Write a fraction equivalent to 21/30 with numerator 7 denominator 120
The Correct Answer and Explanation is:
To find a fraction equivalent to 2130\frac{21}{30}3021 with a numerator of 7 and a denominator of 120, we need to determine a common factor between the numerator and denominator that allows us to adjust the fraction accordingly. Here’s how we can approach it:
Step 1: Simplify 2130\frac{21}{30}3021
We begin by simplifying the fraction 2130\frac{21}{30}3021. The greatest common divisor (GCD) of 21 and 30 is 3. Dividing both the numerator and the denominator by 3:2130=21÷330÷3=710\frac{21}{30} = \frac{21 \div 3}{30 \div 3} = \frac{7}{10}3021=30÷321÷3=107
Step 2: Find the Scaling Factor
Now, we want to transform 710\frac{7}{10}107 into a fraction with a numerator of 7 and a denominator of 120. To do this, we need to find the scaling factor, or the number by which we multiply the denominator of 710\frac{7}{10}107 to get 120. We do this by dividing the new denominator (120) by the old denominator (10):12010=12\frac{120}{10} = 1210120=12
Step 3: Scale the Numerator
Now that we know we need to multiply the denominator by 12, we do the same for the numerator. Multiply the numerator of 710\frac{7}{10}107 by 12:7×12=847 \times 12 = 847×12=84
Thus, we have:710×1212=84120\frac{7}{10} \times \frac{12}{12} = \frac{84}{120}107×1212=12084
Step 4: Verify the Result
Finally, we check if 84120\frac{84}{120}12084 is equivalent to 2130\frac{21}{30}3021. Simplifying 84120\frac{84}{120}12084 by dividing both the numerator and the denominator by their GCD, which is 12:84120=84÷12120÷12=710\frac{84}{120} = \frac{84 \div 12}{120 \div 12} = \frac{7}{10}12084=120÷1284÷12=107
Since 710\frac{7}{10}107 is equivalent to 2130\frac{21}{30}3021, our result is correct.
Conclusion:
The fraction 84120\frac{84}{120}12084 is equivalent to 2130\frac{21}{30}3021, with the numerator being 7 and the denominator 120.
