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

2 Answers

3 votes


\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


\huge\text{Good luck on your assignment \& enjoy your day!}

~
\frak{Amphitrite1040:)}

User Rjf
by
4.5k points
5 votes

Answer:


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)

User Chan
by
4.0k points