Question
EXERCISE 1.4 Write all ratios in their simplest form. 1. There are three children in the Skosana family. Each week the eldest earns R270, the middle child earns R180 and the youngest earns R90. Express the: amounts as a ratio.
Ask by Schmidt Harrington. in South Africa
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The ratio of the children's earnings is 3:2:1.
Solution
To express the earnings of the Skosana children as a ratio in its simplest form, follow these steps:
1. **List the Earnings:**
- Eldest child: R270
- Middle child: R180
- Youngest child: R90
2. **Form the Initial Ratio:**
\[
270 : 180 : 90
\]
3. **Find the Greatest Common Divisor (GCD):**
- The GCD of 270, 180, and 90 is **90**.
4. **Simplify Each Term by Dividing by the GCD:**
\[
\frac{270}{90} : \frac{180}{90} : \frac{90}{90} = 3 : 2 : 1
\]
**Simplest Form of the Ratio:**
\[
3 : 2 : 1
\]
This means for every **3 parts** that the eldest child earns, the middle child earns **2 parts**, and the youngest child earns **1 part**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The amounts earned by the Skosana children can be expressed as a ratio of their earnings: R270 (eldest) : R180 (middle) : R90 (youngest). To simplify this ratio, we divide each amount by the smallest amount, which is R90. So, R270 ÷ R90 = 3, R180 ÷ R90 = 2, and R90 ÷ R90 = 1. Therefore, the simplified ratio is 3:2:1. This ratio of 3:2:1 shows the proportional earnings of each child. In practical terms, this means that for every R3 earned by the eldest, the middle child earns R2, and the youngest earns R1, illustrating how their earnings relate to one another in an easy-to-understand way!
