CONVERTING IMPROPER FRACTION INTO MIXED FRACTION

To convert the improper fraction to mixed fraction, we follow the procedure given below.

Convert 11/4 as mixed fraction.

Rewrite the improper fraction as a mixed number.

Problem 1 :

3/2

Solution :

Dividend = 3, divisor = 2

When we divide 3 by 2, we get

quotient = 1 and remainder = 1

So, the improper fraction is

= 1  1/2

Problem 2 :

5/3

Solution :

= 5/3

Dividend = 5, divisor = 3

When we divide 5 by 3, we get

quotient = 1 and remainder = 2

= 1  2/3`

Problem 3 :

11/4

Solution :

= 11/4

Dividend = 11, divisor = 4

When we divide 11 by 4, we get

quotient = 2 and remainder = 3

= 2  3/4

Problem 4 :

13/5

Solution :

= 13/5

Dividend = 13, divisor = 5

When we divide 13 by 5, we get

quotient = 2 and remainder = 3

= 2  3/5

Problem 5 :

25/6

Solution :

= 25/6

Dividend = 25, divisor = 6

When we divide 25 by 6, we get

quotient = 4 and remainder = 1

= 4  1/6

Problem 6 :

28/9

Solution :

= 28/9

Dividend = 28, divisor = 9

When we divide 28 by 9, we get

quotient = 3 and remainder = 1

= 3  1/9

Problem 7 :

42/13

Solution :

= 42/13

Dividend = 42, divisor = 13

When we divide 42 by 13, we get

quotient = 3 and remainder = 3

= 3  3/13

Problem 8 :

47/15

Solution :

= 47/15

Dividend = 47, divisor = 15

When we divide 47 by 15, we get

quotient = 3 and remainder = 2

= 3  2/15

Problem 9 :

Purnit completed a science challenge in 1 3/ 5 hours. Hailey completed the same challenge in less time than Purnit. Which of these could be the amount of time it took Hailey to complete the challenge?

a)  1 3/4 hours     b) 1 2/3 hours    c)  1 2/ 6 hours

d)  1 1/8 hours      e)  1 6/10 hours

Solution :

Time taken by Purnit :

1  3/5 hour = 8/5 hours

1  3/4 = 7/4

1  2/3 = 5/3

1  2/6 = 8/6

1  1/8 = 9/8

1  6/10 = 16/10

LCM(3, 4, 5, 6, 8, 10)

LCM = 3 x 2 x 2 x 5 x 2

= 120

1  3/4 = 7/4 x 30/30 ==> 210/120

1  2/3 = 5/3 x 40/40 ==> 200/120

1  2/6 = 8/6 x 20/20 ==> 160/120

1  1/8 = 9/8 x 15/15 ==> 135/120

1  6/10 = 16/10 x 12/12 ==> 192/120

Time taken by Purnit :

8/5 x 24/24 ==> 192/120

160/120 and 135/120 are lesser than 192/120

So, the answers are 1  1/8 hours and 1  2/6 hours.

Problem 10 :

The walking path in a park is 56/100 mile long. Which decimal represents the length of the walking path in miles?

a) 5,600      b) 0.56      c) 5.60       d) 560

Solution :

Length of path = 56/100 miles

Converting into decimal, we get

= 0.56 miles

Option b is correct.

Problem 11 :

Reza sorted a box of books.

• 3/5 of the books were mysteries.
• 1/3 of the books were science fiction.
• The rest of the books were biographies.

How could the books in the box be described?

a)  __________ half the books in the box were mysteries.

a) Exactly       b) More than     c) Less than

b)  __________  half the books in the box were biographies.

a) Exactly       b) More than     c) Less than

Solution :

= 1 - [(3/5) + (1/3)]

= 1 - [(9 + 5)/15]

= 1 - 14/15

= 1/15

Let us assume the total number of books as 15 (which is least common multiple of 3, 5 and 15).

Number of mystry books = 3/5 of 15

= 9

Number of science fiction books = 1/3 of 15

= 5

Number of biograph books = 1/15 of 15

= 1

a)  More than half the books in the box were mysteries. 

b)  Less than half the books in the box were biographies.

Problem 12 :

A store sells bags of potato chips.

• 1/3 of the bags are barbecue-flavored chips.
• 3/5 of the bags are cheese-flavored chips.
• The rest of the bags are plain chips.

Which statement is true?

a) More than 1/2 of the bags are plain chips.

b) There are no bags of plain chips.

c)  Exactly 1/2 of the bags are plain chips.

d)  Less than 1/2 of the bags are plain chips.

Solution :

Quantity of plain chise = 1 - [(1/3) + (3/5)]

= 1 - (5/15 + 9/15)

= 1 - 14/15

= 1/15

• 1/3 = 0.333
• 3/5 = 0.6
• 1/15 = 0.066........

a) More than 1/2 of the bags are plain chips False

b) There are no bags of plain chips. False 

c)  Exactly 1/2 of the bags are plain chips False

d)  Less than 1/2 of the bags are plain chips True

Problem 13 :

Four people are mowing their lawns. The table shows the fraction of each lawn that has already been mowed by each person.

Which of these people have mowed greater than 3/4 of a lawn?

a) Nate, Rudy, Marc, and Santos     b) Nate and Marc only

c)  Rudy only        d)  Santos only

Solution :

Nate = 10/15 ==> 2/3

Rudy = 5/6

Marc = 12/18 ==> 2/3

Santos = 68 ==> 3/4

LCM (3, 4, 6) = 12

Nate = 2/3 or 8/12

Rudy = 5/6 or 10/12

Marc = 2/3 or 8/12

Santos = 3/4 or 9/12

10/12 > 9/12

So, answer is Rudy only, option c.