1. Solve these measurement of distance problems. a. \( \frac{1}{2} \) of a kilometre Example: What is one hall of a metre? b. \( \frac{1}{4} \) of a kilometre C. \( \frac{1}{4} \) of a cenfimetre \( \square \) d. \( \frac{1}{5} \) of a kilometre \( \square \) \( =\frac{1}{2} \times \frac{1000}{1} \mathrm{~mm} \) \( =\frac{1000}{2} \mathrm{~mm} \quad(1000+2) \) e. \( \frac{1}{4} \) of a metre \( \square \) \[ =500 \mathrm{~mm} \] 1. \( \frac{1}{2} \) of a centimetre \( \square \) 2. Solve these travel distance problems. If I completed \( \qquad \) of the distance of 500 km , how for do I still have to travel? Example: I completed one fifth of my 200 km journey. How far do I still need to travel? \[ \begin{array}{l} =\frac{1}{5} \times 200 \mathrm{~km} \\ =\frac{1}{5} \times \frac{200}{1} \mathrm{~km} \\ =\frac{200}{5} \mathrm{~km} \\ =40 \mathrm{~km} \end{array} \] I still need to travel 160 km . \( (200 \mathrm{~km} \) - 40 km ) a. \( \frac{1}{10} \) \( \square \) b. \( \frac{1}{12} \) \( \square \) C. \( \frac{1}{2} \) \( \square \) d. \( \frac{1}{3} \) \( \square \) e. \( \frac{1}{4} \) \( \square \) f. \( \frac{1}{6} \)

### 1. Measurement Distance Problems #### a. \(\frac{1}{2}\) of a kilometre A kilometre is \(1000\) metres. Therefore, \[ \frac{1}{2} \times 1000 = 500 \text{ metres} \] --- #### b. \(\frac{1}{4}\) of a kilometre \[ \frac{1}{4} \times 1000 = 250 \text{ metres} \] --- #### c. \(\frac{1}{4}\) of a centimetre A centimetre is the basic unit here so: \[ \frac{1}{4} \times 1 = 0.25 \text{ centimetres} \] If needed in millimetres (since \(1\,\text{cm} = 10\,\text{mm}\)): \[ 0.25 \times 10 = 2.5 \text{ mm} \] --- #### d. \(\frac{1}{5}\) of a kilometre \[ \frac{1}{5} \times 1000 = 200 \text{ metres} \] --- #### e. \(\frac{1}{4}\) of a metre A metre is \(1000\) millimetres. Thus, \[ \frac{1}{4} \times 1\,\text{m} = 0.25\,\text{m} \] Converting to millimetres: \[ 0.25 \times 1000 = 250 \text{ mm} \] --- #### f. \(\frac{1}{2}\) of a centimetre \[ \frac{1}{2} \times 1 = 0.5 \text{ centimetres} \] Converting to millimetres: \[ 0.5 \times 10 = 5 \text{ mm} \] --- ### 2. Travel Distance Problems The total journey is \(500\) km. For each part, we first compute the distance already completed and then subtract from \(500\) km. #### a. \(\frac{1}{10}\) of 500 km Completed distance: \[ \frac{1}{10} \times 500 = 50 \text{ km} \] Remaining distance: \[ 500 - 50 = 450 \text{ km} \] --- #### b. \(\frac{1}{12}\) of 500 km Completed distance: \[ \frac{1}{12} \times 500 = \frac{500}{12} \text{ km} \] Remaining distance (written as a fraction): \[ 500 - \frac{500}{12} = \frac{500 \times 12}{12} - \frac{500}{12} = \frac{6000 - 500}{12} = \frac{5500}{12} \text{ km} \] This can be simplified by dividing numerator and denominator by 2: \[ \frac{5500}{12} = \frac{2750}{6} \text{ km} \] Or expressed as a decimal, approximately: \[ \frac{500}{12} \approx 41.67 \text{ km} \quad \text{and} \quad 500 - 41.67 \approx 458.33 \text{ km} \] --- #### c. \(\frac{1}{2}\) of 500 km Completed distance: \[ \frac{1}{2} \times 500 = 250 \text{ km} \] Remaining distance: \[ 500 - 250 = 250 \text{ km} \] --- #### d. \(\frac{1}{3}\) of 500 km Completed distance: \[ \frac{1}{3} \times 500 = \frac{500}{3} \text{ km} \quad (\approx 166.67 \text{ km}) \] Remaining distance: \[ 500 - \frac{500}{3} = \frac{1500 - 500}{3} = \frac{1000}{3} \text{ km} \quad (\approx 333.33 \text{ km}) \] --- #### e. \(\frac{1}{4}\) of 500 km Completed distance: \[ \frac{1}{4} \times 500 = 125 \text{ km} \] Remaining distance: \[ 500 - 125 = 375 \text{ km} \] --- #### f. \(\frac{1}{6}\) of 500 km Completed distance: \[ \frac{1}{6} \times 500 = \frac{500}{6} \text{ km} \quad (\approx 83.33 \text{ km}) \] Remaining distance: \[ 500 - \frac{500}{6} = \frac{3000 - 500}{6} = \frac{2500}{6} \text{ km} \quad (\approx 416.67 \text{ km}) \]