Fractions continued

What happens if the fractions that you were adding not only have different denominators but you had to convert both into equivalent fractions instead of just one!?

There's a nice little trick that you can do that won't involve any messy multiplying!

Example ²/₅ + ¹/₃

Draw two rectangles with 5 rows and 3 colomns.
On the first rectangle, shade in 2 rows.
On the second rectangle, shade in 1 column.
The total number of shaded sections is the numerator. The total number of sections in one rectangle is your denominator. Which leaves you with ¹¹/₁₅.

Note that when you convert both the fractions into their equivalents so that the denominator is 15, you get ⁶/₁₅ and ⁵/₁₅.
When you add these two equivalent fractions together, you should get ¹¹/₁₅.

Finding Fractions of a number

You've learnt how to find equivalent fractions and how to add fractions. You are now about to use them for finding fractions of a number.
How would you find ¹/₄ of 24? You probably can guess that the answer is 6 but how can you tell?
First of all finding a unit fraction of a number is the same as dividing by the denominator.

So for example, ¹/₄ of 24 is the same as

24 ÷ 4
¹/₄ × 24

"What about something like ²/₃ of 15?" I hear you say.
This is the same as doing the following:

²/₃ × 15
2 × (15 ÷ 3)
2 × (¹/₃ × 15)

Fractions of fractions

Now, you know how to find fractions of a number so it shouldn't be hard then for you to find something like ¹/₂ of ³/₄!
Confused? You shouldn't be! This is the same as

³/₄ ÷ 2
¹/₂ × ³/₄.

There's a nice little trick that will help you remember.

Draw a 2 by 4 rectangle. That's 2 rows with 4 columns.
Shade 3 columns in blue and shade 1 row in red.
The number of sesctions where the colours meet (the purple bits) is the numerator. The total number of sections is the denominator. You can check this just by multiplying ¹/₂ by ³/₄.

Try this quick exercise Back

More about fractions

Adding fractions (II)

Finding Fractions of a number

Fractions of fractions