CONVERTING MIXED FRACTIONS TO DECIMALS WORKSHEET

Covert the following mixed fractions to decimals.

Problem 1 :

3 3/20

Problem 2 :

5 7/10

Problem 3 :

9 3/50

Problem 4 :

9 1/2

Problem 5 :

24 3/4

Problem 6 :

5 2/3

Problem 7 :

7 3/8

Problem 8 :

27 5/6

Problem 9 :

13 4/9

Problem 10 :

1 5/8

Find the area of the triangle given below.

Problem 11 :

Problem 12 :

Problem 13 :

A cube is made with sides of length 1  1/2 cm. Find the volume and surface area of the cube.

Problem 14 :

A petrol can holds 5  1/2 liters when full. How much petrol is in the can if it is 3/4 full ?

Problem 15 :

A car travels at 50 miles per hour for 3/4 hour. How far does the car travel ?

Detailed Answer Key

Problem 1 : 

3 3/20

Solution : 

In  the given mixed number, the denominator is 20 which is convertible to 100 using multiplication by 5.

So, we have 

3 3/20 = 3 (3 ⋅ 5)/(20 ⋅ 5)

3 3/20  =  3 15/100

3 3/20  = 3.15

Problem 2 :

5 7/10

Solution : 

In  the given mixed number, the denominator is 10. 

So, we have 

5 7/10  =  5.7 

Problem 3 :

9 3/50

Solution : 

In  the given mixed number, the denominator is 50 which is convertible to 100 using multiplication by 2. 

So, we have 

9 3/50  =  9 (3 ⋅ 2)/(50 ⋅ 2)

9 3/50  =  9 6/100

9 3/50  =  9.06

Problem 4 :

9 1/2

Solution : 

In  the given mixed number, the denominator is 2 which is convertible to 10 using multiplication by 5. 

So, we have 

9 1/2 = 9 (1 ⋅ 5)/(2 ⋅ 5)

9 1/2  =  9 5/10

9 1/2  =  9.5

Problem 5 :

24 3/4

Solution : 

In  the given mixed number, the denominator is 4 which is convertible to 100 using multiplication by 25. 

So, we have 

24 3/4  =  24 (3 ⋅ 25)/(4 ⋅ 25)

24 3/4  =  24 75/100

24 3/4  =  24.75

Problem 6 :

5 2/3

Solution : 

In  the given mixed number, the denominator is 3 which is not convertible to 10 or 100 using multiplication.  

Now, we have to get the decimal form of the fraction 2/3 using long division method as explained above. 

When we do so, we get

2/3 ≈ 0.67

So, we have

5 2/3  ≈  5.67

Problem 7 :

7 3/8

Solution : 

In  the given mixed number, the denominator is 8 which is not convertible to 10 or 100 using multiplication.  

Now, we have to get the decimal form of the fraction 3/8 using long division method as explained above. 

When we do so, we get

3/8  =  0.375 

So, we have

7 3/8  =  7.375

Problem 8 :

27 5/6

Solution : 

In  the given mixed number, the denominator is 6 which is not convertible to 10 or 100 using multiplication.  

Now, we have to get the decimal form of the fraction 5/6 using long division method as explained above. 

When we do so, we get

5/6  ≈  0.83

27 5/6  ≈  27.83

Problem 9 :

13 4/9

Solution : 

In  the given mixed number, the denominator is 9 which is not convertible to 10 or 100 using multiplication.  

Now, we have to get the decimal form of the fraction 4/9 using long division method as explained above. 

When we do so, we get

4/9  ≈  0.44

So, we have

13 4/9  ≈  13.44

Problem 10 :

1 5/8

Solution : 

In  the given mixed number, the denominator is 8 which is not convertible to 10 or 100 using multiplication.  

Now, we have to get the decimal form of the fraction 5/8 using long division method as explained above. 

When we do so, we get

5/8  =  0.625

So, we have

1 5/8  =  1.625

Problem 11 :

Solution :

Length of rectangle = 3  1/4

Width of rectangle =  2  1/10

Converting into improper fraction, we get

3  1/4  =  (12 + 1)/4  ==> 13/4

3  2/10  =  (30 + 2)/10  ==> 32/10

Area of rectangle = length x width

= 13/4 ⋅ 32/10

= 52/5

Area of rectangle = 10.4 square units

Problem 12 :

Solution :

Length of rectangle = 2  2/5

Width of rectangle =  1  1/3

Converting into improper fraction, we get

2  2/5  =  (10 + 2)/5  ==> 12/5

1  1/3  =  (3 + 1)/3  ==> 4/3

Area of rectangle = length x width

= 12/5 ⋅ 4/3

= 16/5

Area of rectangle = 3.2 square units

Problem 13 :

Solution :

Length = 1  1/2 cm, width = 1  1/2 cm and height = 1  1/2 cm

Converting into improper fraction, we get

1  1/2  =  (2 + 1)/2  ==> 3/2

Volume of cube = length x width x height

= (3/2) ⋅ (3/2) ⋅ (3/2)

= 27/8 cm³

Problem 14 :

A petrol can holds 5  1/2 liters when full. How much petrol is in the can if it is 3/4 full ?

Solution :

Capacity of petrol tank = 5  1/2 liters

Capacity when it is 3/4 full

= 3/4 of 5  1/2

= 3/4 ⋅ 11/2

= 33/8

= 4  1/8 liters.

Problem 15 :

A car travels at 50 miles per hour for 3/4 hour. How far does the car travel ?

Solution :

Speed of the car = 50 miles per hour

Distance = time x speed

Time taken = 3/4 hour

= 3/4 ⋅ 50

= 75/2

= 37.5 miles.

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