Respuestas
Respuesta:
Dividir fracciones
Dividir fracciones es lo mismo que multiplicar por el recíproco (inverso).
Por ejemplo:
\dfrac34\goldD{\div}\dfrac{\blueD2}{\greenD3}
4
3
÷
3
2
start fraction, 3, divided by, 4, end fraction, start color #e07d10, divided by, end color #e07d10, start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 3, end color #1fab54, end fraction=\dfrac34\goldD{\times}\dfrac{\greenD3}{\blueD2}=
4
3
×
2
3
equals, start fraction, 3, divided by, 4, end fraction, start color #e07d10, times, end color #e07d10, start fraction, start color #1fab54, 3, end color #1fab54, divided by, start color #11accd, 2, end color #11accd, end fraction
Ya que tengamos un problema de multiplicación, multiplicamos los numeradores y después, los denominadores.
Ejemplo 1: fracciones
\dfrac{3}{2} \div \dfrac{8}{3} = {?}
2
3
÷
3
8
=?start fraction, 3, divided by, 2, end fraction, divided by, start fraction, 8, divided by, 3, end fraction, equals, question mark
El recíproco de \dfrac{8}{3}
3
8
start fraction, 8, divided by, 3, end fraction es \dfrac{3}{8}
8
3
start fraction, 3, divided by, 8, end fraction.
Por lo tanto:
\dfrac{3}{2} \div \dfrac{8}{3} = \dfrac{3}{2} \times \dfrac{3}{8}
2
3
÷
3
8
=
2
3
×
8
3
start fraction, 3, divided by, 2, end fraction, divided by, start fraction, 8, divided by, 3, end fraction, equals, start fraction, 3, divided by, 2, end fraction, times, start fraction, 3, divided by, 8, end fraction
\phantom{\dfrac{3}{2} \times \dfrac{3}{8}} = \dfrac{3 \times 3}{2 \times 8}
2
3
×
8
3
=
2×8
3×3
empty space, equals, start fraction, 3, times, 3, divided by, 2, times, 8, end fraction
\phantom{\dfrac{3}{2} \times \dfrac{3}{8}} = \dfrac{9}{16}
2
3
×
8
3
=
16
9
empty space, equals, start fraction, 9, divided by, 16, end fraction
Ejemplo 2: números mixtos
3\dfrac{1}{2} \div 1\dfrac{1}{4} =3
2
1
÷1
4
1
=3, start fraction, 1, divided by, 2, end fraction, divided by, 1, start fraction, 1, divided by, 4, end fraction, equals
Empecemos por convertir los números mixtos a fracciones.
\phantom{=}3\dfrac{1}{2} \div 1\dfrac{1}{4}=3
2
1
÷1
4
1
empty space, 3, start fraction, 1, divided by, 2, end fraction, divided by, 1, start fraction, 1, divided by, 4, end fraction
= \dfrac{7}{2}\div\dfrac{5}{4}=
2
7
÷
4
5
equals, start fraction, 7, divided by, 2, end fraction, divided by, start fraction, 5, divided by, 4, end fraction
=\dfrac{7}{2}\cdot\dfrac{4}{5} ~~~~~~~\text{Multiplica por el recíproco.}=
2
7
⋅
5
4
Multiplica por el rec
ı
ˊ
proco.equals, start fraction, 7, divided by, 2, end fraction, dot, start fraction, 4, divided by, 5, end fraction, space, space, space, space, space, space, space, start text, M, u, l, t, i, p, l, i, c, a, space, p, o, r, space, e, l, space, r, e, c, ı, with, \', on top, p, r, o, c, o, point, end text
=\dfrac{7}{\blueD{1}\cancel{2}}\cdot \dfrac{\blueD{2}\cancel{4}}{5} ~~~~~~~\text{Simplifica.}=
1
2
7
⋅
5
2
4
Simplifica.equals, start fraction, 7, divided by, start color #11accd, 1, end color #11accd, start cancel, 2, end cancel, end fraction, dot, start fraction, start color #11accd, 2, end color #11accd, start cancel, 4, end cancel, divided by, 5, end fraction, space, space, space, space, space, space, space, start text, S, i, m, p, l, i, f, i, c, a, point, end text
=\dfrac{7}{\blueD{1}}\cdot \dfrac{\blueD{2}}{5}=
1
7
⋅
5
2
equals, start fraction, 7, divided by, start color #11accd, 1, end color #11accd, end fraction, dot, start fraction, start color #11accd, 2, end color #11accd, divided by, 5, end fraction
=\dfrac{14}{5}\text{ o }2\dfrac45=
5
14
o 2
5
4
Explicación paso a paso: