Question

Of the teacups in Judith's Tea Shop, ( 1)/(2) are purple and another ( 3)/(8) are yellow. What fraction of the teacups are either purple or yellow?

Answer 1

To determine the fraction of teacups that are purple or yellow in Judith's Tea Shop, one adds ½ (purple) and ¾ (yellow), resulting in ¿ of the teacups being either purple or yellow after converting to a common denominator.

Step-by-step explanation:

To find out what fraction of the teacups are either purple or yellow, we simply add the fractions that represent the purple and yellow teacups. Judith's Tea Shop has ½ of the teacups that are purple and another ¾ that are yellow. To perform the addition of these two fractions, they need to have a common denominator.

The least common denominator (LCD) for 2 and 8 is 8. So, we need to convert the fraction for the purple teacups (½) to an equivalent fraction with a denominator of 8. We do this by multiplying both the numerator and the denominator by 4, giving us ¾. Now we can add ¾ and ¾.

Addition of the fractions:¾ (purple) + ¾ (yellow) = ¾ + ¾ = ¿

Therefore, the fraction of teacups that are either purple or yellow is ¿.