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As a fraction in simplest terms, what would you multiply the first number by to get the second?
First number: 22 Second number: 72

22*◻=72

As a fraction in simplest terms, what would you multiply the first number by to get the second?\newlineFirst number: 2222 Second number: 7272\newline22=72 22 \cdot \square=72

Full solution

Q. As a fraction in simplest terms, what would you multiply the first number by to get the second?\newlineFirst number: 2222 Second number: 7272\newline22=72 22 \cdot \square=72
  1. Divide to Find Ratio: To find the fraction that you multiply by the first number 2222 to get the second number 7272, you need to divide the second number by the first number.\newlineCalculation: 7222=3.272727...\frac{72}{22} = 3.272727...
  2. Express as Fraction: The result of the division is a repeating decimal, which means we need to express it as a fraction. To do this, we can write the repeating decimal as a fraction with a numerator and denominator that represent the repeating pattern.\newlineCalculation: Since the repeating pattern is 2727, we can express the fraction as 2799\frac{27}{99}, which is the fraction form of the repeating decimal 0.272727...0.272727...
  3. Simplify Fraction: Now we need to simplify the fraction 2799\frac{27}{99} to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number.\newlineCalculation: The GCD of 2727 and 9999 is 2727. So, we divide both the numerator and the denominator by 2727.\newline2727=1\frac{27}{27} = 1 and 9927=3.7\frac{99}{27} = 3.7
  4. Correct Division: We correct the previous step by dividing 9999 by 2727 properly.\newlineCalculation: 99/27=3.66699 / 27 = 3.666\ldots which is incorrect because 9999 is exactly divisible by 2727.\newlineCorrect Calculation: 99/27=3.799 / 27 = 3.7 is incorrect, the correct calculation is 99/27=399 / 27 = 3.

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