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# publicKhan/khan-exercises

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file 90 lines (85 sloc) 4.344 kb
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89         Converting multi-digit repeating decimals to fractions

randRangeWeighted( 0, 3, 0, 0.5 )        randRange( 1, 8 )        randRange( 10, 99 )        N1 + N2 / 9        0        1        pow( 10, D2 )        pow( 10, D1 )        floorTo( 4,( MULT1 * N4 ) )        floorTo( 4,( MULT2 * N4 ) )        round( RES1 - RES2 )

Rewrite as a simplified fraction.

\large{N1.\overline{N2} = {?}}

N4

N1 + N3 / 99                2

Rewrite as a simplified fraction.

\large{N1.\overline{N3} = {?}}

N4

randRange( 1, 8 )                N1 + N2 / 10 + N3 / 90                1                2

Rewrite as a simplified fraction.

\large{N1.N2\overline{N3} = {?}}

N4

randRange( 1, 9 )                N1 + N2 / 10 + N3 / 990                1                3

Rewrite as a simplified fraction.

\large{N1.N2\overline{N3} = {?}}

N4

randRange( 1, 8 )                N1 + N3 / 100 + N2 / 900                2                3

Rewrite as a simplified fraction.

\large{N1.N3\overline{N2} = {?}}

N4

Let x equal the decimal. Set up two equations such that the digits after the decimal point are identical.

\large{\begin{align*}MULT1x &= RES1...\\        MULT2x &= RES2...\end{align*}}

Subtracting the two equations, we have:

\large{(MULT1 - MULT2)x = DIFF}

\large{x = fraction( DIFF, MULT1 - MULT2 )}\quad \text{or} \quad\large{mixedFractionFromImproper( DIFF, MULT1 - MULT2 )}

\large{x = fraction( toFraction( N4 )[ 0 ], toFraction( N4 )[ 1 ])}\quad \text{or} \quad\large{mixedFractionFromImproper( toFraction( N4 )[ 0 ], toFraction( N4 )[ 1 ] )}

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