As an aid in drawing the human body, artists divide the body into three parts. Each part is then expressed as a fraction of the total body height. For example, the torso is 4/15
of the body height. What fraction of body height is the head? Below the waist the 3/5
4/15 + x + 3/5 = 1
4/15 + x + 9/14 = 15/15
...
To find the fraction of body height that represents the head, we need to subtract the fractions assigned to the torso and the lower body from 1, since we want to find the remaining fraction.
Given:
Torso fraction = 4/15
Lower body fraction = 3/5
To find the head fraction:
1 - (Torso fraction + Lower body fraction) = 1 - (4/15 + 3/5)
Now, let's simplify the expression:
1 - (4/15 + 3/5) = 1 - (4/15 + 9/15) = 1 - (13/15) = (15/15) - (13/15)
Subtracting the fractions give us:
(15/15) - (13/15) = 2/15
Therefore, the fraction of body height that represents the head is 2/15.
To find the fraction of the body height that represents the head, we need to subtract the fractions representing the torso and waist from the total height fraction.
Given that the torso is 4/15 of the body height and the waist is 3/5 below the waist, the sum of these two fractions is:
4/15 + 3/5
To add these fractions, we need to find a common denominator. In this case, the smallest common multiple of 15 and 5 is 15. Therefore, we can convert both fractions:
(4/15) + (3/5) = (4/15) + (9/15)
Now that the fractions have a common denominator, we can add them:
(4/15) + (9/15) = 13/15
So, the fraction of the body height that represents the head is 13/15.