Understanding Equivalent Fractions
Equivalent fractions are fractions that have the same value but different numerators and denominators. To find the equivalent fraction of 5/10, we need to understand the concept of equivalent fractions and how to simplify them. When we simplify a fraction, we reduce the numerator and denominator to their simplest form. For example, the fraction 10/20 can be simplified to 1/2. To simplify a fraction, we divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both numbers evenly.Step 1: Finding the Greatest Common Divisor (GCD)
To find the equivalent fraction of 5/10, we need to find the GCD of the numerator (5) and denominator (10). The GCD of 5 and 10 is 5. We can find the GCD by listing the factors of each number and finding the greatest common factor. Here are the factors of 5 and 10:- Factors of 5: 1, 5
- Factors of 10: 1, 2, 5, 10
Step 2: Simplifying the Fraction
Now that we have found the GCD, we can simplify the fraction by dividing both the numerator and denominator by 5. 5 ÷ 5 = 1 10 ÷ 5 = 2 Therefore, the simplified fraction is 1/2.Step 3: Finding the Equivalent Fraction
Comparing Fractions with Different Denominators
Sometimes, we may need to compare fractions with different denominators. One way to do this is to find the least common multiple (LCM) of the denominators. Here is a table comparing fractions with different denominators:| Denominator | Equivalent Fraction |
|---|---|
| 2 | 1/2 |
| 3 | 1/3 |
| 4 | 1/4 |
| 5 | 1/5 |