Video: Finding Equivalent Fractions

Fill in the blanks: 5/2 = 15/_ = 3/_ = _/(14 4/5) = _/8.

03:42

Video Transcript

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 answer.

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