Question

1. calculate the perimeter of this dining room tabletop.

perimeter of straight sides =
perimeter of curved side =
total perimeter of all sides =

1. label these angles as \\(30^\circ\\), \\(60^\circ\\), or \\(90^\circ\\).

a)
b)
c)

1. complete each equivalent fraction.

a) \\(\frac{4}{16} = \frac{\quad}{4}\\)
b) \\(\frac{3}{4} = \frac{\quad}{8}\\)
c) \\(\frac{6}{16} = \frac{\quad}{8}\\)
d) \\(\frac{3}{4} = \frac{\quad}{16}\\)
e) \\(\frac{2}{8} = \frac{\quad}{4}\\)
f) \\(\frac{7}{8} = \frac{\quad}{16}\\)

1. fill in each blank with one of these words to complete the story.

budget, change, discount, sale price, tip
a) betty has \\(\\$10\\) to spend on dinner. this amount is called her
b) a basket of cheese fries is regularly \\(\\$5.99\\). tonight, each basket is \\(\frac{1}{2}\\) off. so, betty estimates that the is \\(\\$3\\) per basket.
c) betty rounds the regular price of 1 basket to \\(\\$6\\). then, she estimates that the is \\(\\$6 - \\$3\\).
d) betty had very good service in the restaurant. so, she is going to leave a \\(20\\%\\) instead of \\(15\\%\\).
e) betty gave her server \\(\\$10\\) and is waiting for her

Explanation:

🆕 New Concept Discovered: Unit Conversion in Geometry
Matching units before calculating

Step 1: Convert units to be consistent

The tabletop has straight sides measured in meters (\(1.5\text{ m}\)) and a width/diameter measured in centimeters (\(76\text{ cm}\)). We need to convert them to the same unit. Let's use centimeters:

\[
1.5\text{ m} = 1.5 \times 100\text{ cm} = 150\text{ cm}
\]

Step 2: Calculate the perimeter of the straight sides

The tabletop consists of a rectangular middle section with semicircles on the ends. The straight sides are the top and bottom edges of this middle section:

\[
\text{Perimeter of straight sides} = 150\text{ cm} + 150\text{ cm} = 300\text{ cm} \quad (\text{or } 3\text{ m})
\]

Step 3: Calculate the perimeter of the curved sides

The two semicircular ends combine to make one full circle with a diameter of \(d = 76\text{ cm}\):

\[
\text{Perimeter of curved sides} = \pi \times d \approx 3.14 \times 76\text{ cm} \approx 238.64\text{ cm} \quad (\text{or } 2.39\text{ m})
\]

Step 4: Calculate the total perimeter

Add the straight sides and the curved sides together:

\[
\text{Total perimeter} = 300\text{ cm} + 238.64\text{ cm} = 538.64\text{ cm} \quad (\text{or } 5.39\text{ m})
\]

---

Step 5: Label the angles (Question 13)

• a) This is a right angle: \(90^\circ\)
• b) This is a sharp, acute angle: \(30^\circ\)
• c) This is a wider, acute angle: \(60^\circ\)

---

Step 6: Complete the equivalent fractions (Question 14)

Find the missing numbers by multiplying or dividing the numerator and denominator by the same value:

• a) \(\frac{4}{16} = \frac{1}{4}\) (divide top and bottom by 4)
• b) \(\frac{3}{4} = \frac{6}{8}\) (multiply top and bottom by 2)
• c) \(\frac{6}{16} = \frac{3}{8}\) (divide top and bottom by 2)
• d) \(\frac{3}{4} = \frac{12}{16}\) (multiply top and bottom by 4)
• e) \(\frac{2}{8} = \frac{1}{4}\) (divide top and bottom by 2)
• f) \(\frac{7}{8} = \frac{14}{16}\) (multiply top and bottom by 2)

---

Step 7: Fill in the blanks (Question 15)

• a) Betty has \$10 to spend on dinner. This amount is called her budget.
• b) A basket of cheese fries is regularly \$5.99. Tonight, each basket is LXI0 off. So, Betty estimates that the **sale price** is \$3 per basket.
• c) Betty rounds the regular price of 1 basket to \$6. Then, she estimates that the **discount** is \$6 - \$3.
• d) Betty had very good service in the restaurant. So, she is going to leave a 20% tip instead of 15%.
• e) Betty gave her server \$10 and is waiting for her change.

Answer:

Question 12:

• Perimeter of straight sides = \(300\text{ cm}\) (or \(3\text{ m}\))
• Perimeter of curved side = \(238.64\text{ cm}\) (or \(2.39\text{ m}\))
• Total perimeter of all sides = \(538.64\text{ cm}\) (or \(5.39\text{ m}\))

Question 13:

• a) \(90^\circ\)
• b) \(30^\circ\)
• c) \(60^\circ\)

Question 14:

• a) \(1\)
• b) \(6\)
• c) \(3\)
• d) \(12\)
• e) \(1\)
• f) \(14\)

Question 15:

• a) budget
• b) sale price
• c) discount
• d) tip
• e) change