Final answer:
Jade can make 2 and 5/8 bows from 1 3/4 yards of ribbon.
Step-by-step explanation:
To find out how many bows Jade can make from 1 3/4 yards of ribbon, we need to divide the total length of ribbon by the length required for each bow. Each bow requires 2/3 yard of ribbon. First, we convert 1 3/4 yards to an improper fraction. This is done by multiplying the whole number (1) by the denominator (4) and adding the numerator (3), then placing the result over the denominator. So, 1 3/4 yards is equal to 7/4 yards. Next, we divide 7/4 by 2/3 using the division of fractions rule, which states that dividing fractions is the same as multiplying by the reciprocal of the second fraction. Therefore, we multiply 7/4 by 3/2.
Now, let's multiply the numerators (7 and 3) and the denominators (4 and 2) separately. We get 21/8. This fraction can be simplified by finding a common factor for both the numerator and the denominator. Since 21 and 8 do not have a common factor other than 1, the fraction 21/8 is already in its simplest form. Therefore, Jade can make 2 and 5/8 bows from 1 3/4 yards of ribbon.