Understanding Equivalent Fractions
Equivalent fractions are different fractions that represent the same value or proportion. To find equivalent fractions for the fraction 14/35, we can simplify it or multiply it by the same number.
Method 1: Simplifying the Fraction
1. Find the Greatest Common Divisor (GCD):
- Determine the GCD of the numerator (14) and the denominator (35).
- The GCD of 14 and 35 is 7.
2. Divide Both the Numerator and Denominator by the GCD:
- 14 ÷ 7 = 2
- 35 ÷ 7 = 5
3. Conclusion:
- The simplified fraction is 2/5.
- Thus, 14/35 is equivalent to 2/5.
Method 2: Generating Equivalent Fractions by Multiplication
1. Choose a Multiplier:
- Select any whole number (e.g., 2, 3, 4).
2. Multiply the Numerator and Denominator by that Number:
- For example, if we choose 2:
- 14 × 2 = 28
- 35 × 2 = 70
- This gives us the equivalent fraction 28/70.
3. More Examples:
- If we multiply by 3:
- 14 × 3 = 42
- 35 × 3 = 105
- Resulting in the fraction 42/105.
Conclusion
You can find various equivalent fractions for 14/35 by simplifying it to 2/5 or by multiplying both the numerator and denominator by any non-zero integer. Mastering this concept can significantly enhance your understanding of fractions in mathematics.