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# Two thirds divided by one third?

1 third.

This answer is incorrect. When you use the words "divided by", that means you use the regular process of dividing by a fraction. To do this, you take the reciprocal of the fraction (1/2 here) and then multiply. The actual problem here is 2/3 TIMES 2/1. The answer is 4/3.

If you want to find half of some number, you multiply by half, not divide. The wording should be "divide into half" not "divide by half."

These two are completely different. This is a frightfully common misunderstanding and leads to great confusion.

Another example: 8 divided into half is 4

` but

8 divided by half is 16. (8 times the reciprocal of 1/2)

Just for background:

I teach high school algebra; my husband has a BSc and a MSc in both Mathematics and Math Education. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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One half divided by two thirds is equal to three quarters. This can be calculated by multiplying one half by three halves, as the denominator is a fraction and needs to be inversed and multiplied. 2/3 divided by 1/3 = 2/3 x 3/1 = 6/3 = 2 Also, you have two thirds, and one third. You have twice as many thirds in the two thirds than in the one third. The answer to one twelfth divided by two thirds is 1/72. 1/5 divided by 2/3 = 1/5 * 3/2 = 3/10. 2/3 ÷ 1/4 = 22/3 1/12 9 `527341  Earn +20 pts  