Grafting in rib
If you can graft in Stockinette stitch, you can graft in rib. This tutorial is for grafting in rib head to toe (the end of a piece grafted to the beginning of a provisionally cast-on piece).
First to clarify what we mean by knitwise and purlwise ... when we insert the tapestry needle knitwise, it approaches the stitch from left to right ... pointing in the same direction as the knitting needle.
When we insert the tapestry needle purlwise, it approaches the stitch from right to left ... pointing at the knitting needle.

Before beginning to graft, make sure that all the stitches are on the needles with right shoulders forward.
The needle with the row that has been most recently knit will be referred to as Needle 1;
the needle with the initial provisionally cast-on row is Needle 2.
Let's begin ...

Needle 1: With a tapestry needle threaded on the strand from Needle 1, insert tapestry needle purlwise into the first stitch on Needle 1 and draw through.

Needle 2: Insert purlwise into first stitch removing stitch,

Needle 2 (cont): insert knitwise into next stitch; draw through.

Needle 1: Insert knitwise into first stitch removing stitch,

Needle 1 (cont): insert knitwise into next stitch; draw through.

Needle 2:Insert knitwise into first stitch removing stitch,

Needle 2 (cont): insert purlwise into next stitch; draw through.

* Needle 1: Insert purlwise into first stitch removing stitch, insert purlwise into next stitch; draw through.

Needle 2: Insert purlwise into first stitch removing stitch, insert knitwise into next stitch; draw through.

Needle 1:Insert knitwise into first stitch removing stitch, insert knitwise into next stitch; draw through.

Needle 2: Insert knitwise into first stitch removing stitch, insert purlwise into next stitch; draw through.
Repeat from "*".

Neat!.
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