Question

81/100*6/7=____.multiply the following.

Answer 1

Answer:

$\dfrac{81}{100}\cdot \dfrac{6}{7}=\dfrac{243}{350}\quad \left(\mathrm{Decimal:\quad }\:0.69429\dots \right)$

Step-by-step explanation:

$\dfrac{81}{100}\cdot \dfrac{6}{7}$

$\black{\mathrm{Cross-cancel\:common\:factor}}$

$6,\:100$

$\green{\mathrm{Greatest\:Common\:Divisor\:\left(GCD\right)}}$

$\bullet~~\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}$

$\gray{\mathrm{Prime\:factorization\:of\:}6:\quad 2\cdot \:3}$

$\gray{\mathrm{Prime\:factorization\:of\:}100:\quad 2\cdot \:2\cdot \:5\cdot \:5}$

$\gray{\mathrm{The\:prime\:factors\:common\:to\:}6,\:100\mathrm{\:are\:}}$

$=2$

$=\dfrac{81}{50}\cdot \dfrac{3}{7}$

$\gray{\mathrm{Multiply\:fractions}:\quad \dfrac{a}{b}\cdot \dfrac{c}{d}=\dfrac{a\:\cdot \:c}{b\:\cdot \:d}}$

$=\dfrac{81\cdot \:3}{50\cdot \:7}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:81\cdot \:3=243}$

$=\dfrac{243}{50\cdot \:7}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:50\cdot \:7=350}$

$=\dfrac{243}{350}$