a science experiment calls for mixing $3\frac{2}{3}$ cups of distilled water with $1\frac{3}{4}$ cups of…

a science experiment calls for mixing $3\frac{2}{3}$ cups of distilled water with $1\frac{3}{4}$ cups of vinegar and $\frac{2}{3}$ cups of liquid detergent. how much liquid in all, in cups, is needed?\n$2\frac{1}{12}$\n$4\frac{1}{12}$\n$5\frac{1}{12}$\n$6\frac{1}{12}$

a science experiment calls for mixing $3\frac{2}{3}$ cups of distilled water with $1\frac{3}{4}$ cups of vinegar and $\frac{2}{3}$ cups of liquid detergent. how much liquid in all, in cups, is needed?\n$2\frac{1}{12}$\n$4\frac{1}{12}$\n$5\frac{1}{12}$\n$6\frac{1}{12}$

Answer

Explanation:

Step1: Convert mixed - numbers to improper fractions

$3\frac{2}{3}=\frac{3\times3 + 2}{3}=\frac{11}{3}$, $1\frac{3}{4}=\frac{1\times4+3}{4}=\frac{7}{4}$

Step2: Find a common denominator

The common denominator of 3, 4, and 3 is 12.

Step3: Rewrite fractions with common denominator

$\frac{11}{3}=\frac{11\times4}{3\times4}=\frac{44}{12}$, $\frac{7}{4}=\frac{7\times3}{4\times3}=\frac{21}{12}$, $\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}$

Step4: Add the fractions

$\frac{44}{12}+\frac{21}{12}+\frac{8}{12}=\frac{44 + 21+8}{12}=\frac{73}{12}=6\frac{1}{12}$

Answer:

$6\frac{1}{12}$