Question

2 2/3 * 2 2/3 = how many thirds as a fraction

Answer 1

`\huge\text{Hey there!}`

`\mathsf{2(2)/(3)* 2 (2)/(3)}`

`\mathsf{= (2*3+2)/(3)*(2* 3 + 2)/(3)}}`

`\mathsf{= (6 + 2)/(3)* (6 + 2)/(3)}`

`\mathsf{= (8)/(3)*(8)/(3)}`

`\mathsf{= (8*8)/(3*3)}`

`\mathsf{= (8 + 8 + 8 + 8 + 8 + 8 + 8 + 8)/(3 + 3 + 3)}`

`\mathsf{= (16 + 16 + 16 + 16)/(6 + 3)}`

`\mathsf{= (32 + 32)/(9)}`

`\mathsf{= (64)/(9)}`

`\mathsf{= 7 (1)/(9)}`

`\approx{\mathsf{21 (1)/(3)}}`

`\huge\textbf{Therefore, your answer should be:}`

`\huge\boxed{\frak{21(1)/(3)}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`

Answer 2

`21 (1)/(3)` fit into the product

Explanation:

so you want to convert
`2 (2)/(3)` into a fraction by multiplying 2 by 3 and adding it to the 2. This will give you (3 * 2) = 6 => 6+2=8 which is the numerator. So the fraction becomes
`(8)/(3)` and since the two fractions are equal they both become this. So now you have
`(8)/(3) * (8)/(3)` which can be calculated by multiplying the numerators and denominators. This gives you
`(8*8)/(3*3) = (64)/(9)`. Now this just gives you the product but the question is asking you how many one thirds is the product. This is essentially saying how many 1/3 fit into the product or in other words what is the product divided by 1/3. This gives you the equation
`(64)/(9) / (1)/(3)` which can be calculated by changing the sign to multiplication and flipping the second fraction (1/3 => 3/1) This gives you the equation
`(64)/(9) * (3)/(1) = (64 * 3)/(3 * 3) = (64)/(3)`. I rewrote the 9 as 3 * 3 in the equation so you can see that we can just cancel out the 3. Since if have a number and multiply it by "x" and divide by "x" you just have the original number. So now you have 64/3 which simplifies to
`21 (1)/(3)`