Generate equivalent fractions numerically

Equivalent fractions name the same quantity even when their numerators and denominators differ; this relationship is generated by multiplying or, when exact, dividing both by the same nonzero whole number. A number line or area model shows that the fraction’s location or shaded amount is unchanged, preventing the misconception that changing only one part preserves value. This understanding supports comparing, ordering, and adding fractions with related denominators and later proportional reasoning.

Detailed Explanation: Generate equivalent fractions numerically

Equivalent fractions have the same value, even though their numbers look different.

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

Example: Find a fraction equivalent to $\frac{3}{4}$ by multiplying by $2$ .

Multiply the numerator by $2$ :

3 \times 2=6

Multiply the denominator by $2$ :

4 \times 2=8

Write the new fraction:

\frac{3}{4}=\frac{6}{8}

So, $\frac{6}{8}$ is equivalent to $\frac{3}{4}$ .

Both fractions name the same amount. For example, shading $3$ out of $4$ equal parts covers the same amount as shading $6$ out of $8$ equal parts. Remember: multiply both parts by the same number, not just one.

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Fractions - Equivalent, Find Fraction - 1 digit with Equation

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