Step 1a

First, convert the given mixed fractions into improper fractions.
\$3 8/10\$ = \$38/10\$
\$4 15/20\$ = \$95/20\$

To find a common denominator. The least common multiple (LCM) of 10 and 20 is 20.

Explanation: In this step, convert the given mixed fractions to improper fractions. For the mixed fraction 3 8/10, the improper fraction is 38/10. For 4 15/20, the improper fraction is 95/20. Since the denominators are different, find the least common multiple (LCM) of the denominators. In this case, 20 is a common multiple of 10 and 20.

Step 1b

In this step, to make the denominators equal, we must multiply \$2/2\$ by \$38/10\$ and \$1/1\$ by \$95/20\$.

This results in \$76/20\$ and \$95/20\$, respectively. Finally add the numerators,
⇒ \$76/20\$ + \$95/20\$ = \$171/20\$.

Explanation: In this step, to find the LCM as the new denominator, multiply both the numerator and denominator of each fraction by a number, \$76/20\$ and \$95/20\$. To find the sum of the fractions, add their numerators and keep the denominator as 20. The result is \$171/20\$.

Step 2a

Firstly, convert the given mixed fractions into improper fractions i.e., multiply the denominator with the whole number and then add the resultant to the numerator.
⇒\$5 28/14\$ = \$98/14\$.

⇒\$3 24/16\$ = \$72/16\$.

Multiply the two improper fractions - \$98/14 times 72/16\$.
After multiplying the two numerators and denominators, we get 7056 and 224 respectively.

Explanation: In this step, convert the mixed fractions to improper fractions: \$5 28/14 = 98/14\$ and \$3 24/16 = 72/16\$. Then multiply the two improper fractions: \$98/14 times 72/16 = 7056/224\$.

Step 2b

Reduce by dividing both the numerator and denominator \$\cancel(7056)^(63)/\cancel(224)^(2)\$ we get \$63/2\$. Divide the resultant fraction \$63/2\$.

\$"Mixed fraction"\$ = \$"Whole number" + "Numerator" /"Denominator"\$

Explanation: To simplify the fraction \$(\cancel7056^63/\cancel224^2)\$, divide both the numerator and denominator by their greatest common factor to get \$63/2\$, which can be represented as the mixed fraction \$31 1/2\$.