Answer:
Last week Mike caught 6 fish
Step-by-step explanation:
The unknown is he number of fish Mike caught last week, so let's use the letter "x" to represent that quantity.
Next, write 3 and 2/3 as an improper fraction: ![3+\frac{2}{3} =\frac{9}{3} +\frac{2}{3} =\frac{11}{3}](https://tex.z-dn.net/?f=3%2B%5Cfrac%7B2%7D%7B3%7D%20%3D%5Cfrac%7B9%7D%7B3%7D%20%2B%5Cfrac%7B2%7D%7B3%7D%20%3D%5Cfrac%7B11%7D%7B3%7D)
Now use it in the equation we create from translating the words into a mathematical expression: "22 fish this week, or 3 2/3rds times as many as last week." which translates into:
"22 fish is 3 2/3 (or 11/3) of "x" (last's week catch)"
and in math terms:
![22=\frac{11}{3} \,* x](https://tex.z-dn.net/?f=22%3D%5Cfrac%7B11%7D%7B3%7D%20%5C%2C%2A%20x)
and to find the unknown "x" we isolate it on one side of the equal sign by multiplying both sides of the equation by
:
![22=\frac{11}{3} \,* x\\22\,*\,\frac{3}{11} = \,\frac{3}{11}\,*\,\frac{11}{3} \,* x\\6=x](https://tex.z-dn.net/?f=22%3D%5Cfrac%7B11%7D%7B3%7D%20%5C%2C%2A%20x%5C%5C22%5C%2C%2A%5C%2C%5Cfrac%7B3%7D%7B11%7D%20%3D%20%5C%2C%5Cfrac%7B3%7D%7B11%7D%5C%2C%2A%5C%2C%5Cfrac%7B11%7D%7B3%7D%20%5C%2C%2A%20x%5C%5C6%3Dx)
So last week Mike caught 6 fish.