Multiply [tex]$\frac{3}{\sqrt{17}-\sqrt{2}}$[/tex] by which fraction will produce an equivalent fraction with a ratio
[tex]$\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}$[/tex]
[tex]$\frac{\sqrt{17}-\sqrt{2}}{\sqrt{17}-\sqrt{2}}$[/tex]
[tex]$\frac{\sqrt{2}-\sqrt{17}}{\sqrt{2}-\sqrt{17}}$[/tex]
Answer (2)
To produce an equivalent fraction from 17 − 2 3 , any of the given fractions can be multiplied, as all are equivalent to 1. Specifically, the fractions 17 − 2 17 − 2 , 17 + s q r t 2 17 + s q r t 2 , and 2 − 17 2 − 17 will all work. Thus, the answer is that any given fraction will create an equivalent result.
;
Multiplying a fraction by 1 results in an equivalent fraction.
Check if the given fractions are equal to 1.
All the given fractions 17 − 2 17 − 2 , 17 + 2 17 + 2 , and 2 − 17 2 − 17 are equal to 1.
Therefore, multiplying by any of the given fractions will result in an equivalent fraction.
Explanation
Understanding the Problem We are given the fraction 17 − 2 3 and asked to find which of the given fractions, when multiplied by it, will produce an equivalent fraction. An equivalent fraction is a fraction that has the same value as the original fraction.
Strategy A fraction multiplied by 1 will result in an equivalent fraction. Therefore, we need to check which of the given fractions is equal to 1.
Analyzing the First Option The first option is 17 − 2 17 − 2 . Since the numerator and denominator are the same, this fraction is equal to 1. Multiplying 17 − 2 3 by this fraction will result in an equivalent fraction.
Analyzing the Second Option The second option is 17 + 2 17 + 2 . Since the numerator and denominator are the same, this fraction is equal to 1. Multiplying 17 − 2 3 by this fraction will result in an equivalent fraction.
Analyzing the Third Option The third option is 2 − 17 2 − 17 . Since the numerator and denominator are the same, this fraction is equal to 1. Multiplying 17 − 2 3 by this fraction will result in an equivalent fraction.
Conclusion Since all three fractions are equal to 1, multiplying 17 − 2 3 by any of them will result in an equivalent fraction.
Examples
In cooking, if you have a recipe that calls for 2 1 cup of flour, but you want to make a double batch, you can multiply the amount of flour by 2 2 , which is equal to 1. This gives you 2 1 × 2 2 = 4 2 cups of flour. 4 2 is an equivalent fraction to 2 1 , but it represents the doubled amount needed for the recipe.
