To add fractions, a rectangle is drawn with the denominators of the fractions as the dimensions. The numerators are then shaded in as portions of the rectangle. Single shaded squares are counted once, and double shaded squares are counted twice. This totals the number of shaded squares over the total number of squares, giving the sum of the fractions. For example, adding 2/1 to 3/1 results in 5/6.

1. Adding Fractions.
To add
2
1
to
3
1
draw a rectangle 2 squares by 3 squares.
2
1
2
1
3
1
3
1
3
1
Shade in
2
1
of the columns.
2
1
2
1
3
1
3
1
3
1
Turn through 90˚ and shade in
3
1
of the columns.
3
1
3
1
3
1
2
1
Count the single shaded
squares once.
2
1
Count the double shaded
squares twice.
This gives you 3 + 2 = 5 shaded squares out of 6 squares.
In other words
6
5
3
1
2
1
=+
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2. Transparency 1
Example 1
Example 2
Question 1
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3. Transparency 2
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4. Transparency 3
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5. KIBCO Mathematics Project

6. KIBCO Mathematics Project