A number when divided by `3 (45)/(49)` gives `(7)/(24)`. Find number.

Answer

To solve the problem step by step, we will find the number \( x \) such that when it is divided by \( \frac{345}{49} \), it equals \( \frac{7}{24} \).

### Step 1: Let the number be \( x \).
We start by letting the unknown number be represented as \( x \).

### Step 2: Set up the equation based on the problem statement.
According to the problem, when \( x \) is divided by \( \frac{345}{49} \), it equals \( \frac{7}{24} \). We can write this as:
\[ \frac{x}{\frac{345}{49}} = \frac{7}{24} \]

### Step 3: Rewrite the division as multiplication.
To eliminate the fraction in the denominator, we can multiply both sides by \( \frac{345}{49} \):
\[ x = \frac{7}{24} \times \frac{345}{49} \]

### Step 4: Simplify the right-hand side.
Now, we will simplify \( \frac{7}{24} \times \frac{345}{49} \):
\[ x = \frac{7 \times 345}{24 \times 49} \]

### Step 5: Calculate \( 7 \times 345 \) and \( 24 \times 49 \).
Calculating the numerator:
\[ 7 \times 345 = 2415 \]
Calculating the denominator:
\[ 24 \times 49 = 1176 \]
So we have:
\[ x = \frac{2415}{1176} \]

### Step 6: Simplify the fraction \( \frac{2415}{1176} \).
We can simplify this fraction by finding the greatest common divisor (GCD) of 2415 and 1176. The GCD is 7.
\[ \frac{2415 \div 7}{1176 \div 7} = \frac{345}{168} \]

### Step 7: Further simplify \( \frac{345}{168} \).
The GCD of 345 and 168 is 3.
\[ \frac{345 \div 3}{168 \div 3} = \frac{115}{56} \]

### Step 8: Convert \( \frac{115}{56} \) to a mixed number.
To convert \( \frac{115}{56} \) into a mixed number, we perform long division:
- 115 divided by 56 gives 2 (since \( 56 \times 2 = 112 \)).
- The remainder is \( 115 - 112 = 3 \).

Thus, we can write:
\[ \frac{115}{56} = 2 \frac{3}{56} \]

### Final Answer:
The number \( x \) is:
\[ x = 2 \frac{3}{56} \]

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