Find: `(21)/(4) xx (30)/(49) + (5)/(7)`

Answer

To solve the problem `(21/4) × (30/49) + (5/7)`, we will follow these steps:

### Step 1: Multiply the fractions
We start by multiplying the two fractions `(21/4)` and `(30/49)`.

\[ \frac{21}{4} \times \frac{30}{49} = \frac{21 \times 30}{4 \times 49} \]

### Step 2: Calculate the numerator and denominator
Now we calculate the products in the numerator and the denominator.

\[ 21 \times 30 = 630 \]
\[ 4 \times 49 = 196 \]

So, we have:

\[ \frac{630}{196} \]

### Step 3: Simplify the fraction
Next, we simplify the fraction `630/196`. We can find the greatest common divisor (GCD) of 630 and 196.

The GCD of 630 and 196 is 14. Now we divide both the numerator and the denominator by 14:

\[ \frac{630 \div 14}{196 \div 14} = \frac{45}{14} \]

### Step 4: Add the second fraction
Now we need to add `(5/7)` to `(45/14)`. To do this, we need a common denominator. The least common multiple (LCM) of 7 and 14 is 14.

We convert `(5/7)` to have a denominator of 14:

\[ \frac{5}{7} = \frac{5 \times 2}{7 \times 2} = \frac{10}{14} \]

### Step 5: Add the fractions
Now we can add the two fractions:

\[ \frac{45}{14} + \frac{10}{14} = \frac{45 + 10}{14} = \frac{55}{14} \]

### Final Answer
Thus, the final answer is:

\[ \frac{55}{14} \]

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