The word quarter means "4 parts the same," "four equal parts".
To find a quarter of any amount, cut the whole into "4 parts the same" and take any one part. The trick to doing this easily is to "cut it in half and then cut the half in half and take any piece." A quarter also means "half-of-a-half."
To find one quarter of 8 we cut the whole of 8 circles into "4 parts the same" by cutting the whole in half, and then the half in half. Taking any one part, we have a half-of-a-half of 8 is 2, or:
quarter of 8 = 2.
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