grate, great

Grate or grate means the frame of crossed metal bars that may make the bottom of a fireplace or the cover of a vent or window--
When the fire went out, she swept the ashes out of the grate.
The grate that covers the basement windows can't be removed.
To "grate" something means to shred it on the teeth or openings of a metal kitchen gadget--
Will you grate the cheese while I make the dough?
She likes to grate carrots for the salad.
Something may "grate" on one's nerves--
Her endless chatter may grate on your nerves.

Great or great ( rhymes with grate ) means extremely large or important--
They study great men of letters at school.
There are statues of  great generals in the park.
"Humpty Dumpty had a great fall..."
There is a great crowd of people at the mall.
Great is also used to mean very good--
That was a great movie!
They make great burgers there!
What a great idea!

Now that you know that, you can say--
"Will you help me grate the carrots to make that great carrot cake we had last Thanksgiving?"

Note--"greater" means larger than, in size, number, or importance--
Six is greater than four.
The taxes will be a greater problem.
"Grater" means the device used for grating cheese or other food--
Don't let the grater get rusty.
Where's the grater? I want to make a pizza.