lesson
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Imagine you order a fresh pizza cut into 6 equal slices, and you grab 1 slice.
Your friend gives you 2 more slices from the same pizza — how much of the whole pizza do you have now?
📊An interactive or clean visual showing a pizza divided into 6 equal slices. On the left, 1 slice is highlighted in bright orange labeled '1/6'. In the middle, 2 slices are highlighted in teal labeled '2/6'. An arrow points to the right showing the combined pizza with 3 out of 6 slices filled in, labeled '3/6'. Clear text labels at bottom: '1 slice + 2 slices = 3 slices of size 1/6'. Responsive layout, light gray background (#f8f9fa), border (#e6e6e6).
In every fraction, the bottom number (the denominator) tells us the total number of equal parts that make up one whole.
The top number (the numerator) simply counts how many of those equal parts we are talking about.
What happens when we put fractions together on a grid?
Combining Parts in an Area Model
An area model is a shape, like a rectangle or circle, divided into equal sections to represent a fraction.
Let's add 82+83 using a rectangle cut into 8 equal squares.
📊Step-by-step area model addition diagram. Top: A 1x8 rectangular bar divided into 8 equal squares. First bar shows 2 squares shaded in blue (labeled '2/8'). A '+' sign. Second bar shows 3 squares shaded in green (labeled '3/8'). An '=' sign. Result bar shows 5 squares shaded (2 blue, 3 green) out of 8, labeled '5/8'. Each square represents 1/8. Text below: '2 eighths + 3 eighths = 5 eighths'. Modern clean UI, #1e2945 text, responsive down to 350px width.
Because both fractions have the same denominator, all the pieces are the exact same size: each piece is 81.
So we just count up the total number of shaded pieces: 2+3=5 pieces, giving us 85.
Why do we leave the bottom number alone instead of adding 8+8?