Question

item #5
what is the sum of 4 sixths and 2 thirds?
(1 point)

one and 2 sixths

6 sixths

6 thirds

one and 2 thirds

Explanation:

Step1: Convert to fractions

4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$.

Step2: Find a common denominator

The common denominator of 6 and 3 is 6. Convert $\frac{2}{3}$ to sixths: $\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}$.

Step3: Add the fractions

$\frac{4}{6}+\frac{4}{6}=\frac{8}{6}$.

Step4: Simplify the result

$\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$? Wait, no, wait. Wait, 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}=\frac{4}{6}$. So $\frac{4}{6}+\frac{4}{6}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$? Wait, but the options: let's check again. Wait, maybe I made a mistake. Wait, 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$. Let's convert 2 thirds to sixths: $\frac{2}{3}=\frac{4}{6}$. Then sum: $\frac{4}{6}+\frac{4}{6}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$? But the options are one and 2 sixths (which is $1\frac{2}{6}=1\frac{1}{3}$), 6 sixths ($\frac{6}{6}=1$), 6 thirds ($\frac{6}{3}=2$), one and 2 thirds ($1\frac{2}{3}$). Wait, $\frac{8}{6}$ simplifies to $1\frac{2}{6}$ (since $\frac{8}{6}=1+\frac{2}{6}$) or $\frac{4}{3}=1\frac{1}{3}$, and $1\frac{2}{6}$ is equivalent to $1\frac{1}{3}$. Wait, but let's re - calculate: 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$. Let's add them without converting to sixths first. $\frac{4}{6}+\frac{2}{3}=\frac{4}{6}+\frac{4}{6}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$, and $1\frac{2}{6}$ is also $1\frac{1}{3}$ (because $\frac{2}{6}=\frac{1}{3}$). Wait, but the first option is "one and 2 sixths", which is $1\frac{2}{6}=1\frac{1}{3}$, and our result is $1\frac{1}{3}$. But wait, maybe I misread the problem. Wait, the problem says "the sum of 4 sixths and 2 thirds". 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$. Let's do it again:

$\frac{4}{6}+\frac{2}{3}=\frac{4}{6}+\frac{4}{6}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$. Now, $1\frac{2}{6}$ is equal to $1\frac{1}{3}$ (since $\frac{2}{6}=\frac{1}{3}$). But let's check the options:

- Option 1: one and 2 sixths = $1\frac{2}{6}=1\frac{1}{3}$
- Option 2: 6 sixths = 1
- Option 3: 6 thirds = 2
- Option 4: one and 2 thirds = $1\frac{2}{3}$

Wait, but maybe I made a mistake in the conversion. Wait, 2 thirds is $\frac{2}{3}$, 4 sixths is $\frac{4}{6}=\frac{2}{3}$. So $\frac{2}{3}+\frac{2}{3}=\frac{4}{3}=1\frac{1}{3}$, which is equal to $1\frac{2}{6}$. But let's check the options again. Wait, the first option is "one and 2 sixths", which is $1\frac{2}{6}$, and that's equal to $1\frac{1}{3}$, which is our result. But wait, maybe there's a miscalculation. Wait, 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$. Let's add them:

$\frac{4}{6}+\frac{2}{3}=\frac{4 + 4}{6}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}=1\frac{2}{6}$. So the correct option should be "one and 2 sixths"? But wait, let's check the options again. Wait, maybe I made a mistake in the problem understanding. Wait, "4 sixths" is 4 times $\frac{1}{6}$, so $\frac{4}{6}$, "2 thirds" is 2 times $\frac{1}{3}$, so $\frac{2}{3}$.

Wait, another way: 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$. Let's convert $\frac{4}{6}$ to thirds: $\frac{4}{6}=\frac{2}{3}$. Then the sum is $\frac{2}{3}+\frac{2}{3}=\frac{4}{3}=1\frac{1}{3}$, which is equal to $1\frac{2}{6}$ (since $\frac{2}{6}=\frac{1}{3}$). So the first option "one and 2 sixths" is correct? But wait, let's check the options again. Wait, maybe I made a mistake in the problem. Wait, 4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$. Let's add them:

$\frac{4}{6}+\frac{2}{3}=\frac{4 + 4}{6}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$, and $1\frac{2}{6}$ is $1\frac{1}{3}$, so the first option is correct? But wait, the last option is "one and 2 thirds" which is $1\frac{2}{3}$, which is $\frac{5}{3}$, not our result. Wait, maybe I messed up the conversion. Wait, 2 thirds is $\frac{2}{3}$, 4 sixths is $\frac{4}{6}=\frac{2}{3}$. So $\frac{2}{3}+\frac{2}{3}=\frac{4}{3}=1\frac{1}{3}$, and $1\frac{2}{6}$ is $1\frac{1}{3}$ (because $\frac{2}{6}=\frac{1}{3}$). So the first option "one and 2 sixths" is equal to our result. But let's check the options again:

- Option 1: one and 2 sixths = $1+\frac{2}{6}=1+\frac{1}{3}=1\frac{1}{3}$
- Option 2: 6 sixths = $\frac{6}{6}=1$
- Option 3: 6 thirds = $\frac{6}{3}=2$
- Option 4: one and 2 thirds = $1+\frac{2}{3}=\frac{5}{3}$

And our result is $\frac{4}{3}=1\frac{1}{3}$, so the correct option is A. one and 2 sixths? Wait, but let's do the calculation once more:

4 sixths is $\frac{4}{6}$, 2 thirds is $\frac{2}{3}$.

Find a common denominator, which is 6.

$\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}$.

Now add: $\frac{4}{6}+\frac{4}{6}=\frac{8}{6}$.

Simplify $\frac{8}{6}$: divide numerator and denominator by 2, we get $\frac{4}{3}$, which is $1\frac{1}{3}$.

Now, $1\frac{2}{6}$ is equal to $1\frac{1}{3}$ (because $\frac{2}{6}=\frac{1}{3}$). So the first option is correct. But wait, maybe the problem was written as "4 sixths" and "2 thirds", and maybe I made a mistake in the problem's numbers. Wait, no, the problem is as given. So the correct option is "one and 2 sixths". But wait, let's check the options again. Wait, the first option is "one and 2 sixths", which is $1\frac{2}{6}$, and our result is $1\frac{1}{3}$, which is equal to $1\frac{2}{6}$. So the answer should be the first option.

Answer:

A. one and 2 sixths