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What is the rule for subtracting fractions with different denominators?
- a)Multiply the numerators and denominators
- b)Find the LCM of the denominators and make them common
- c)Subtract the numerators and denominators
- d)Divide the numerators and denominators
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
What is the rule for subtracting fractions with different denominators...
To subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and make them the same.
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What is the rule for subtracting fractions with different denominators...
Explanation:
To subtract fractions with different denominators, we need to find a common denominator and then subtract the numerators. The common denominator is the least common multiple (LCM) of the denominators.
Step-by-step process:
1. Find the LCM of the denominators:
- Identify the denominators of the fractions you want to subtract.
- Find the LCM of these denominators.
- The LCM is the smallest multiple that is divisible by both denominators.
2. Make the denominators common:
- To make the denominators common, you need to convert the fractions so that they have the same denominator.
- Divide the LCM by the original denominator of each fraction to get the factor by which you need to multiply the numerator and denominator.
- Multiply the numerator and denominator of each fraction by the respective factors.
3. Subtract the numerators:
- Once the denominators are the same, subtract the numerators of the fractions.
- Write the result as the numerator of the new fraction.
4. Simplify the fraction (if necessary):
- If the resulting fraction can be simplified, divide both the numerator and denominator by their greatest common divisor (GCD) to simplify it.
- Simplifying the fraction gives the final answer.
Example:
Let's subtract the fractions 1/4 and 1/3.
1. Find the LCM of the denominators:
- The denominators are 4 and 3.
- The LCM of 4 and 3 is 12.
2. Make the denominators common:
- For the fraction 1/4, multiply the numerator and denominator by 3 (12/12).
- For the fraction 1/3, multiply the numerator and denominator by 4 (4/12).
3. Subtract the numerators:
- 12/12 - 4/12 = 8/12.
4. Simplify the fraction (if necessary):
- Divide both the numerator and denominator by their GCD, which is 4.
- 8/12 simplifies to 2/3.
So, 1/4 - 1/3 = 2/3.
Answer:
The rule for subtracting fractions with different denominators is to find the LCM of the denominators and make them common.
To subtract fractions with different denominators, we need to find a common denominator and then subtract the numerators. The common denominator is the least common multiple (LCM) of the denominators.
Step-by-step process:
1. Find the LCM of the denominators:
- Identify the denominators of the fractions you want to subtract.
- Find the LCM of these denominators.
- The LCM is the smallest multiple that is divisible by both denominators.
2. Make the denominators common:
- To make the denominators common, you need to convert the fractions so that they have the same denominator.
- Divide the LCM by the original denominator of each fraction to get the factor by which you need to multiply the numerator and denominator.
- Multiply the numerator and denominator of each fraction by the respective factors.
3. Subtract the numerators:
- Once the denominators are the same, subtract the numerators of the fractions.
- Write the result as the numerator of the new fraction.
4. Simplify the fraction (if necessary):
- If the resulting fraction can be simplified, divide both the numerator and denominator by their greatest common divisor (GCD) to simplify it.
- Simplifying the fraction gives the final answer.
Example:
Let's subtract the fractions 1/4 and 1/3.
1. Find the LCM of the denominators:
- The denominators are 4 and 3.
- The LCM of 4 and 3 is 12.
2. Make the denominators common:
- For the fraction 1/4, multiply the numerator and denominator by 3 (12/12).
- For the fraction 1/3, multiply the numerator and denominator by 4 (4/12).
3. Subtract the numerators:
- 12/12 - 4/12 = 8/12.
4. Simplify the fraction (if necessary):
- Divide both the numerator and denominator by their GCD, which is 4.
- 8/12 simplifies to 2/3.
So, 1/4 - 1/3 = 2/3.
Answer:
The rule for subtracting fractions with different denominators is to find the LCM of the denominators and make them common.
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