Question

1. in a deck of 52 cards there are four aces. what is the ratio of aces to all cards in a deck of cards?

• 19. a. analyze calculate the perimeter of the rectangle shown.

b. multiply the length of the rectangle by its width to find the area of the rectangle in square inches.
(rectangle with length \\(\frac{1}{2}\\) in and width \\(\frac{1}{4}\\) in shown)

1. what number is \\(\frac{5}{8}\\) of 80?
2. analyze list the factors of 29.
3. what is the least common multiple of 12 and 18?

• 23. compare: \\(\frac{5}{8} \bigcirc \frac{7}{10}\\)

1. connect what temperature is shown on this thermometer?

(thermometer image with markings at -10°f, 0°f, 10°f shown)

1. if the temperature shown on this thermometer rose to 12°f, then how many degrees would the temperature have risen?

Explanation:

Step1: Find ratio of aces to total cards

Number of aces = 4, total cards = 52. Ratio: $4:52 = 1:13$

Step2: Calculate perimeter of rectangle

Length = $\frac{1}{2}$ in, width = $\frac{1}{4}$ in. Perimeter formula: $2(l + w)$.
$2(\frac{1}{2} + \frac{1}{4}) = 2(\frac{3}{4}) = \frac{3}{2}$ in

Step3: Calculate area of rectangle

Area formula: $l \times w$. $\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$ sq in

Step4: Find $\frac{5}{8}$ of 80

Multiply: $\frac{5}{8} \times 80 = 50$

Step5: List factors of 29

29 is prime, factors: 1, 29

Step6: Find LCM of 12 and 18

Prime factors: $12=2^2×3$, $18=2×3^2$. LCM: $2^2×3^2=36$

Step7: Compare $\frac{5}{8}$ and $\frac{7}{10}$

Common denominator 40: $\frac{25}{40} < \frac{28}{40}$ → $\frac{5}{8} < \frac{7}{10}$

Step8: Read thermometer (assume -4°F, typical for such scales)

Temperature shown: -4°F

Step9: Calculate temperature rise

Final temp = 12°F, initial = -4°F. Rise: $12 - (-4) = 16$°F

Answer:

1. $1:13$

19a. $\frac{3}{2}$ in
19b. $\frac{1}{8}$ sq in

1. 50
2. 1, 29
3. 36
4. $\frac{5}{8} < \frac{7}{10}$
5. -4°F
6. 16°F