Question

1. test to see whether each equality statement is true by using the cross products test. show the products that lead to your true/false answer.

(a) \\(\frac{16}{24} = \frac{24}{36}\\)
(b) \\(\frac{15}{45} = \frac{3}{15}\\)
(b) \\(\frac{10}{14} = \frac{15}{20}\\)
(d) \\(\frac{18}{4} = \frac{9}{2}\\)

1. in a shoe store the ratio of men’s shoes to women’s shoes is 5 to 9.

(a) why can’t the number of women’s shoes be 40?
(b) if there are 25 pairs of men’s shoes, solve the following equation to find the number of pairs of women’s shoes, \\(w\\), there are in the shoe store.
\\(\frac{5}{9} = \frac{25}{w}\\)

1. the ratio of white milk to chocolate milk sold by a cafeteria yesterday was 5:4. there were 60 chocolate milks sold. solve the equation \\(\frac{5}{4} = \frac{w}{60}\\) for \\(w\\) to find the number of white milks that were sold yesterday.

n.gen math™ 7, unit 3 - practice with fractions and algebra
emathinstruction, east northport, ny 11731, © 2023

Explanation:

Problem 6: Cross Products Test

6(a): Cross-multiply to test equality

Calculate cross products: $16 \times 36 = 576$, $24 \times 24 = 576$

6(a): Compare cross products

$576 = 576$, so equality is true.

6(b): Cross-multiply to test equality

Calculate cross products: $15 \times 15 = 225$, $45 \times 3 = 135$

6(b): Compare cross products

$225
eq 135$, so equality is false.

6(c): Cross-multiply to test equality

Calculate cross products: $10 \times 20 = 200$, $14 \times 13 = 182$

6(c): Compare cross products

$200
eq 182$, so equality is false.

6(d): Cross-multiply to test equality

Calculate cross products: $18 \times 2 = 36$, $4 \times 9 = 36$

6(d): Compare cross products

$36 = 36$, so equality is true.

Problem 7

7(a): Explain ratio divisibility

The ratio $5:9$ means women's shoes must be a multiple of 9. $40 \div 9 \approx 4.44$, not an integer, so it cannot be 40.

7(b): Cross-multiply to solve for $w$

Cross products: $5w = 25 \times 9$

7(b): Simplify and solve for $w$

$5w = 225$, so $w = \frac{225}{5} = 45$

Problem 8

Step1: Cross-multiply to solve for $w$

Cross products: $4w = 5 \times 60$

Step2: Simplify and solve for $w$

$4w = 300$, so $w = \frac{300}{4} = 75$

Answer:

1. (a) TRUE

(b) FALSE
(c) FALSE
(d) TRUE

1. (a) The number of women's shoes must be a multiple of 9, and 40 is not divisible by 9.

(b) 45

1. 75