CONVERTING MIXED FRACTIONS TO DECIMALS

To convert a mixed number to decimal, check whether the denominator of the mixed fraction is convertible to 10 or 100 using multiplication.  

If it is convertible to 10 or 100 using multiplication, we can convert the mixed number to decimal as explained below. 

If it is not convertible to 10 or 100 using multiplication, we can convert the given mixed number into decimal as explained below.  

Practice Problems

Covert the following mixed fractions to decimals.

Problem 1 :

3 3/20

Solution :

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

3 3/20 = 3 (3 ⋅ 5)/(20 ⋅ 5)

= 3 15/100

= 3.15

Problem 2 :

5 7/10

Solution :

In  the given mixed number, the denominator is 10.

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 6/100

= 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 5/10

= 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.

24 3/4 = 24 (3 ⋅ 25)/(4 ⋅ 25)

= 24 75/100

= 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 :

State true or false

The fraction 14  2/5 is equal to 4.2

Solution :

Given mixed fraction is, 14  2/5

Converting into improper fraction, we get

= [(14 x 5) + 2] / 5

= (70 + 2)/5

= 72/5

Making the denominator as 100,

= (72/5) x (20/20)

= 1440/100

= 14.4

So, the given statement is false.

Problem 12 :

The decimal 0.238 is equal to the fraction

(A) 119/500   (B) 238/25   (C) 119/25   (D) 119/50

Solution :

0.238

Since we have three digits after the decimal, we have to multiply and divide the decimal by 1000.

= 0.238 x (1000/1000)

= 238/1000

Simplifying using 2 times table, we get

= 119/500

Problem 13 :

13   5/18 is a __________ fraction

Solution :

13  5/18 is a mixed fraction.

Problem 14 :

A vitamin C tablet contains 1/40 of a gram of vitamin C. You take 1  1/2 tablets every day. How many grams of vitamin C do you take every day ?

Solution :

In one tablet, quantity of vitamin C = 1/40

Number of tablets taken = 1  1/2

= 3/2

Quantity of vitamin C = (3/2) x 1/40

= 3/80 grams

Problem 15 :

One serving of tortilla soup is 1 2/3 cups. A restaurant cook makes 50 cups of soup. Is there enough to serve 35 people? Explain.

Solution :

Divide 50 by 1 2/3 to find the number of available servings.

= 50 / (1  2/3)

= 50/(5/3)

= 50 x 3/5

= 10 x 3

= 30

No. Because 30 is less than 35, there is not enough soup to serve 35 people.

Problem 16 :

A bag contains 42 cups of dog food. Your dog eats 2 1/3 cups of dog food each day. How many days does the bag of dog food last?

Solution :

Number of cups of dog food a bag contain = 42

Quantity of cups of dog food on each day = 2  1/3

42 / 2  1/3

= 42 / (7/3)

= 42 x (3/7)

= 6 x 3

= 18 days

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