# Khan/khan-exercises

Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
139 lines (133 sloc) 7.29 KB
 Comparing fractions 1
randRange(1, 10) NUM_1 randFromArray([2, 3, 4, 6, 8]) randFromArray([2, 3, 4, 6, 8]) 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 bigger slice. This is more pizza than NUM_2 smaller slice. There are NUM_1 bigger slices. This is more pizza than NUM_2 smaller slices.

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

randFromArray([3, 4, 6, 8]) 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}.