Question
2. Write the numbers to the simplest form \[ 24: 72: 124 \]
Ask by Lynch Lambert. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified ratio is 6:18:31.
Solution
We need to simplify the ratio 24:72:124 by dividing each number by the greatest common factor (GCF) of all three numbers.
Step 1: Find the GCF of 24, 72, and 124.
Break each number into its prime factors:
• 24 = 2³ × 3
• 72 = 2³ × 3²
• 124 = 2² × 31
The common prime factor in all three numbers is 2, where the smallest exponent is 2 (from 124). Thus, the GCF is 2² = 4.
Step 2: Divide each term in the ratio by 4.
• 24 ÷ 4 = 6
• 72 ÷ 4 = 18
• 124 ÷ 4 = 31
The simplified ratio is 6:18:31.
Since there is no common factor (beyond 1) among 6, 18, and 31, this is the simplest form of the ratio.
Final Answer: 6:18:31.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
Let's simplify that ratio step by step! First, we find the greatest common divisor (GCD) of 24, 72, and 124. The GCD here is 4. So, we’ll divide each number by 4. - For 24: \( 24 ÷ 4 = 6 \) - For 72: \( 72 ÷ 4 = 18 \) - For 124: \( 124 ÷ 4 = 31 \) Now, when we put it all together, we get the simplest form of the ratio: **6 : 18 : 31**. Remember, ratios can really help in real-world scenarios like cooking or mixing ingredients, so it's always handy to know how to simplify them! And don’t forget, making a mistake in a common factor can lead to a whole new recipe, so triple-check those numbers!
