Multiply by a unit fraction

What is 1 third times 1 third? Well, multiplying fractions is easy: []we just multiply the numerators, and multiply the denominators, []so our answer is 1 ninth, because 1 times 1 is 1 and 3 times 3 is 9. And the reason why we do that is because, with fractions, times and ‘of’ mean the same thing, so if we have 1 third times 1 third, []we’re really finding 1 third of 1 third, so that’s 1 ninth.[]
Now, for 3 fifths times 1 quarter, we do the same thing, []so if we multiply our numerators and multiply our denominators, []we get our answer, 3 twentieths. So if we start with 3 fifths, and we’re multiplying by a quarter, []we’re really splitting each of those fifths into quarters, we’re really dividing by 4, and that gives us 3 twentieths.[]
So what is 7 tenths times 1 half? []We’re multiplying our numerators, then multiplying our denominators, []so we have 7 twentieths, because if we start with 7 tenths, multiplying by a half is the same as finding half of something, []so we’re dividing each of those 7 tenths in half, giving us 7 twentieths as our answer.