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Generate equivalent fractions with models

Equivalent fractions represent the same quantity even when they have different numerators and denominators. Area models, fraction strips, and number lines show that partitioning each unit fraction into the same number of equal parts multiplies both numerator and denominator by the same whole number, such as 1/2=2/4=4/81/2=2/4=4/8; changing only one part does not preserve value. This understanding supports comparing, adding, and subtracting fractions with related denominators.

Detailed Explanation: Generate equivalent fractions with models

Equivalent fractions name the same amount, even though they use different numbers.

To make an equivalent fraction, partition each part into the same number of smaller equal parts. This multiplies both the numerator and denominator by the same whole number.

Example: Find a fraction equivalent to 34\frac{3}{4} by splitting each part into 2 equal pieces.

Start with a rectangle divided into 4 equal parts. Shade 3 parts:

shaded shaded shaded unshaded\boxed{\text{shaded}}\ \boxed{\text{shaded}}\ \boxed{\text{shaded}}\ \boxed{\text{unshaded}}

This shows 34\frac{3}{4}.

Now split each fourth into 2 equal pieces. The rectangle has:

  • 4×2=84 \times 2=8 equal parts altogether
  • 3×2=63 \times 2=6 shaded parts

So the new model shows:

34=68\frac{3}{4}=\frac{6}{8}

We can also show this with multiplication:

34×22=68\frac{3}{4}\times\frac{2}{2}=\frac{6}{8}

The value does not change because both the shaded parts and the total parts were multiplied by 2. Multiplying only the numerator or only the denominator would not make an equivalent fraction.

Learn by doing: Generate equivalent fractions with models

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Fraction Strips - Two Strips and Fraction to Equivalent Fraction


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