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 8-inch piece of sausage if each piece is to be two-thirds of an inch?
Solution
Since you are trying to find out how many two-thirds 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 six-fourths?
Again, since you are trying to find out how many halves there are in six-fourths, 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 six-fourths.
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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