What is 9 and 1/2 + 12 and 11/20

2 answers:

8 0

$9\left(\frac{1}{2}\right)+12\left(\frac{11}{20}\right) \ \textgreater \ \mathrm{Remove\:parentheses}:\ \left(a\right)=a \ \textgreater \ 9\cdot \frac{1}{2}+12\cdot \frac{11}{20}$

$9\cdot \frac{1}{2} \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\ \textgreater \ \frac{1\cdot \:9}{2} \ \textgreater \ \mathrm{Apply\:rule}\:1\cdot \:a=a$
$\frac{9}{2}$

$2\cdot \frac{11}{20} \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ \frac{11\cdot \:12}{20}$

$\mathrm{Multiply\:the\:numbers:}\:11\cdot \:12=132 \ \textgreater \ \frac{132}{20}$

$\mathrm{Cancel\:the\:common\:factor:}\:4 \ \textgreater \ \frac{33}{5} \ \textgreater \ \frac{9}{2}+\frac{33}{5}$

Now we want to find the LCD which is least common denominator.
$\mathrm{Find\:the\:least\:common\:denominator\:}2\cdot \:5=10 \ \textgreater \ 10$

$\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{9\cdot \:5}{10}+\frac{33\cdot \:2}{10}$

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

$\frac{5\cdot \:9+2\cdot \:33}{10} \ \textgreater \ 5\cdot \:9+2\cdot \:33 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:5\cdot \:9=45$

$45+2\cdot \:33 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:2\cdot \:33=66 \ \textgreater \ 45+66 \ \textgreater \ 111$

$Therefore\;\frac{111}{10}\;is\;our\;answer!$

Also the decimal is 11.1.

Hope this helps!