Answer :
To solve the equation [tex]\( \frac{3}{f} = \frac{9}{21} \)[/tex], let's go through it step by step:
1. Simplify the Right Side of the Equation:
- The fraction [tex]\( \frac{9}{21} \)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
- So, [tex]\( \frac{9}{21} = \frac{3}{7} \)[/tex].
2. Equate the Fractions:
- Now, the equation looks like [tex]\( \frac{3}{f} = \frac{3}{7} \)[/tex].
3. Cross-Multiply to Solve for [tex]\( f \)[/tex]:
- Cross-multiplying gives us: [tex]\( 3 \times 7 = 3 \times f \)[/tex].
4. Solve for [tex]\( f \)[/tex]:
- This simplifies to: [tex]\( 21 = 3f \)[/tex].
5. Divide Both Sides by 3:
- To isolate [tex]\( f \)[/tex], divide both sides of the equation by 3: [tex]\( f = \frac{21}{3} \)[/tex].
6. Calculate the Result:
- Performing the division gives: [tex]\( f = 7 \)[/tex].
Therefore, the value of [tex]\( f \)[/tex] is 7.
1. Simplify the Right Side of the Equation:
- The fraction [tex]\( \frac{9}{21} \)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
- So, [tex]\( \frac{9}{21} = \frac{3}{7} \)[/tex].
2. Equate the Fractions:
- Now, the equation looks like [tex]\( \frac{3}{f} = \frac{3}{7} \)[/tex].
3. Cross-Multiply to Solve for [tex]\( f \)[/tex]:
- Cross-multiplying gives us: [tex]\( 3 \times 7 = 3 \times f \)[/tex].
4. Solve for [tex]\( f \)[/tex]:
- This simplifies to: [tex]\( 21 = 3f \)[/tex].
5. Divide Both Sides by 3:
- To isolate [tex]\( f \)[/tex], divide both sides of the equation by 3: [tex]\( f = \frac{21}{3} \)[/tex].
6. Calculate the Result:
- Performing the division gives: [tex]\( f = 7 \)[/tex].
Therefore, the value of [tex]\( f \)[/tex] is 7.
