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Module_05 // Operations

ADVANCED FRACTIONS

In foundational math, fractions are just pieces of pie. In algebra, fractions are operations waiting to happen. It's time to learn how to add, multiply, and divide them together.

Adding & Subtracting

You cannot add slices of pizza if the slices are different sizes. You must find the Lowest Common Denominator (LCD) to make the pieces match before combining the tops.

1
2
+
1
3
3
6
+
2
6
=
5
6

Division (The Trick)

Dividing by a fraction is the exact same thing as multiplying by its opposite (its Reciprocal). We use the phrase: Keep, Change, Flip.

  • KEEP the first fraction exactly the same.
  • CHANGE the division sign to a multiplication sign.
  • FLIP the second fraction upside down.
Interactive Lab

Multiplying Fractions

Unlike addition, you do not need a common denominator to multiply. You just multiply straight across! The Area Model below proves why overlapping fractions creates a new, smaller grid.

Fraction Multiplication Visualizer

Fraction 1 (Rows)

Fraction 2 (Columns)

2
3
1
4
=
2
12

The grid has 12 total boxes (Denominator).
2 boxes are overlapped (Numerator).

Verification Protocol

Knowledge Check: Fraction Operations1 / 3

Before you can add or subtract two fractions, what MUST be true?

Rule Mastery

You can manipulate any part of a whole.

Next: Exponents