What type of cement should you buy, to fix small crack. Is a mortar type better that aggregate.
It must be smooth. Is there a ready made mix for this type of repair in the marketplace?

I have to ask if this is inside or outside and can you give us an idea of how large the crack or cracks are?

There are several different "preffered" methods based on how large it is and the location. A repair for a garage floor can be different from a driveway or walkway.

Keep us posted.

It just outside the front door. There is piece of cement loose and a hairline crack see
Attachments

If it were me I would use an epoxy based crack repair in this situation. Here is one product with tips for installation.

Its called expoxy-toxy.

CONCRETE CRACK REPAIR, Repairing cracks in Concrete, Patch Concrete Cracks. - Lone Star Epoxies

CONCRETE REPAIR CONCRETE RESTORATION SEALANT CONCRETE REPAIR EPOXY ROOFING MASTIC SEALING CONCRETE TREATMENT Lone Star Epoxies PARKING LOT REPAIR EPOXY FLOORING MATERIAL WATERPROOFING CONCRETE