Let's solve this problem step-by-step.
STEP-BY-STEP SOLUTION:
To begin with, let's convert the worded problem into an equation.
Let unknown fraction = x
x × 22 / 7 = 22 / 21
Next we will make ( x ) the subject by keeping ( x ) on the left-hand side of the equation and all other numbers on the right-hand side of the equation.
x = 22 / 21 ÷ 22 / 7
Then we will turn this division problem into a multiplication problem by changing the division symbol ( ÷ ) into a multiplication symbol ( × ) and changing the fraction after the symbol into its reciprocal. Reciprocal basically means that the numerator becomes the denominator and the denominator becomes the numerator.
x = 22 / 21 × 7 / 22
After that, we will multiply the numerators of each fraction together and the denominators of each fraction together to make one fraction.
x = 154 / 462
Now we will simplify the fraction by dividing both the numerator and denominator by their HCF ( Highest Common Factor ) which is 154.
x = 1 / 3
FINAL ANSWER:
Therefore, the unknown fraction is 1 / 3.
Hope this helps! :)
Have a lovely day! <3