How many sixths are there in 2/3
The correct answer and explanation is:
To find how many sixths are in 23\frac{2}{3}, the question asks: how many parts of size 16\frac{1}{6} fit into 23\frac{2}{3}?
The process involves dividing 23\frac{2}{3} by 16\frac{1}{6}.
Step 1: Write the division expression: 23÷16\frac{2}{3} \div \frac{1}{6}
Step 2: Division of fractions means multiplying the first fraction by the reciprocal of the second: 23×61=2×63×1=123=4\frac{2}{3} \times \frac{6}{1} = \frac{2 \times 6}{3 \times 1} = \frac{12}{3} = 4
So, there are 4 sixths in 23\frac{2}{3}.
Explanation
A fraction represents a part of a whole divided into equal parts. For example, 23\frac{2}{3} means two parts out of three equal parts. The question wants to know how many sixths (parts of size 16\frac{1}{6}) make up 23\frac{2}{3}.
Since sixths are smaller parts compared to thirds, there will be more sixths than thirds in the same amount.
To find the number of sixths in 23\frac{2}{3}, the division operation helps by answering: how many 16\frac{1}{6} units fit into 23\frac{2}{3}?
Dividing by a fraction means multiplying by its reciprocal. The reciprocal of 16\frac{1}{6} is 61\frac{6}{1}. Multiplying 23\frac{2}{3} by 61\frac{6}{1} scales the fraction accordingly.
The calculation 23×61=123=4\frac{2}{3} \times \frac{6}{1} = \frac{12}{3} = 4 shows there are 4 parts of size 16\frac{1}{6} in 23\frac{2}{3}.
Another way to understand this is to convert 23\frac{2}{3} to sixths. Since one third equals two sixths (13=26\frac{1}{3} = \frac{2}{6}), two thirds equal four sixths (23=46\frac{2}{3} = \frac{4}{6}). This directly shows the answer is 4.
Thus, the answer is 4.