(2) Converting The Fraction Of And 14 7 Into Like Fractions =​

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Introduction

In mathematics, converting fractions into like fractions is an essential skill that helps in simplifying complex calculations and solving various mathematical problems. A like fraction is a fraction that has the same denominator as another fraction. In this article, we will discuss how to convert the fraction of 14/7 into like fractions.

What are Like Fractions?

Like fractions are fractions that have the same denominator. For example, 1/4 and 2/4 are like fractions because they have the same denominator, which is 4. Similarly, 3/8 and 5/8 are like fractions because they have the same denominator, which is 8.

Why Convert Fractions into Like Fractions?

Converting fractions into like fractions is helpful in various mathematical operations such as addition, subtraction, multiplication, and division. When fractions have the same denominator, it becomes easier to perform these operations. For instance, when adding two fractions with the same denominator, we simply add the numerators and keep the denominator the same.

Converting the Fraction of 14/7 into Like Fractions

To convert the fraction of 14/7 into like fractions, we need to find the least common multiple (LCM) of 7 and the desired denominator. The LCM of 7 and any other number is the smallest number that is a multiple of both numbers.

Finding the Least Common Multiple (LCM)

To find the LCM of 7 and the desired denominator, we can list the multiples of each number and find the smallest number that appears in both lists.

For example, if we want to convert the fraction of 14/7 into like fractions with a denominator of 10, we can list the multiples of 7 and 10 as follows:

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 Multiples of 10: 10, 20, 30, 40, 50, 60, 70

The smallest number that appears in both lists is 70, which is the LCM of 7 and 10.

Converting the Fraction

Now that we have found the LCM, we can convert the fraction of 14/7 into like fractions with a denominator of 10.

To do this, we can multiply the numerator and denominator of the fraction by the LCM, which is 70.

14/7 = (14 × 10) / (7 × 10) = 140/70

Therefore, the fraction of 14/7 can be converted into like fractions with a denominator of 10 as 140/70.

Simplifying the Fraction

The fraction 140/70 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 140 and 70 is 70.

140 ÷ 70 = 2 70 ÷ 70 = 1

Therefore, the simplified fraction is 2/1, which is equal to 2.

Conclusion

In conclusion, converting the fraction of 14/7 into like fractions is an essential skill that helps in simplifying complex calculations and solving various mathematical problems. By finding the least common multiple (LCM) of 7 and the desired denominator, we can convert the fraction into like fractions. We can then simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). With practice and patience, anyone can master the art of converting fractions into like fractions.

Frequently Asked Questions

Q: What is a like fraction?

A: A like fraction is a fraction that has the same denominator as another fraction.

Q: Why convert fractions into like fractions?

A: Converting fractions into like fractions is helpful in various mathematical operations such as addition, subtraction, multiplication, and division.

Q: How do I find the least common multiple (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: 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).

Examples

Example 1: Converting the Fraction of 14/7 into Like Fractions with a Denominator of 10

To convert the fraction of 14/7 into like fractions with a denominator of 10, we can multiply the numerator and denominator of the fraction by the LCM, which is 70.

14/7 = (14 × 10) / (7 × 10) = 140/70

Therefore, the fraction of 14/7 can be converted into like fractions with a denominator of 10 as 140/70.

Example 2: Simplifying the Fraction 140/70

The fraction 140/70 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 140 and 70 is 70.

140 ÷ 70 = 2 70 ÷ 70 = 1

Therefore, the simplified fraction is 2/1, which is equal to 2.

Tips and Tricks

Tip 1: Use the Least Common Multiple (LCM) to Convert Fractions

When converting fractions into like fractions, use the least common multiple (LCM) of the two numbers to find the new denominator.

Tip 2: Simplify Fractions by Dividing by the Greatest Common Divisor (GCD)

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

Tip 3: Practice, Practice, Practice!

The more you practice converting fractions into like fractions, the more comfortable you will become with the process.

