Math Problem Statement
If a:b = 2:3 and b:c = 4:5 and c:d = 3:6 .then a:b:c:d is
Solution
We are given the following ratios:
We want to express in a simplified form. To do this, we need to adjust these ratios so that the common terms (like and ) match across the different ratios.
Step 1: Combine the ratios for
From and , we need to make the value of consistent. To do this, find the least common multiple (LCM) of the values for in both ratios. The values for are 3 and 4, and their LCM is 12.
- Multiply by 4 to get .
- Multiply by 3 to get .
Now, we have:
Step 2: Incorporate the ratio
From , simplify this to . We need to adjust this ratio so that matches the value from , where .
- Multiply by 15 to get .
Step 3: Final ratio for
Now, combine all the ratios:
Thus, the ratio is .
Would you like more details on any part of the solution?
Here are 5 related questions:
- How do you find the LCM of two numbers in general?
- Can ratios always be simplified in the same way?
- How can this method be applied to three or more terms in a ratio?
- What is the relationship between ratios and fractions?
- How do we know when to simplify ratios?
Tip: Always ensure that the common terms between ratios match before combining them. This helps in getting the correct proportional relationship.
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Math Problem Analysis
Mathematical Concepts
Ratios
Proportionality
Least Common Multiple (LCM)
Simplification
Formulas
LCM of two numbers
Ratio simplification
Theorems
Proportionality Theorem
Suitable Grade Level
Grades 6-8
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