When it comes to fractions, finding an equivalent fraction is essential in mathematics. Equivalent fractions have the same value but are expressed in different forms. In this case, we will explore which fraction is equivalent to 2/6 and how we can determine it.
Understanding Equivalent Fractions
Equivalent fractions are fractions that represent the same value but are written in different forms. To find an equivalent fraction, you need to multiply or divide both the numerator and the denominator by the same number. By doing so, you can create a new fraction that is equivalent to the original fraction.
Factors of 2 and 6
Before we determine which fraction is equivalent to 2/6, let’s first look at the factors of 2 and 6.
Factors of 2:
- 1
- 2
Factors of 6:
- 1
- 2
- 3
- 6
From the factors listed above, we can see that both 2 and 6 have a common factor of 2. This common factor will help us simplify 2/6 into its equivalent fraction.
Simplifying 2/6
To simplify 2/6 into its equivalent fraction, we need to divide both the numerator and denominator by their greatest common factor, which is 2 in this case.
Step 1: Divide the numerator and denominator by 2.
2 ÷ 2 = 1
6 ÷ 2 = 3
Therefore, the simplified fraction of 2/6 is 1/3. This means that 1/3 is equivalent to 2/6 as they represent the same value.
Checking the Equivalent Fractions
It’s essential to check if two fractions are equivalent by calculating their decimal values. This can help confirm that they represent the same quantity.
Decimal value of 2/6:
2 ÷ 6 = 0.3333…
Decimal value of 1/3:
1 ÷ 3 = 0.3333…
As we can see, both 2/6 and 1/3 have the same decimal value of 0.3333…, confirming that they are equivalent fractions.
Visual Representation
It can be helpful to visually represent equivalent fractions to better understand their relationship. Let’s represent 2/6 and 1/3 on a fraction model:
Fraction Model:
1 1
___ ___
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| | | |
|2| |3|
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From the fraction model above, we can see that both 2/6 and 1/3 represent the same portion of the whole, further illustrating their equivalence.
Conclusion
Understanding equivalent fractions is crucial in mathematics as it helps simplify fractions and compare quantities accurately. In the case of determining which fraction is equivalent to 2/6, we found that 1/3 is the equivalent fraction. By dividing both the numerator and denominator by their greatest common factor, we simplified 2/6 into its equivalent form. Checking the decimal values and visual representation helped confirm the equivalence of the fractions. Always remember that equivalent fractions have the same value but are expressed differently, making them essential tools in mathematical operations.
