Dividing fractions word problems
Dividing fractions word problems arise in numerous situations. We will show you some examples. I recommend that you review the lesson about division of fractions before starting this lesson.
Dividing fractions word problems: a few examples
Example #1:
An Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8inch piece of sausage if each piece is to be twothirds of an inch?
Solution
Since you are trying to find out how many twothirds there are in 8, it is a division of fractions problem.
You will need to divide 8 by 2/3 in order to get the answer.
8 ÷ 2/3 = 8/1 ÷ 2/3
8 ÷ 2/3 = 8/1 × 3/2
8 ÷ 2/3 = (8 × 3)/(1 × 2)
8 ÷ 2/3 = 24/2
8 ÷ 2/3 = 12
Therefore, you can make 12 pieces of sausages having a length of 2/3 inches from an 8 inches long Italian sausage.
Example #2
How many halves are there in sixfourths?
Again, since you are trying to find out how many halves there are in sixfourths, it is a division of fractions problem.
You will need to divide 6/4 by 1/2 to get the answer.
6/4 ÷ 1/2 = 6/4 × 2/1
6/4 ÷ 1/2 = (6 × 2)/(4 × 1)
6/4 ÷ 1/2 = 12/4
6/4 ÷ 1/2 = 3
Therefore, there are 3 halves in sixfourths.
Example #3:
An airplane covers 50 miles in 1/5 of an hour. How many miles can the airplane cover in 5 hours?
This problem is a combination of division and multiplication of fractions.
First, find out how many fifths (1/5) are there in 5. This is a division of fractions problem.
You will need to divide 5 by 1/5.
5 ÷ 1/5 = 5/1 ÷ 1/5
5 ÷ 1/5 = 5/1 × 5/1
5 ÷ 1/5 = (5 × 5)/(1 × 1)
5 ÷ 1/5 = 25/1
5 ÷ 1/5 = 25
Then, you need to multiply 50 by 25 to get the answer.
50 × 30 = 1250
In 5 hours, the airplane will cover 1250 miles.
Example #4
3 friends share 4/5 of a pizza. what fraction of pizza does each person get?
The amount to share is 4/5
Since the amount will be shared between 3 friends, the amount must be divided between 3 people.
So each person must get 4/5 divided by 3
(4 / 5) / 3 = (4 / 5) / (3 / 1) = 4 / 5 × 1 / 3 = (4 × 1) / (5 × 3)= 4 / 15
Each person will eat 4/15.
Indeed, 4 / 15 + 4 / 15 + 4 / 15 = 12 / 15 = 4/5 (divide 12 and 15 by 3 to get 4 / 5)
Example #4
On June 21st, there were 9/10 of a billion stars visible to the naked eye.
On December 21st, there were 4/5 of a billion stars out visible to the naked eye.
How many times more stars were there visible on June 21st than December 21st?
Set it up.
9/10 divided by 4/5 = ?
Find the reciprocal of the divisor.
9/10 × 5/4 = ?
Simplify
9/10 × 5/4 = 9/2 × 1/4
Solve
9/2 × 1/4 = 9/8
Simplify again
9/8= 1 1/8
Did you have a hard time understanding the problems above? Did you not understand them at all? Take a look at this figure !
Do you need to master fractions once and for all? Check out my book about fractions.
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