from Arthur J. Baroody in Fostering Children's Mathematical Power (page 9-22)

For example, for 2/3 and 3/4, the cake can be cut in three in one direction and in four in the other.

Three-fourths

Two-Thirds

Comparing Fractions

Two-thirds is represented by 8 equal pieces and Three-fourths by 9 equal pieces. Three-fourths must be larger.

Adding/Subtracting Fractions

There are 12 equal pieces in the whole cake. Each piece is one-twelfth.

If someone ate 2/3 of one cake and 3/4 of another they would have eaten 17-twelfths.
Or, they would need four pieces from the second cake to make a whole cake with the pieces from the first, leaving 5 pieces in the second. They would have one and five-twelfths altogether.

If someone took 3/4 of the cake home, and then someone ate 2/3 of a whole cake from that, there would only be one-twelfth left.
Or, three-fourths is bigger than two-thirds by one-twelfth.

Multiplying Fractions

Though not addressed on the page reference above, finding that two-thirds of three-fourths is six-twelfths
or that three-fourths of two-thirds is six-twelfths is a fairly standard procedure using rectangular models.

Dividing Fractions

Getting a common denominator is a very effective way of dividing fractions (again, not from Baroody).

Eight-ninths is equivalent to 800/900 or 0.8/0.9 or 8-twelfths/9-twelfths.

## Rectangular Cake Cutting Model

from Arthur J. Baroody in

Fostering Children's Mathematical Power(page 9-22)For example, for 2/3 and 3/4, the cake can be cut in three in one direction and in four in the other.

## Comparing Fractions

Two-thirds is represented by 8 equal pieces and Three-fourths by 9 equal pieces. Three-fourths must be larger.## Adding/Subtracting Fractions

There are 12 equal pieces in the whole cake. Each piece is one-twelfth.If someone ate 2/3 of one cake and 3/4 of another they would have eaten 17-twelfths.

Or, they would need four pieces from the second cake to make a whole cake with the pieces from the first, leaving 5 pieces in the second. They would have one and five-twelfths altogether.

If someone took 3/4 of the cake home, and then someone ate 2/3 of a whole cake from that, there would only be one-twelfth left.

Or, three-fourths is bigger than two-thirds by one-twelfth.

## Multiplying Fractions

Though not addressed on the page reference above, finding that two-thirds of three-fourths is six-twelfthsor that three-fourths of two-thirds is six-twelfths is a fairly standard procedure using rectangular models.

## Dividing Fractions

Getting a common denominator is a very effective way of dividing fractions (again, not from Baroody).Eight-ninths is equivalent to 800/900 or 0.8/0.9 or 8-twelfths/9-twelfths.

Grade 7 Fractions