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

Sure, let's solve each part step by step. ### 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**.