Conclusion

In conclusion, converting the fraction of 14/7 into like fractions is an essential skill that helps in simplifying complex calculations and solving various mathematical problems. By finding the least common multiple (LCM) of 7 and the desired denominator, we can convert the fraction into like fractions. We can then simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). With practice and patience, anyone can master the art of converting fractions into like fractions.

Introduction

Converting fractions into like fractions is an essential skill in mathematics that helps in simplifying complex calculations and solving various mathematical problems. In this article, we will answer some frequently asked questions (FAQs) on converting fractions into like fractions.

Q&A

Q: What is a like fraction?

A: A like fraction is a fraction that has the same denominator as another fraction.

Q: Why convert fractions into like fractions?

A: Converting fractions into like fractions is helpful in various mathematical operations such as addition, subtraction, multiplication, and division.

Q: How do I find the least common multiple (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: 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 a like fraction and a unlike fraction?

A: A like fraction is a fraction that has the same denominator as another fraction, while a unlike fraction is a fraction that has a different denominator.

Q: Can I convert a fraction into a like fraction with any denominator?

A: No, you can only convert a fraction into a like fraction with a denominator that is a multiple of the original denominator.

Q: How do I convert a fraction into a like fraction with a specific denominator?

A: To convert a fraction into a like fraction with a specific denominator, you need to find the least common multiple (LCM) of the original denominator and the desired denominator.

Q: Can I simplify a fraction by dividing both the numerator and denominator by a number that is not their greatest common divisor (GCD)?

A: No, you can only simplify a fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: How do I check if a fraction is in its simplest form?

A: To check if a fraction is in its simplest form, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.

Q: Can I convert a fraction into a like fraction with a negative denominator?

A: No, you cannot convert a fraction into a like fraction with a negative denominator.

Q: How do I convert a fraction into a like fraction with a decimal denominator?

A: To convert a fraction into a like fraction with a decimal denominator, you need to convert the decimal to a fraction and then find the least common multiple (LCM) of the two denominators.

Examples

Example 1: Converting the Fraction of 14/7 into Like Fractions with a Denominator of 10

To convert the fraction of 14/7 into like fractions with a denominator of 10, we can multiply the numerator and denominator of the fraction by the LCM, which is 70.

14/7 = (14 × 10) / (7 × 10) = 140/70

Therefore, the fraction of 14/7 can be converted into like fractions with a denominator of 10 as 140/70.

Example 2: Simplifying the Fraction 140/70

The fraction 140/70 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 140 and 70 is 70.

140 ÷ 70 = 2 70 ÷ 70 = 1

Therefore, the simplified fraction is 2/1, which is equal to 2.

Tips and Tricks

Tip 1: Use the Least Common Multiple (LCM) to Convert Fractions

When converting fractions into like fractions, use the least common multiple (LCM) of the two numbers to find the new denominator.

Tip 2: Simplify Fractions by Dividing by the Greatest Common Divisor (GCD)

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

Tip 3: Practice, Practice, Practice!

The more you practice converting fractions into like fractions, the more comfortable you will become with the process.

Conclusion

In conclusion, converting fractions into like fractions is an essential skill that helps in simplifying complex calculations and solving various mathematical problems. By finding the least common multiple (LCM) of 7 and the desired denominator, we can convert the fraction into like fractions. We can then simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). With practice and patience, anyone can master the art of converting fractions into like fractions.

Additional Resources

  • Math Is Fun: A website that provides interactive math lessons and games.
  • Khan Academy: A website that provides free online math lessons and exercises.
  • Mathway: A website that provides step-by-step math solutions and explanations.

Glossary

  • Like fraction: A fraction that has the same denominator as another fraction.
  • Unlike fraction: A fraction that has a different denominator.
  • Least common multiple (LCM): The smallest number that is a multiple of two or more numbers.
  • Greatest common divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.
  • Simplify: To reduce a fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).