Question

simplify: 3/4(45/24+10/15) kindly step by step explanation.​

Answer 1

Answer:

Refer to the above attachment ✌️

Answer 2

Answer: $\frac{151}{96}$

Step-by-step explanation:

$\frac{3}{4}\left(\frac{45}{24}+\frac{10}{45}\right)$

$\frac{45}{24}$ (cancel the common factor which is 3)

$\frac{45}{28} =\frac{15}{8}$

$\frac{10}{45}$ (cancel the common factor which is 5)

$\frac{10}{45} =\frac{2}{9}$

∴$\frac{3}{4} (\frac{15}{8} +\frac{2}{9} )$

Find the LCM of 8 & 9: 72

$(\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}$ $\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:72)$

$(\mathrm{For}\:\frac{15}{8}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:9)$

$\frac{15}{8}=\frac{15\cdot \:9}{8\cdot \:9}=\frac{135}{72}$

$(\mathrm{For}\:\frac{2}{9}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:8)$

$\frac{2}{9}=\frac{2\cdot \:8}{9\cdot \:8}=\frac{16}{72}$

$=\frac{135}{72}+\frac{16}{72}$

$(\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c})$

$\frac{135}{72}+\frac{16}{72}$ $=\frac{135+16}{72}$

$(\mathrm{Add\:the\:numbers:}\:135+16=151)$

$=\frac{151}{72}$

$=\frac{3}{4}\cdot \frac{151}{72}\\(\mathrm{Cross-cancel\:common\:factor:}\:3)\\(\mathrm{The\:prime\:factors\:common\:of\:}3and\:72\mathrm{\:is\:}=3)$

$=\frac{1}{4}\cdot \frac{151}{24}\\\mathrm{Multiply\:fractions}\\\\=\frac{151}{4\cdot \:24}\\\\=\frac{151}{96}$