Question

NEED HELP!! WILL GIVE BRAINLIEST!! PLEASE COMPLETE BOTH!

Answer 1

Consider the first radical :

${:\implies \quad \sf 5\times 2\dfrac16}$

Using the properties of mixed fraction, writing the mixed fraction as an improper fraction, we will be having

${:\implies \quad \sf 5\times \bigg(\dfrac{6\times 2+1}{6}\bigg)}$

${:\implies \quad \sf 5\times \bigg(\dfrac{12+1}{6}\bigg)}$

${:\implies \quad \sf 5\times \dfrac{13}{6}}$

${:\implies \quad \sf \dfrac{65}{6}}$

${:\implies \quad \boxed{\bf{10\dfrac56}}}$

Hence, Option D) is correct

Now, coming to the 2nd question :

${:\implies \quad \sf 3\dfrac{1}{2}\times 1\dfrac{2}{3}}$

${:\implies \quad \sf \bigg(\dfrac{3\times 2+1}{2}\bigg)\times \bigg(\dfrac{3\times 1+2}{3}\bigg)}$

${:\implies \quad \sf \bigg(\dfrac{6+1}{2}\bigg)\times \bigg(\dfrac{3+2}{3}\bigg)}$

${:\implies \quad \sf \dfrac{7}{2}\times \dfrac{5}{3}}$

${:\implies \quad \sf \dfrac{35}{6}}$

Now, Rewriting this improper fraction as mixed fraction, we will be having :

${:\implies \quad \boxed{\bf{5\dfrac56}}}$

Hence, Option C) is correct

Answer 2

Answer:

$10 \frac{5}{6}\\\\5 \frac{5}{6}$

Step-by-step explanation:

$5 \times 2 \frac{1}{6} \\ \\ = 5 \times \frac{13}{6} \\ \\ = \frac{65}{6} \\ \\ = 10 \frac{5}{6} \\ \\ \\ 3 \frac{1}{2} \times 1 \frac{2}{3} \\ \\ = \frac{7}{2} \times \frac{5}{3} \\ \\ = \frac{35}{6} \\ \\ = 5 \frac{5}{6}$