The fraction equivalent to 14/16 is 7/8. This is the simplest form of the fraction, representing the same numerical value.
Understanding Equivalent Fractions
Equivalent fractions are different fractions that represent the exact same proportion or part of a whole. For instance, 1/2, 2/4, and 4/8 all represent the same amount, even though they use different numbers. The key is that the relationship between the numerator (top number) and the denominator (bottom number) remains constant.
How to Find Equivalent Fractions
To find an equivalent fraction, you perform the same operation (multiplication or division) on both the numerator and the denominator by the same non-zero number.
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Simplifying Fractions (Dividing): This is the most common way to find the simplest equivalent fraction. You divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides evenly into both numbers.
- For the fraction 14/16:
- List the factors of the numerator (14): 1, 2, 7, 14
- List the factors of the denominator (16): 1, 2, 4, 8, 16
- The greatest common divisor (GCD) of 14 and 16 is 2.
- Now, divide both the numerator and the denominator by their GCD:
- 14 ÷ 2 = 7
- 16 ÷ 2 = 8
- Therefore, 14/16 simplifies to 7/8.
- For the fraction 14/16:
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Creating Equivalent Fractions (Multiplying): You can also generate other equivalent fractions by multiplying both the numerator and the denominator by the same whole number. For example, starting with the simplified form 7/8:
- Multiply by 2: (7 × 2) / (8 × 2) = 14/16
- Multiply by 4: (7 × 4) / (8 × 4) = 28/32
- Multiply by 8: (7 × 8) / (8 × 8) = 56/64
Common Equivalent Fraction Representations
Understanding equivalent fractions is fundamental in mathematics, especially when comparing, adding, or subtracting fractions. Here's a table showing 14/16 and some of its equivalent forms, along with other common fraction equivalencies:
| Fraction (Simplest Form) | Equivalent Fractions |
|---|---|
| 7/8 | 14/16, 56/64 |
| 1/9 | 2/18, 8/72 |
| 2/9 | 4/18, 16/72 |
| 4/9 | 8/18, 32/72 |
As shown in the table, 14/16 is indeed equivalent to 7/8. Expressing fractions in their simplest form makes them more concise and easier to work with in various calculations.
