randRange(1, 10) NUM_1 randRange(NUM_1 + 1, 12) randRangeExclude(NUM_1 + 1, 12, [DEN_1]) DEN_1 > DEN_2 ? "<": ">"

Compare.

`\dfrac{NUM_1}{DEN_1}` ____ `\dfrac{NUM_2}{DEN_2}`

`SOLUTION`

- `<`
- `>`
- `=`

This is like comparing two equally sized pizzas where one is cut into `DEN_1` equal slices and the other is cut into `DEN_2` equal slices.

init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_1, DEN_1 - NUM_1], [RED, "#999"], 2 );
init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_2, DEN_2 - NUM_2], [RED, "#999"], 2 );

Cutting a pizza into more slices means that each slice will be smaller.

The left fraction represents a pizza with more slices, and so each slice is smaller.

The left fraction represents a pizza with fewer slices, and so each slice is bigger.

There is `NUM_1` smaller slice. This is less pizza than `NUM_2` bigger slice. There are `NUM_1` smaller slices. This is less pizza than `NUM_2` bigger slices.

There is `NUM_1` smaller slice. This is more pizza than `NUM_2` bigger slice. There are `NUM_1` smaller slices. This is more pizza than `NUM_2` bigger slices.

So, `\dfrac{NUM_1}{DEN_1} SOLUTION \dfrac{NUM_2}{DEN_2}`.

randRange(3, 12) DEN_1 randRange(1, DEN_1 - 1) randRangeExclude(1, DEN_1 - 1, [NUM_1]) NUM_1 < NUM_2 ? "<": ">"

Compare.

`\dfrac{NUM_1}{DEN_1}` ____ `\dfrac{NUM_2}{DEN_2}`

`SOLUTION`

- `<`
- `>`
- `=`

This is like considering two equally sized pizzas that have been cut into `DEN_1` equal slices.

Since both pizzas have the same number of slices, all the slices are the same size.

init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_1, DEN_1 - NUM_1], [RED, "#999"], 2 );
init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_2, DEN_2 - NUM_2], [RED, "#999"], 2 );

`NUM_1` slices is more than `NUM_2` slice of the same size. `NUM_1` slices is more than `NUM_2` slices of the same size.

`NUM_1` slice is less than `NUM_2` slices of the same size. `NUM_1` slices is less than `NUM_2` slices of the same size.

So, `\dfrac{NUM_1}{DEN_1} SOLUTION \dfrac{NUM_2}{DEN_2}`.