**Solving problems with rational numbers worksheets :**

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

1. The area of a rectangular sandbox is 56 2/3 square feet. The length of the sandbox is 8 1/2 feet. What is the width ?

2. Mr. Webster is buying carpet for an exercise room where the basement of the room is in the shape of rectangle. The length and width of the room are 18 2/5 feet and 12 1/2 feet respectively. Find the total cost of the carpet, if the price of the carpet is $3 per square feet ?

3. Mr. Webster is buying carpet for an exercise room where the basement of the room is in the shape of rectangle. The length and width of the room are 18 2/5 feet and 12 1/2 feet respectively. Find the total cost of the carpet, if the price of the carpet is $3 per square feet ?

4. David is cooking enough lentils for lentil barley soup and lentil salad. The lentil barley soup recipe calls for 3/4 cup of dried lentils. The lentil salad recipe calls for 1 1/2 cups of dried lentils. David has a 1/8 -cup scoop. How many scoops of dried lentils will David need to have enough for the soup and the salad?

5. If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 1. In case, the numerator is decreased by 4 and the denominator by 2, it becomes 1/2. Find the fraction.

**Problem 1 : **

The area of a rectangular sandbox is 56 2/3 square feet. The length of the sandbox is 8 1/2 feet. What is the width ?

**Solution :**

We know the formula to find area of the rectangle.

That is,

Area of the rectangle = length x width

Plug the known values area and length and solve for the unknown value width.

56 2/3 = 8 1/2 x width

170/3 = 17/2 x width

(170/3) x (2/17) = width

20/3 = width

6 2/3 = width

Therefore, the width of the rectangle is 6 2/3 feet.

Let us look at the next problem on "Solving problems with rational numbers worksheets"

**Problem 2 : **

Mr. Webster is buying carpet for an exercise room where the basement of the room is in the shape of rectangle. The length and width of the room are 18 2/5 feet and 12 1/2 feet respectively. Find the total cost of the carpet, if the price of the carpet is $3 per square feet ?

**Solution :**

To know the total cost of the carpet, first we have to know the area of the basement.

Area of the basement = length x width

= 18 2/5 x 12 1/2

= (92/5) x (25/2)

= 46 x 5

= 230 square feet

So, we need 230 square feet of carpet.

The cost each square feet of carpet = $3

Then, the cost of 230 square ft of carpet is

= 3 x 230

= $690

Therefore, the total cost of the carpet is $690

Let us look at the next problem on "Solving problems with rational numbers worksheets"

**Problem 3 : **

Mr. Webster is buying carpet for an exercise room where the basement of the room is in the shape of rectangle. The length and width of the room are 18 2/5 feet and 12 1/2 feet respectively. Find the total cost of the carpet, if the price of the carpet is $3 per square feet ?

**Solution :**

To know the total cost of the carpet, first we have to know the area of the basement.

Area of the basement = length x width

= 18 2/5 x 12 1/2

= (92/5) x (25/2)

= 46 x 5

= 230 square feet

So, we need 230 square feet of carpet.

The cost each square feet of carpet = $3

Then, the cost of 230 square ft of carpet is

= 3 x 230

= $690

Therefore, the total cost of the carpet is $690

Let us look at the next problem on "Solving problems with rational numbers worksheets"

**Problem 4 : **

David is cooking enough lentils for lentil barley soup and lentil salad. The lentil barley soup recipe calls for 3/4 cup of dried lentils. The lentil salad recipe calls for 1 1/2 cups of dried lentils. David has a 1/8 -cup scoop. How many scoops of dried lentils will David need to have enough for the soup and the salad?

**Solution :**

David needs 3/4 cup of dried lentils for soup and 1 1/2 cups for salad.

Total amount dried lentils that David need is

= (3/4) + (1 1/2)

= 3/4 + 3/2

= 3/4 + 6/4

= (3+6) / 4

= 9/4

David needs 9/4 cups of dried lentils for both the soup and the salad.

To find how many 1/8 -cup scoops he needs, divide the total amount of dried lentils into groups of 1/8.

Then, we have

= 9/4 ÷ 1/8

= 9/4 x 8/1

= 9 x 2

= 18

Hence, David will need 18 scoops of dried lentils to have enough for both the lentil barley soup and the lentil salad.

Let us look at the next problem on "Solving problems with rational numbers worksheets"

**Problem 5 :**

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 1. In case, the numerator is decreased by 4 and the denominator by 2, it becomes 1/2. Find the fraction.

**Solution :**

Let "x/y" be the required fraction.

"If the numerator is increased by 2 and the denominator by 1, the fraction becomes 1"

From the above information, we have (x+2) / (y+1) = 1

(x+2) / (y+1) = 1 -----> x+2 = y+1 ----->** x-y = -1 ---(1)**

"In case the numerator is decreased by 4 and the denominator by 2, the fraction becomes 1/2"

From the above information, we have (x-4) / (y-2) = 1/2

(x-4) / (y-2) = 1/2 ---> 2(x-4) = y-2 --->** 2x-y = 6---(1)**

Solving (1) and (2), we get x = 7 and y = 8

So, x/y = 7/8

Hence, the required fraction is 7/8

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

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