The Importance of Simplifying Fractions

Oct 13, 2025 by miodeya.com 32 views

Understanding the Problem

When evaluating expressions involving fractions, it's essential to follow a step-by-step approach to ensure accuracy and simplify the resulting fraction. In this article, we'll focus on evaluating the expression shown below and provide a clear explanation of the process.

${ -\frac{7}{10} + \frac{7}{50} }$

The Importance of Simplifying Fractions

Simplifying fractions is a crucial skill in mathematics, as it helps to:

Reduce complex expressions to their simplest form
Make calculations easier and more efficient
Improve understanding of mathematical concepts

Step 1: Find a Common Denominator

To add or subtract fractions, we need to find a common denominator. In this case, the denominators are 10 and 50. To find the least common multiple (LCM), we can list the multiples of each denominator:

Multiples of 10: 10, 20, 30, 40, 50
Multiples of 50: 50, 100, 150, 200

The smallest number that appears in both lists is 50, which is the least common multiple of 10 and 50.

Step 2: Convert Each Fraction to Have the Common Denominator

Now that we have the common denominator, we can convert each fraction to have a denominator of 50.

${ -\frac{7}{10} = -\frac{7 \times 5}{10 \times 5} = -\frac{35}{50} }$

${ \frac{7}{50} = \frac{7}{50} }$

Step 3: Add or Subtract the Fractions

Now that both fractions have the same denominator, we can add or subtract them.

${ -\frac{35}{50} + \frac{7}{50} = -\frac{28}{50} }$

Step 4: Simplify the Resulting Fraction

To simplify the resulting fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 28 and 50 is 2.

${ -\frac{28}{50} = -\frac{14}{25} }$

The final answer is: -14/25

Understanding the Problem

${ -\frac{7}{10} + \frac{7}{50} }$

The Importance of Simplifying Fractions

Simplifying fractions is a crucial skill in mathematics, as it helps to:

Reduce complex expressions to their simplest form
Make calculations easier and more efficient
Improve understanding of mathematical concepts

Step 1: Find a Common Denominator

Multiples of 10: 10, 20, 30, 40, 50
Multiples of 50: 50, 100, 150, 200

The smallest number that appears in both lists is 50, which is the least common multiple of 10 and 50.

Step 2: Convert Each Fraction to Have the Common Denominator

Now that we have the common denominator, we can convert each fraction to have a denominator of 50.

${ -\frac{7}{10} = -\frac{7 \times 5}{10 \times 5} = -\frac{35}{50} }$

${ \frac{7}{50} = \frac{7}{50} }$

Step 3: Add or Subtract the Fractions

Now that both fractions have the same denominator, we can add or subtract them.

${ -\frac{35}{50} + \frac{7}{50} = -\frac{28}{50} }$

Step 4: Simplify the Resulting Fraction

To simplify the resulting fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 28 and 50 is 2.

${ -\frac{28}{50} = -\frac{14}{25} }$

The final answer is: -14/25

Frequently Asked Questions (FAQs)

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, you can divide both the numerator and denominator by their greatest common divisor (GCD).

Q: What is the difference between adding and subtracting fractions?

A: When adding fractions, you add the numerators and keep the same denominator. When subtracting fractions, you subtract the numerators and keep the same denominator.

Q: Can I add or subtract fractions with different denominators?

A: No, you cannot add or subtract fractions with different denominators. You need to find a common denominator before adding or subtracting fractions.

Q: How do I find a common denominator?

A: To find a common denominator, you can list the multiples of each denominator and find the smallest number that appears in both lists.

Q: What is the importance of simplifying fractions?

A: Simplifying fractions is a crucial skill in mathematics, as it helps to reduce complex expressions to their simplest form, make calculations easier and more efficient, and improve understanding of mathematical concepts.

Q: Can I simplify a fraction with a negative sign?

A: Yes, you can simplify a fraction with a negative sign by following the same steps as simplifying a positive fraction.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator by the denominator.

Q: Can I convert a decimal to a fraction?

A: Yes, you can convert a decimal to a fraction by finding the greatest common divisor (GCD) of the decimal and the denominator, and then dividing both the numerator and denominator by the GCD.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a part of a whole as a number with a decimal point.

Q: Can I add or subtract decimals?

A: Yes, you can add or subtract decimals by following the same rules as adding or subtracting fractions.

Q: How do I round a decimal to a specific number of places?

A: To round a decimal to a specific number of places, you can look at the digit in the next place and decide whether to round up or down.

Q: Can I convert a fraction to a percentage?

A: Yes, you can convert a fraction to a percentage by dividing the numerator by the denominator and then multiplying by 100.

Q: Can I convert a percentage to a fraction?

A: Yes, you can convert a percentage to a fraction by dividing the percentage by 100 and then simplifying the resulting fraction.

Q: What is the difference between a fraction and a mixed number?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a mixed number is a way of expressing a part of a whole as a combination of a whole number and a fraction.

Q: Can I add or subtract mixed numbers?

A: Yes, you can add or subtract mixed numbers by following the same rules as adding or subtracting fractions.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you can multiply the whole number by the denominator and then add the numerator.

Q: Can I convert an improper fraction to a mixed number?

A: Yes, you can convert an improper fraction to a mixed number by dividing the numerator by the denominator and then writing the result as a whole number and a fraction.

Q: What is the difference between an improper fraction and a proper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator, while a proper fraction is a fraction where the numerator is less than the denominator.

Q: Can I add or subtract improper fractions?

A: Yes, you can add or subtract improper fractions by following the same rules as adding or subtracting fractions.

Q: How do I simplify an improper fraction?

A: To simplify an improper fraction, you can divide both the numerator and denominator by their greatest common divisor (GCD).

Q: Can I convert an improper fraction to a decimal?

A: Yes, you can convert an improper fraction to a decimal by dividing the numerator by the denominator.

Q: Can I convert a decimal to an improper fraction?

A: Yes, you can convert a decimal to an improper fraction by finding the greatest common divisor (GCD) of the decimal and the denominator, and then dividing both the numerator and denominator by the GCD.

Q: What is the difference between a fraction and a ratio?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a ratio is a way of expressing the relationship between two quantities.

Q: Can I add or subtract ratios?

A: Yes, you can add or subtract ratios by following the same rules as adding or subtracting fractions.

Q: How do I simplify a ratio?

A: To simplify a ratio, you can divide both the numerator and denominator by their greatest common divisor (GCD).

Q: Can I convert a ratio to a fraction?

A: Yes, you can convert a ratio to a fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: Can I convert a fraction to a ratio?

A: Yes, you can convert a fraction to a ratio by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: What is the difference between a fraction and a proportion?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a proportion is a statement that two ratios are equal.

Q: Can I add or subtract proportions?

A: Yes, you can add or subtract proportions by following the same rules as adding or subtracting fractions.

Q: How do I simplify a proportion?

A: To simplify a proportion, you can divide both the numerator and denominator by their greatest common divisor (GCD).

Q: Can I convert a proportion to a fraction?

A: Yes, you can convert a proportion to a fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: Can I convert a fraction to a proportion?

A: Yes, you can convert a fraction to a proportion by dividing both the numerator and denominator by their greatest common divisor (GCD