An equivalent fraction by division is a new fraction created by dividing both the numerator (top number) and the denominator (bottom number) of an original fraction by the same non-zero number. The resulting fraction represents the same value as the original fraction, just in simpler terms.
How Division Creates Equivalent Fractions
The key concept is that dividing both the numerator and denominator by the same number is essentially dividing the entire fraction by 1 (since any number divided by itself equals 1). Multiplying or dividing a number by 1 doesn't change its value. Therefore, the resulting fraction is equivalent to the original.
Example
Let's say we have the fraction 6/8. To find an equivalent fraction by division, we need to find a number that divides evenly into both 6 and 8. The number 2 works perfectly.
- Divide the numerator (6) by 2: 6 ÷ 2 = 3
- Divide the denominator (8) by 2: 8 ÷ 2 = 4
Therefore, 6/8 is equivalent to 3/4. We have simplified the fraction using division.
Why it Works
Imagine a pie cut into 8 slices, and you have 6 of those slices. That's 6/8 of the pie. Now, imagine grouping those slices into pairs. You'd have 3 pairs of slices, and the whole pie would be divided into 4 pairs. You still have the same amount of pie, but now it's represented as 3 out of 4 groups, or 3/4.
Important Considerations
- The divisor must be a factor of both the numerator and denominator. You can't divide if the result isn't a whole number.
- Dividing by the Greatest Common Factor (GCF) results in the simplest form (lowest terms) of the fraction. In the example above, 2 was the GCF of 6 and 8.
- The value of the fraction remains the same. Even though the numbers are different, both fractions represent the same proportion.
