Question
YERCISE 4 You may use a calculator in this exercise.
Express the following as a ratio in its simplest form:
Express the following as a ratio in its simplest form:
Ask by Wheeler Chambers. in South Africa
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the simplified ratios:
- 3 : 2
- 3 : 4
- 3 : 5
- 3 : 2
- 3 : 5 : 7
- 100 : 1 : 10
- 8 : 5
- 6 : 1
- 10 : 1
- 15 : 5 : 1
- 1 : 5
- 10 : 1 : 5
Solution
To express the given ratios in their simplest form, we will follow these steps for each ratio:
- Divide each term of the ratio by the greatest common divisor (GCD) of the terms.
- If there are more than two terms, find the GCD of all terms and divide each term by that GCD.
Let’s solve each ratio step by step.
(1)
- GCD of 18 and 12 is 6.
- Simplified ratio:
(2)
- GCD of 24 and 32 is 8.
- Simplified ratio:
(3)
- GCD of 15 and 25 is 5.
- Simplified ratio:
(4)
- GCD of 30 and 20 is 10.
- Simplified ratio:
(5)
- GCD of 9, 15, and 21 is 3.
- Simplified ratio:
(6)
- GCD of 1000, 10, and 100 is 10.
- Simplified ratio:
(7)
- To eliminate the decimal, multiply both terms by 10:
. - GCD of 16 and 10 is 2.
- Simplified ratio:
(8)
- To eliminate the decimal, multiply both terms by 100:
. - GCD of 36 and 6 is 6.
- Simplified ratio:
(9)
- To eliminate the decimal, multiply both terms by 100000:
. - GCD of 1 and 0.1 is 0.1.
- Simplified ratio:
(10)
- To eliminate the decimal, multiply all terms by 100:
. - GCD of 240, 80, and 16 is 16.
- Simplified ratio:
(11)
- Convert 1.5 m to cm:
. - Ratio:
. - GCD of 30 and 150 is 30.
- Simplified ratio:
(12)
- Convert 6 kg to g:
. - Ratio:
. - GCD of 6000, 600, and 3000 is 600.
- Simplified ratio:
Summary of Simplified Ratios:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To express ratios in their simplest form, you need to find the greatest common divisor (GCD) of the numbers involved and divide each number by that GCD. This process can greatly help in various situations where you need to understand proportions and relationships between quantities clearly.
For example, in real-world applications, expressing quantities as ratios helps in cooking, mixing chemicals, or even in finance, where you might need to compare profitability or costs. Imagine you’re baking a cake and the recipe calls for 18 cups of flour for every 12 cups of sugar. Simplifying the ratio to 3:2 makes it easier to scale up or down according to your needs!
