 :

Convert the fraction 17/5 into mixed number.

Solution :

The picture given below clearly illustrates, how to convert the fraction 17/5 into mixed number.

Hence, 17/5  =  3 2/5

Problem 6 :

Multiply 2/3 and 4/5.

Solution :

To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators.

That is,

2/3 x 4/5   =  8/15

Problem 7 :

Divide 6 by 2/5.

Solution :

To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.

That is,

÷  2/5  =  6 x 5/2  =  30/2  =  15

Problem 8 :

Divide 1/5 by  3/7

Solution :

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.

That is,

1/5 ÷  3/7  =  1/5 x 7/3  =  7/15

Problem 9 :

Lily earned \$54 mowing lawns in two days. She worked 2.5 hours yesterday and 4.25 hours today. If Naomi was paid the same amount for every hour she works, how much did she earn per hour ?

Solution :

Analyze Information :

Identify the important information.

• Naomi made \$54 mowing lawns.

• Naomi worked 2.5 hours yesterday and 4.25 hours today.

• We are asked to find how much she earned per hour

Formulate a plan :

• The total amount she earned divided by the total hours she worked gives the amount she earns per hour.

• Use the expression 54 ÷ (2.5 + 4.25) to find the amount she earned per hour.

Solve :

(2.5 + 4.25)  =  6.75  ---- > (Add inside parentheses)

54 ÷ 6.75  =  8 ---- > (Divide)

Lily earned \$8 per hour mowing lawns.

Let us look at the next problem on "Operations with rational numbers worksheet"

Problem 10 :

David traveled from A to B in 3 hours at the rate of 50 miles per hour. Then he traveled from B to C in 2 hours at the rate of 60 miles per hour. What is the average speed of David from A to C ?

Solution :

Analyze Information :

Identify the important information.

• David traveled from A to B in 3 hours @ 50 mph.

• David traveled from B to C in 2 hours @ 60 mph.

• We are asked to find the average speed from A to C.

Formulate a plan :

• The total distance covered from A to C divided by total time taken gives the average speed from A to C.

• Use the expression (3 x 50) + (2 x 60)  to find the total distance from A to C.

That is, 270 miles

• Use the expression (3 + 2)  to find the total time taken from A to C.

That is, 5 hours

Solve :

Divide the total distance (A to C) by the total time taken (A to C)

270 ÷ 5  =  54 ---- > (Divide)

Hence, the average speed from A to C is 54 miles per hour.

Let us look at the next problem on "Operations with rational numbers worksheet"

Problem 11 :

Each part of a multipart question on a test is worth the same number of points. The whole question is worth 37.5 points. Daniel got 1/2 of the parts of a question correct. How many points did Daniel receive ?

Solution :

To find the total points received by Daniel, we have to multiply 1/2 and 37.5

Step 1 :

Convert the decimal 3.75 as the fraction 75/2

(1/2) x 37.5  =  (1/2) x (75/2)

Step 2 :

Multiply. Write the product in simplest form.

(1/2) x (75/2)  =  75/4  =  18 3/4

Hence, Daniel received 18 3/4 points.

Let us look at the next problem on "Operations with rational numbers worksheet"

Problem 12 :

The bill for a pizza was \$14.50. Charles paid for 3/5 of the bill. How much did he pay ?

Solution :

To find the amount paid by Charles, we have to multiply 3/5 and 14.50

Step 1 :

Convert the decimal 14.50 as the fraction 29/2

(3/5) x 14.50  =  (3/5) x (29/2)

Step 2 :

Multiply. Write the product in simplest form.

(3/5) x (29/2)  =  87/10  =  8 7/10

Hence, Charles paid \$8 7/10.

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

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