Syntax Error 1064 (I am a newbie)

[Elizabeth Block]

INSERT INTO 'jobs.companyID' SELECT*FROM 'companies.companyID' WHERE 'jobs.company=companies.company';

The above is resulting in a #1064 error, "#1064 - You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ''jobs.companyID' SELECT*FROM 'companies.companyID' WHERE 'jobs.company=companies' at line 1

My tables are 'companies' and 'jobs' and the referenced fields are correctly labeled.

I am trying to match a company name between the two tables and then if there is a match, to place the company ID which is primary in the company table into the jobs field called companyID. I am using MYSQL 5.1.55