Video Transcript
Calculate one and one-half times three and three-fourths times one and seven-ninths.
These are considered mixed numbers. And in order to multiply three mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is a larger number and the denominator is the smaller number.
So as we said, to multiply three mixed numbers, we need to convert them to improper fractions and then multiply the numerators together multiply the denominators together and then simplify.
So let’s begin converting these mixed numbers to be improper fractions. So one and one-half, let’s rewrite one so that it has a denominator of two. Two over two is equal to one.
And it’s one and one-half. So we need two over two and one-half. So we need to add the one-half. Well when we add fractions, we add the numerators and keep the denominators if they’re the same.
So we get three-halves. Now let’s keep going. Three and three-fourths, so how can we rewrite three as something over four? Well, we can take the four times three and make it 12 because the exact opposite, 12 divided by four, would give us three.
So 12 fourths is equal to three and then we add three-fourths. So 12 plus three is 15. And we keep our common denominator, so fifteen-fourths.
One and seven-ninths, one we can rewrite as nine over nine plus seven-ninths. We add our numerators and get 16 and then keep our denominator and have nine. So we have 16 ninths. So as we said before, we need to multiply all of our improper fractions together by multiplying all of the numerators together and multiplying all of the denominators together.
Three times 15 times 16 is 720. And two times four times nine is 72. And we’ll reduce that and get an answer of 10. Now there’s another way that we could do that. When multiplying numbers together, we can actually simplify before we multiply numbers.
Three can simplify into nine. How many times does three go into nine? It goes into nine three times and then it goes into itself once. So let’s keep looking.
Now we may be tempted to say the two and the four on the bottom can simplify, but it has to be a number from the numerator and a number from the denominator to simplify. They can’t be on the same either numerator or on the same denominator.
So here we’re looking at four going into 16. We also could’ve done two into 16. Now not both, you have to pick one set to simplify. So four goes into 16 four times and then it goes into itself once. Now there’s two more things that can simplify.
Two can go into four twice and itself once. And then three can go into 15 five times and in itself once. So now let’s multiply cause everything else has been simplified. We can’t simplify anymore.
So on the numerator, we have one times five times two which is 10. And on the denominator, one times one times one is one. And 10 divided by one equals 10. So once again, our final answer will be 10.
