Cut In

to interrupt someone who is speaking or doing something

I was talking to my friend when my brother cut in and started telling his own story.

The teacher asked the student to stop cutting in and let his classmate finish her presentation.

to join a line of people or a conversation

I cut in line at the movie theater because I was running late.

I cut in on the conversation and introduced myself to the group.

to reduce or decrease something

The company had to cut in their spending due to financial difficulties.

I'm trying to cut in my sugar intake by eating less candy.