Write the equivalent like fractions of given pair of fractions: `3/(7) and 10/(9)`

Answer

To find the equivalent like fractions for the given fractions \( \frac{3}{7} \) and \( \frac{10}{9} \), we will follow these steps:

### Step 1: Identify the denominators
The denominators of the given fractions are 7 and 9.

### Step 2: Find the Least Common Multiple (LCM)
To make the fractions like fractions, we need to find the LCM of the denominators 7 and 9.

- The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
- The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, ...

The smallest common multiple is 63. Thus, the LCM of 7 and 9 is 63.

### Step 3: Convert the first fraction to have the denominator of 63
Now, we will convert \( \frac{3}{7} \) to a fraction with a denominator of 63.

To do this, we multiply both the numerator and the denominator by 9 (since \( 63 \div 7 = 9 \)):
\[ \frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63} \]

### Step 4: Convert the second fraction to have the denominator of 63
Next, we will convert \( \frac{10}{9} \) to a fraction with a denominator of 63.

To do this, we multiply both the numerator and the denominator by 7 (since \( 63 \div 9 = 7 \)):
\[ \frac{10}{9} = \frac{10 \times 7}{9 \times 7} = \frac{70}{63} \]

### Step 5: Write the equivalent like fractions
Now we have both fractions with the same denominator:
- The equivalent like fraction of \( \frac{3}{7} \) is \( \frac{27}{63} \).
- The equivalent like fraction of \( \frac{10}{9} \) is \( \frac{70}{63} \).

Thus, the equivalent like fractions are \( \frac{27}{63} \) and \( \frac{70}{63} \).

### Final Answer:
The equivalent like fractions of \( \frac{3}{7} \) and \( \frac{10}{9} \) are \( \frac{27}{63} \) and \( \frac{70}{63} \).

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