Answer:
[tex]21 \frac{1}{3}[/tex] fit into the product
Step-by-step explanation:
so you want to convert [tex]2 \frac{2}{3}[/tex] 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 [tex]\frac{8}{3}[/tex] and since the two fractions are equal they both become this. So now you have [tex]\frac{8}{3} * \frac{8}{3}[/tex] which can be calculated by multiplying the numerators and denominators. This gives you [tex]\frac{8*8}{3*3} = \frac{64}{9}[/tex]. 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 [tex]\frac{64}{9} \div \frac{1}{3}[/tex] which can be calculated by changing the sign to multiplication and flipping the second fraction (1/3 => 3/1) This gives you the equation [tex]\frac{64}{9} * \frac{3}{1} = \frac{64 * 3}{3 * 3} = \frac{64}{3}[/tex]. 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 [tex]21 \frac{1}{3}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2\dfrac{2}{3}\times 2 \dfrac{2}{3}}[/tex]
[tex]\mathsf{= \dfrac{2\times3+2}{3}\times\dfrac{2\times 3 + 2}{3}}}[/tex]
[tex]\mathsf{= \dfrac{6 + 2}{3}\times \dfrac{6 + 2}{3}}[/tex]
[tex]\mathsf{= \dfrac{8}{3}\times\dfrac{8}{3}}[/tex]
[tex]\mathsf{= \dfrac{8\times8}{3\times3}}[/tex]
[tex]\mathsf{= \dfrac{8 + 8 + 8 + 8 + 8 + 8 + 8 + 8}{3 + 3 + 3}}[/tex]
[tex]\mathsf{= \dfrac{16 + 16 + 16 + 16}{6 + 3}}[/tex]
[tex]\mathsf{= \dfrac{32 + 32}{9}}[/tex]
[tex]\mathsf{= \dfrac{64}{9}}[/tex]
[tex]\mathsf{= 7 \dfrac{1}{9}}[/tex]
[tex]\approx{\mathsf{21 \dfrac{1}{3}}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
