Identify equivalent fractions

Equivalent fractions represent the same quantity or point on a number line, even when their numerators and denominators differ; for example, $1/2$ , $2/4$ , and $4/8$ are equal. The relationship is preserved by multiplying or dividing both numerator and denominator by the same nonzero whole number, with area models and number lines making clear why changing only one part changes the value; the focus is not on formal algebraic treatment of rational expressions or unrestricted symbolic fractions.

Detailed Explanation: Identify equivalent fractions

Equivalent fractions are fractions that name the same amount. They may look different because they have different numerators and denominators.

To find an equivalent fraction, multiply or divide both the numerator and denominator by the same nonzero whole number.

Example: Find a fraction equivalent to $\frac{3}{5}$

Choose a whole number to multiply by, such as $2$ .
Multiply the numerator by $2$ :

3 \times 2=6

Multiply the denominator by $2$ :

5 \times 2=10

Write the new fraction:

\frac{3}{5}=\frac{6}{10}

So, $\frac{6}{10}$ is equivalent to $\frac{3}{5}$ . Both fractions represent the same amount. For example, shading $3$ out of $5$ equal parts covers the same amount as shading $6$ out of $(10)$ equal parts.

Remember: multiply or divide the top and bottom by the same number. Changing only one of them would change the value of the fraction.

Learn by doing: Identify equivalent fractions

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Fractions - Equivalent Fraction From Unshaded Image (Circle)

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