Determine whether the proportion is true or false. 1 2 3 3 = 3 1 3 6 \frac{1\frac23}{3}=\frac{3\frac13}{6}

Here, we need to determine if this proportion is true or false. We have the proportion 1 2/3 over 3, and is that equal to 3 1/3 over 6. To do this, I'm going to use the simplifying ratios method. So first, I need to take my mixed numbers here and write them as improper fractions. For my 1st 11 and 2/3, I take 1, multiply it by 3, which is 1, adding 2 is 5, so I have 5/3 in the numerator and 3 in the denominator. And is this equal to 3 1/3 as an improper fraction is 3 times 3, which is 9, plus 1 is 10. So we have 10/3. In the numerator being divided by 6 in the denominator. Now, to continue simplifying, I'm going to treat these whole numbers in my denominators as if they're fractions, simply by dividing by 1. Now that I have a fraction over a fraction, I know that to simplify, I take the bottom fraction, flip it, and multiply. So we have 5/3 multiplied by 1/3, and we want to know is this equal to 10/3 being multiplied by 1/6. Now, before I start multiplying these, I'm going to check if there's any simplifying that I can do first. Here I see that 10 and 6 are both even, so they're both divisible by 2. I know that 10 is equal to 2 times 5, and 6 is equal to 2 times 3, and both of these have a factor of 2, that I can reduce to 1. Now that I have all prime factors, I can go ahead and multiply everything back together, so we have 5 x 1 in my numerator is 5 and 3 x 3 is 9 in the denominator. And is this equal to 5 times 1 in the numerator over 3 x 3 in the denominator? Yes, 5/9 is equal to 5/9, so this proportion is true.

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Proportions

Prealgebra, Beginning Algebra, & Intermediate Algebra

6. Ratio, Proportion, and Percent

Proportions

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Multiple Choice

Determine whether the proportion is true or false.
$\frac{1 \frac{2}{3}}{3} = \frac{3 \frac{1}{3}}{6}$

True

False

Cannot be determined

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Determine whether the proportion is true or false.
$\frac{1 \frac{2}{3}}{3} = \frac{3 \frac{1}{3}}{6}$