Fractions: Types, Simplifying and How to Add Them

If I split a bamboo stalk into 4 equal pieces and eat 3, I ate 3/4 of it. That is it, you already know what a fraction is. The rest is learning to read them and do math with them.

Here you get what a fraction is, how to read one, the types, how to simplify and all four operations, with examples you can do in your head.

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What is a fraction?

A fraction shows parts of a whole. It has two numbers:

• Denominator (bottom): how many equal parts the whole was split into.
• Numerator (top): how many of those parts we take.

In 3/4, the bamboo was split into 4 parts and I took 3.

How to read fractions

• 1/2: one half
• 1/3: one third
• 1/4: one quarter (or one fourth)
• 1/5: one fifth
• 1/10: one tenth
• 1/12: one twelfth
• 1/100: one hundredth
• 3/8: three eighths

Types of fractions

• Proper: the numerator is smaller than the denominator. 2/5.
• Improper: the numerator is bigger than or equal to the denominator. 7/4.
• Mixed number: a whole number plus a fraction. 1 3/4 is the same as 7/4.
• Equivalent: different fractions with the same value. 1/2 = 2/4 = 3/6.
• Unit fraction: a fraction with 1 on top. 1/3, 1/8.

How to simplify

Divide the numerator and the denominator by the same number until you cannot anymore. 6/8: both divide by 2, giving 3/4. When nothing else divides both, the fraction is in simplest form.

How to add and subtract

Same denominator

Add only the numerators and keep the denominator: 1/5 + 2/5 = 3/5.

Different denominators

Turn them into equivalent fractions with a common denominator, then add: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

How to multiply and divide

• Multiply: top times top and bottom times bottom. 2/3 × 3/4 = 6/12 = 1/2.
• Divide: keep the first, flip the second and multiply. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.

Fractions as decimals and percents

To get a decimal, divide the numerator by the denominator:

• 1/2 = 0.5 = 50%
• 1/4 = 0.25 = 25%
• 3/4 = 0.75 = 75%
• 1/5 = 0.2 = 20%
• 1/10 = 0.1 = 10%

Fractions in Plop!

In Plop! Fruit Merge, two matching fruits merge into a bigger one. It is like adding two halves: 1/2 + 1/2 = 1 whole.

PolarzinhoHalf a blueberry plus half a blueberry makes one blueberry. But one blueberry plus one blueberry makes a new fruit: blender math is different.

Merge after merge, the fruits keep growing all the way to the mango.

FAQ

What are the numerator and denominator?

The denominator (bottom) says how many parts the whole was split into; the numerator (top) says how many parts you take.

How do you simplify a fraction?

Divide the top and bottom by the same number until you cannot anymore.

What is 1/2 + 1/3?

5/6.

What is 3/4 as a decimal?

0.75, or 75%.

Your turn

Simplify 10/15. Then: what is 1/4 + 2/4? And what is that as a percent?

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