Question

How do I figure this out?

Answer 1

1/10 is half of 1/5
1/5 × 1/2 = 1/10

3 pieces × 2 = 6 pieces that are 1/10

Answer 2

So, he is using 3  of the 1/5 strips to get a 3/5, 1/5 + 1/5 + 1/5 = 3/5

now, he wants to model the same fraction, but with a different fashion, with a denominator of 10, one-tenth, yet equivalent.

the cheap answer is, multiply top and bottom by 2.

$\bf \cfrac{3}{5}\cdot \cfrac{2}{2}\implies \cfrac{3\cdot 2}{5\cdot 2}\implies \cfrac{6}{10}\qquad thus\\\\ -------------------------------\\\\ \cfrac{1}{10}+\cfrac{1}{10}+\cfrac{1}{10}+\cfrac{1}{10}+\cfrac{1}{10}+\cfrac{1}{10}\implies \cfrac{6}{10}\implies \cfrac{3}{5}$