an analog clock can serve as a visual Reference for twelfths. at 1 o clock the hands mark off 1/12 of a circle at 2 o clock the hands mark off 2/12 of a circle and so on. how many twelfths are in each of these fractions of a circle?
1/2, 1/4, 1/3, 1/6
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To determine how many twelfths are in each of these fractions of a circle, we need to convert the fractions to a common denominator of 12.
Let's go through each fraction:
1/2:
To express 1/2 as a twelfth, we'll multiply both the numerator and denominator by 6 (since 2 multiplied by 6 equals 12). So, 1/2 multiplied by 6/6 equals 6/12. Therefore, there are 6 twelfths in 1/2.
1/4:
To express 1/4 as a twelfth, we'll multiply both the numerator and denominator by 3 (since 4 multiplied by 3 equals 12). So, 1/4 multiplied by 3/3 equals 3/12. Therefore, there are 3 twelfths in 1/4.
1/3:
To express 1/3 as a twelfth, we'll multiply both the numerator and denominator by 4 (since 3 multiplied by 4 equals 12). So, 1/3 multiplied by 4/4 equals 4/12. Therefore, there are 4 twelfths in 1/3.
1/6:
To express 1/6 as a twelfth, we'll multiply both the numerator and denominator by 2 (since 6 multiplied by 2 equals 12). So, 1/6 multiplied by 2/2 equals 2/12. Therefore, there are 2 twelfths in 1/6.
So, to summarize:
1/2 equals 6 twelfths.
1/4 equals 3 twelfths.
1/3 equals 4 twelfths.
1/6 equals 2 twelfths.