6. Find the value of each of the following. (a) $$ 40 \% $$ of 120 cm (b) $$ 15 \% $$ of $$ 360^{\circ} $$ (c) $$ 66 \frac{2}{3} \% $$ of 54 s

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### Problem 6

**Find the value of each of the following:**

#### (a) $$ 40\% $$ of 120 cm

**Solution:**

To find $$ 40\% $$ of 120 cm:

1. Convert the percentage to a decimal:
   $$
   40\% = \frac{40}{100} = 0.40
   $$

2. Multiply the decimal by the given value:
   $$
   0.40 \times 120\, \text{cm} = 48\, \text{cm}
   $$

**Answer:** $$ 40\% $$ of 120 cm is **48 cm**.

#### (b) $$ 15\% $$ of $$ 360^{\circ} $$

**Solution:**

To find $$ 15\% $$ of $$ 360^{\circ} $$:

1. Convert the percentage to a decimal:
   $$
   15\% = \frac{15}{100} = 0.15
   $$

2. Multiply the decimal by the given value:
   $$
   0.15 \times 360^{\circ} = 54^{\circ}
   $$

**Answer:** $$ 15\% $$ of $$ 360^{\circ} $$ is **54 degrees**.

#### (c) $$ 66 \frac{2}{3}\% $$ of 54 s

**Solution:**

To find $$ 66 \frac{2}{3}\% $$ of 54 seconds:

1. Convert the mixed number percentage to an improper fraction or decimal:
   $$
   66 \frac{2}{3}\% = \frac{200}{3}\% = \frac{200}{3} \times \frac{1}{100} = \frac{2}{3} \approx 0.6667
   $$

2. Multiply the decimal or fraction by the given value:
   $$
   \frac{2}{3} \times 54\, \text{s} = 36\, \text{s}
   $$

**Answer:** $$ 66 \frac{2}{3}\% $$ of 54 seconds is **36 seconds**.
- $$ 40\% $$ of 120 cm is **48 cm**. - $$ 15\% $$ of $$ 360^{\circ} $$ is **54 degrees**. - $$ 66 \frac{2}{3}\% $$ of 54 seconds is **36 seconds**.

6. Find the value of each of the following. (a) \( 40 \% \) of 120 cm (b) \( 15 \% \) of \( 360^{\circ} \) (c) \( 66 \frac{2}{3} \% \) of 54 s

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