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Summary

In this video, viewers will learn how to compare fractions using two primary methods: comparing fractions with the same denominator and using the least common multiple (LCM) for fractions with different denominators. Additionally, the cross-multiplication method is explained for easier comparison. The video provides clear, step-by-step examples, making it easy to understand these methods and choose the one that works best for each situation. This educational content aims to help math enthusiasts confidently compare fractions, whether they're equal, smaller, or greater.

Takeaways

• 😀 Fractions can be compared using three main signs: less than (<), greater than (>), and equal (=).
• 😀 To distinguish between the comparison signs, remember the 'k' shape for less than and 'b' shape for greater than.
• 😀 When comparing fractions with the same denominator, compare the numerators directly.
• 😀 Example: **1/5** is smaller than **2/5** because 1 is smaller than 2.
• 😀 Another example: **5/7** is greater than **3/7** because 5 is greater than 3.
• 😀 For fractions with different denominators, two methods can be used: finding the Least Common Multiple (LCM) or cross-multiplication.
• 😀 Using LCM: If the denominators are different, find the LCM to make the denominators the same and then compare the numerators.
• 😀 Example: **7/8** is greater than **2/4** after converting **2/4** to **4/8**.
• 😀 Cross-multiplication: Multiply the numerator of one fraction by the denominator of the other to compare the results.
• 😀 Example: **3/4** is greater than **2/6** after cross-multiplying, giving results of 18 and 8.
• 😀 Always ensure you convert fractions correctly when using LCM or cross-multiplication methods to make accurate comparisons.

Q & A

What are the two ways to compare fractions as mentioned in the video?

The two ways to compare fractions are: 1) By making the denominators the same (using the Least Common Multiple, LCM), and 2) By cross-multiplying the numerators and denominators of the two fractions.

How do we distinguish between the 'greater than' and 'less than' signs?

The 'greater than' sign is drawn in the shape of the letter 'b', while the 'less than' sign is drawn in the shape of the letter 'k'. The open side of the 'b' points to the larger number, and the open side of the 'k' points to the smaller number.

When comparing fractions with the same denominator, how do you determine which one is greater?

When fractions have the same denominator, you compare their numerators. The fraction with the larger numerator is the greater fraction.

How do you compare fractions like 1/5 and 2/5?

Since the denominators are the same (both are 5), you just compare the numerators. 1 is smaller than 2, so 1/5 is smaller than 2/5.

How do you compare fractions with different denominators, like 7/8 and 2/4?

First, find the LCM of the denominators (in this case, 8 and 4). Then adjust the fractions to have the same denominator. For 7/8 and 2/4, the LCM is 8, so 2/4 becomes 4/8. Comparing 7/8 and 4/8, 7/8 is greater.

What is the LCM and why is it used when comparing fractions?

LCM stands for Least Common Multiple. It is used to find a common denominator when comparing fractions with different denominators, so that the fractions can be easily compared.

Can you explain how to convert 1/2 and 4/5 to fractions with a common denominator?

To compare 1/2 and 4/5, find the LCM of 2 and 5, which is 10. Then convert both fractions: 1/2 becomes 5/10, and 4/5 becomes 8/10. Comparing the numerators, 5/10 is smaller than 8/10, so 1/2 is smaller than 4/5.

How do you compare fractions like 3/4 and 2/6 using cross-multiplication?

To compare 3/4 and 2/6 using cross-multiplication, multiply 3 by 6 (18) and 2 by 4 (8). Since 18 is greater than 8, 3/4 is greater than 2/6.

What is the result when comparing 3/12 and 2/3 using cross-multiplication?

For 3/12 and 2/3, multiply 3 by 3 (9) and 2 by 12 (24). Since 9 is smaller than 24, 3/12 is smaller than 2/3.

What should you do if you encounter fractions with different denominators?

If you encounter fractions with different denominators, you can either find the LCM to make the denominators the same or use cross-multiplication to compare the fractions directly.