Question

1. mrs. cross is sewing dresses. she has 18 pink buttons and 20 purple buttons. each dress will have the same number of pink and purple buttons. using all the buttons, what is the greatest number of dresses mrs. cross can sew?

8.
$5\frac{2}{3}\cdot\frac{1}{2} = $
9.
$\frac{2}{3}\div\frac{1}{2} = $

Explanation:

Question 7

Step1: Find GCD of 18 and 20

To find the greatest number of dresses, we need the greatest common divisor (GCD) of 18 and 20. Factorize 18: \(18 = 2\times9 = 2\times3\times3\). Factorize 20: \(20 = 2\times10 = 2\times2\times5\). The common factor is 2.

Step2: Confirm the number of dresses

Since the GCD of 18 and 20 is 2, Mrs. Cross can sew 2 dresses (each with 9 pink and 10 purple buttons, using all buttons).

Step1: Convert mixed number to improper fraction

\(5\frac{2}{3}=\frac{5\times3 + 2}{3}=\frac{17}{3}\)

Step2: Multiply the fractions

\(\frac{17}{3}\times\frac{1}{2}=\frac{17\times1}{3\times2}=\frac{17}{6}=2\frac{5}{6}\)

Step1: Recall division of fractions rule

Dividing by a fraction is multiplying by its reciprocal. So \(\frac{2}{3}\div\frac{1}{2}=\frac{2}{3}\times\frac{2}{1}\)

Step2: Multiply the numerators and denominators

\(\frac{2\times2}{3\times1}=\frac{4}{3}=1\frac{1}{3}\)

Answer:

2

Question 8