Learn French: Elle chante en balayant la cuisine. - She sings while sweeping the kitchen.

To make this form (called the gerund), start with the nous form of the present tense: nous balayons (we sweep). Drop the -ons ending and replace it with -ant to get balayant. Finally, put en in front of it. This creates the meaning 'while sweeping'.

Could en balayant also mean 'by sweeping'?

Yes, it can! The en + -ant structure can describe two things happening at once ('while doing') or the method used to achieve something ('by doing'). In this sentence, 'while sweeping' makes the most logical sense, because sweeping isn't a method used to sing.

Why didn't they use a word like pendant to mean 'while'?

You absolutely can use pendant que to mean 'while', but it requires a full phrase with a subject and a conjugated verb: Elle chante pendant qu'elle balaie. Using en balayant is just a much shorter and smoother way to say it when the exact same person is performing both actions.

I learned that verbs ending in -yer change their y to i. Why doesn't that happen here?