### Example:
Let's take the fraction \( \frac{1}{2} \).

1. **Multiply by 2:**
   \[
   \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
   \]
   So, \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \).

2. **Multiply by 3:**
   \[
   \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
   \]
   So, \( \frac{1}{2} \) is also equivalent to \( \frac{3}{6} \).

3. **Divide by 2:**
   \[
   \frac{2 \div 2}{4 \div 2} = \frac{1}{2}
   \]
   This shows that \( \frac{2}{4} \) is equivalent to \( \frac{1}{2} \).

### General Rule:
If you have a fraction \( \frac{a}{b} \), you can find equivalent fractions by:
- Multiplying: \( \frac{a \times n}{b \times n} \) for any integer \( n \neq 0 \)
- Dividing: \( \frac{a \div n}{b \div n} \) for any integer \( n \) that divides both \( a \) and \( b \)

### Conclusion:
To create equivalent fractions, simply multiply or divide the numerator and denominator by the same number. This principle can be applied to any fraction to find its equivalents.

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Pregunta

quivalent fractions

Ask by Norton O'Quinn. in South Africa

Mar 08,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

Equivalent fractions are fractions that have the same value, even if they look different. You can find them by multiplying or dividing both the top and bottom numbers by the same number. For example, \( \frac{1}{2} \) is the same as \( \frac{2}{4} \) or \( \frac{3}{6} \).

Solución

Equivalent fractions are fractions that represent the same value or proportion, even though they may have different numerators and denominators. To find equivalent fractions, you can multiply or divide both the numerator and the denominator of a fraction by the same non-zero number. ### Example: Let's take the fraction \( \frac{1}{2} \). 1. **Multiply by 2:** \[ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] So, \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \). 2. **Multiply by 3:** \[ \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \] So, \( \frac{1}{2} \) is also equivalent to \( \frac{3}{6} \). 3. **Divide by 2:** \[ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \] This shows that \( \frac{2}{4} \) is equivalent to \( \frac{1}{2} \). ### General Rule: If you have a fraction \( \frac{a}{b} \), you can find equivalent fractions by: - Multiplying: \( \frac{a \times n}{b \times n} \) for any integer \( n \neq 0 \) - Dividing: \( \frac{a \div n}{b \div n} \) for any integer \( n \) that divides both \( a \) and \( b \) ### Conclusion: To create equivalent fractions, simply multiply or divide the numerator and denominator by the same number. This principle can be applied to any fraction to find its equivalents.

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Extra Insights

Equivalent fractions are like those sneaky twins who look different but are actually the same! For example, 1/2 and 2/4 may appear distinct, but they represent the same portion of a whole. You create equivalent fractions by multiplying or dividing both the numerator (top number) and the denominator (bottom number) by the same non-zero number. This property is a key concept in fractions that helps simplify calculations and compare quantities. When working with equivalent fractions, remember that one common mistake is to only change the numerator or denominator without the other. This leads to incorrect fractions! A fun tip is to visualize a pizza: if you slice it into more pieces (like turning 1/2 into 2/4), you still have the same amount of pizza, just cut differently! So, always keep that balance in mind.