Fill in the blanks: five-halves is
equal to 15 divided by blank which is equal to three divided by blank which is equal
to blank divided by 14 and four-fifths which is equal to blank over eight.
So out of all of these fractions,
we only know one whole fraction, the five-halves. So we will use this five-halves to
solve for all of the blanks. Let’s first set it equal to the 15
over blank and the blank part let’s replace it with an 𝑥. And now, we can solve. We can solve a few ways.
You may be able to look at this and
think: to get from five to 15, we would have to multiply by three. And if we did that on the
numerator, we would also have to do that on the denominator. So two times three will give us
that 𝑥 is equal to six.
We also could have solved by cross
multiplying by taking five times 𝑥 and setting it equal to 15 times two which is
30. And then to solve for 𝑥, we would
divide both sides by five. And we would find that 𝑥 is equal
to six, just like we said.
So now, we will take five-halves
and set it equal to three over blank. So let’s replace the blank with 𝑥
and solve. So to get from five to three, what
will we multiply it by? Well, that’s not very easy to
see. So instead, let’s just simply cross
multiply and solve. So we take five times 𝑥 and set it
equal to three times two which is six.
And then to solve for 𝑥, we will
divide both sides by five, resulting in 𝑥 equals six-fifths. And if we were to write that as a
decimal, it would be 1.2. Simply take six and divide it by
five and get 1.2.
Next, we will take five-halves and
set it equal to blank over 14 and four-fifths. So now, we look at this and we say,
“Well, how do we get from five to 𝑥?” Well, this doesn’t make sense. So we don’t look at the numerator
like we do with the other ones. We need to look at the denominator
because both of the whole numbers are there.
So to go from two to 14 and
four-fifths, is there an easy number that we could see? And there’s not. So instead, let’s cross multiply
and solve. It doesn’t matter the order that
you cross multiply. It’s a choice to always multiply
the number with 𝑥 together first. So two times 𝑥 we set equal to
five times 14 and four-fifths.
Well, how do we take five times 14
and four-fifths? Well, first, let’s change 14 and
four-fifths to a decimal. So simply take four divided by
five, which is 0.8, and add it to 14. So we’re actually taking five times
14.8, which is 74. So to solve for 𝑥, we divide both
sides of the equation by two, resulting in 𝑥 equals 37.
Lastly, we set five-halves equal to
blank over eight. So we replaced the blank with 𝑥
and now cross multiply and solve. Actually, before we do that,
looking at the denominator, to go from two to eight, we would simply multiply by
four. So if we did that to the top, the
numerator five times four would give us 20.
And we can cross multiply and solve
to double check. So 𝑥 times two is two 𝑥. We set it equal to five times eight
which is 40. And now, we divide both sides of
the equation by two and find that 𝑥 is equal to 20.
So filling in the blanks, we use
numbers six, 1.2, 37, and 20. So this will be our final