Segaarvu teisendamine liigmurruks

randRange( 1, 10 ) randRange( 1, 30 ) randRange( 1, 30 ) M_NUM / getGCD( M_NUM, M_DENOM ) M_DENOM / getGCD( M_NUM, M_DENOM ) WHOLE * M_REDUCED_DENOM + M_REDUCED_NUM M_REDUCED_DENOM

Teisenda liigmurd fraction( I_NUM, I_DENOM, false, true ) segaarvuks.

I_NUM / I_DENOM

Esiteks jaga murru lugeja nimetajaga.

I_NUM : I_DENOM = \color{#28AE7B}{WHOLE}\ \text{ JÄÄK } \color{purple}{M_REDUCED_NUM}

Seega liigmurrul on WHOLE täisosa, mis on võrdsed arvuga \color{#28AE7B}{WHOLE} \cdot \dfrac{I_DENOM}{I_DENOM} = \color{#28AE7B}{fraction( I_DENOM * WHOLE, I_DENOM, false, false )}.

init({ range: [ [0, 1], [0, WHOLE] ], scale: [250, 25] }); for ( var y = 0; y < WHOLE; y++ ) { rectchart( [M_REDUCED_DENOM, 0], ["#28AE7B", "#999"], y ); }

Jagatise vastusest number WHOLE on segaarvu täisosa.

Jagatisest jäi veel alles jääk M_REDUCED_NUM. See on \dfrac{\color{purple}{M_REDUCED_NUM}}{I_DENOM} liigmurru see osa, mis veel oma väiksuse tõttu omaette täisosa ei moodustanud.

init({ range: [ [0, 1], [0, 1] ], scale: [250, 25] }); rectchart( [M_REDUCED_NUM, M_REDUCED_DENOM - M_REDUCED_NUM], ["purple", "#999"] );

Liigmurrust segaarvu teisendamisel saime vastuseks \color{#28AE7B}{WHOLE}\ \color{purple}{fraction( M_NUM, M_DENOM, false, true )}.

init({ range: [ [0, 1], [0, WHOLE + 1] ], scale: [250, 25] }); for ( var y = 1; y <= WHOLE; y++ ) { rectchart( [M_REDUCED_DENOM, 0], ["#28AE7B", "#999"], y ); } rectchart( [M_REDUCED_NUM, M_REDUCED_DENOM - M_REDUCED_NUM], ["purple", "#999"] );

Pane tähele, et kui liidame segaarvu täis ja murdosa, \color{#28AE7B}{fraction( I_DENOM * WHOLE, I_DENOM, false, false )} + \color{purple}{fraction( M_NUM, M_DENOM, false, true )}, saame tulemuseks algse liigmurru fraction( I_NUM, I_DENOM, false, true ).

Teisenda segaarv WHOLE\ fraction( M_NUM, M_DENOM, false, true ) liigmurruks.

I_NUM / I_DENOM

\color{#FFA500}{WHOLE}\ \color{#6495ED}{fraction( M_NUM, M_DENOM, false, true )}

Antud segaarv on võrdne arvuga \color{#FFA500}{WHOLE} + \color{#6495ED}{fraction( M_NUM, M_DENOM, false, true )}.

Esiteks, teisenda segaarvu täisosa harilikuks murruks, millel on sama nimetaja M_REDUCED_DENOM kui murru osal..

\color{#FFA500}{WHOLE} \times \dfrac{M_REDUCED_DENOM}{M_REDUCED_DENOM} = \color{#FFA500}{\dfrac{WHOLE * M_REDUCED_DENOM}{M_REDUCED_DENOM}}

init({ range: [ [0, 1], [0, WHOLE] ], scale: [250, 25] }); for ( var y = 0; y < WHOLE; y++ ) { rectchart( [M_REDUCED_DENOM, 0], ["#FFA500", "#999"], y ); }

Seega saime vastuseks \color{#FFA500}{\dfrac{WHOLE * M_REDUCED_DENOM}{M_REDUCED_DENOM}} + \color{#6495ED}{fraction( M_NUM, M_DENOM, false, true )}.

init({ range: [ [0, 1], [0, WHOLE + 1] ], scale: [250, 25] }); for ( var y = 1; y <= WHOLE; y++ ) { rectchart( [M_REDUCED_DENOM, 0], ["#FFA500", "#999"], y ); } rectchart( [M_REDUCED_NUM, M_REDUCED_DENOM - M_REDUCED_NUM], ["#6495ED", "#999"] );

Nüüd liida need kaks murdu ja taanda!

\color{#FFA500}{\dfrac{WHOLE * M_REDUCED_DENOM}{M_REDUCED_DENOM}} + \color{#6495ED}{fraction( M_NUM, M_DENOM, false, true )} = fraction( I_NUM, I_DENOM, true, true )

ülesandeid jäänud