What is
\huge{fraction( N1, D1 )} |
\huge{\times} |
\huge{fraction( N2, D2 )} |
\huge{ =\space ?} |
TABLE_1 | TABLE_2 |
( N1 * N2 ) / ( D1 * D2 )
Another way to word this problem is:
What is fraction( N1, D1 )
of fraction( N2, D2 )
?
Let's overlay the two boxes on top of each other.
Notice how there are cardinal( N1 * N2 ) boxes in the overlap, and cardinal( D1 * D2 ) boxes total.
So this is equivalent to having cardinal( N1 * N2 ) out of cardinal( D1 * D2 ) slices of pie.
Notice how there are N1\timesN2=N1*N2
out of D1\timesD2=D1*D2
slices of pie.
This explains why the resulting fraction is fraction( N1 * N2, D1 * D2 )
.
Optionally, this reduces to fractionReduce( N1*N2, D1*D2 )
.
What is
fraction( N, D ) |
\huge{\times} |
\huge{B} |
\huge{ = \space ?} |
createVertTable( N, D ) |
B * N / D
Another way to word this is:
What is fraction( N, D )
of B
?
So we have cardinal( B ) of these partially-filled in boxes.
createVertTable( N, D, cardinal( i ) ) |
Let's put all these pieces together.
So there are mixedFractionFromImproper( N*B, D )
boxes filled in.
Or, since we have N*B
pieces and D
pieces per box, this is the same as fraction( N*B, D )
.