(1) 80 Divide the following numbers in a ratio \( 1: 5: 5 \)

To divide the number **80** in the ratio \( 1 : 5 : 5 \), follow these steps: ### Step 1: Calculate the Total Number of Parts Add up all parts of the ratio: \[ 1 + 5 + 5 = 11 \text{ parts} \] ### Step 2: Determine the Value of One Part Divide the total number (80) by the total number of parts (11): \[ \text{Value of one part} = \frac{80}{11} \approx 7.27 \] ### Step 3: Allocate the Numbers Based on the Ratio - **First Portion (1 part):** \[ 1 \times \frac{80}{11} = \frac{80}{11} \approx 7.27 \] - **Second Portion (5 parts):** \[ 5 \times \frac{80}{11} = \frac{400}{11} \approx 36.36 \] - **Third Portion (5 parts):** \[ 5 \times \frac{80}{11} = \frac{400}{11} \approx 36.36 \] ### Summary of the Divided Amounts - **First Number:** \( \frac{80}{11} \) or **7 3⁄11** - **Second Number:** \( \frac{400}{11} \) or **36 4⁄11** - **Third Number:** \( \frac{400}{11} \) or **36 4⁄11** **Verification:** \[ 7\,\frac{3}{11} + 36\,\frac{4}{11} + 36\,\frac{4}{11} = 80 \] ### Decimal Representation If you prefer decimal values: - **First Number:** ≈ **7.27** - **Second Number:** ≈ **36.36** - **Third Number:** ≈ **36.36** These rounded values also add up to approximately **80**. --- **Final Answer:** Dividing 80 in the ratio 1 : 5 : 5 gives: • 7 3⁄11, • 36 4⁄11, and • 36 4⁄11. In decimal form: • 7.27, • 36.36, and • 36.36.