Lesson 10: Some Applications of Fractions.
- Finding a Fraction of a Quantity.
- Writing One Quantity as a Fraction of a Another Quantity.
- Practice Game.
FINDING A FRACTION OF A QUANTITY
Finding a fraction of a quantity is a very popular exam question.
The question will usually have the word "of" (as in the examples below).
REMEMBER: The word
OF in fractions' maths means
MULTIPLY.
Example:
Solution:
| 2 |
of 15 = |
2 |
x 15 |
"OF" means
multiply. |
| 3 |
3 |
| = |
2 |
x |
15 |
|
Write 15 as |
15 |
| 3 |
1 |
1 |
| = |
2 x 15 |
= |
2 x 5 |
|
|
|
Simplify before multiplying
|
| 3 x 1 |
1 x 1 |
|
|
|
(Divide 15 and 3 by 3). |
| Answer: |
2 |
of 15 oranges is 10 oranges. |
| 3 |
Sometimes you will
need to change a larger unit into a smaller unit.
In the example below you have to change dollars to cents before
multiplying.
Example
Solution:
| $4 = 400 cents |
First change dollars to
cents. |
| 1 |
of 400 = |
1 |
x 400 |
|
|
"OF" means
multiply. |
| 8 |
8 |
|
|
| = |
1 |
x |
400 |
|
Write 400 as |
400 |
| 8 |
1 |
|
1 |
| = |
1 |
x 400 |
= |
400 |
= 50 |
|
Multiply numerators and
denominators. |
| 8 |
x 1 |
8 |
|
Vinculum means divide. |
| Answer: |
1 |
of $4 is 50
cents. |
| 8 |
WRITING ONE QUANTITY AS A FRACTION OF ANOTHER QUANTITY
This question is easy to answer if you understand the concept of a fraction
and what the numerator and denominator is.
Example
What fraction is 15 minutes of 1 hour?
Solution:
We first change 1 hour to 60 minutes.
REMEMBER:
Both quantities must be in the
same units.
| The fraction is : |
15 |
= |
1 |
|
Simplify the fraction by
dividing both the numerator |
| 60 |
4 |
|
and the denominator by 15. |
| Answer: 15 minutes is |
1 |
of 1 hour. |
| 4 |
How can you tell which quantity to write as a numerator and which one
as a dominator?
You have to decide which quantity represents the
whole object.
This is your denominator.
The numerator is the quantity which represents the
part of the object.
In the example above the whole object was 1 hour, or 60 minutes.
Example:
Express 45 cm as a fraction of 1 m.
Solution:
| 1 m = 100 cm |
Make units the same. |
The whole object is 1 m, or 100 cm.
The part is 45 cm.
| The fraction is |
45 |
= |
9 |
|
Simplify the fraction by
dividing both the numerator |
| 100 |
20 |
|
and the denominator by 5. |
| Answer: 45 cm is |
9 |
of 1 m. |
| 20 |
|
