Final answer:
To find the numerator for the equivalent fraction of 2/5 with a denominator of 15, set up a proportion and cross-multiply to solve for x: 2/5 = x/15. The solution is x = 6, so the equivalent fraction is 6/15.
Step-by-step explanation:
The student's question asks, 'What will be the numerator for these equivalent fractions? 2/5=?/15'. To find the equivalent fraction, one can write a proportion by setting the two ratios equal to one another since equivalent fractions are fractions that have the same value when simplified. The original fraction given is 2/5, and the goal is to find the numerator for an equivalent fraction with a denominator of 15.
To do this, we use cross-multiplication. The equation is set up as follows:
2/5 = x/15
Cross-multiply to find the value of x:
2 × 15 = 5 × x
30 = 5x
x = 30 / 5
x = 6
So, the equivalent fraction to 2/5 with a denominator of 15 is 6/15. Canceling equivalent terms in the numerator and denominator is not necessary in this case because 6/15 is already the simplest form of the equivalent fraction that can be created with a denominator of 15.