5.2.A* 5.2.B*

Equivalent Fractions 5th Grade

Texas Essential Knowledge and Skills (TEKS): 5.2.A*
generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3;
Texas Essential Knowledge and Skills (TEKS): 5.2.B*
generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number;

Equivalent fractions are equal.

One way to find an equivalent fraction is
to multiply by a fraction equivalent to 1.

Multiply

\frac{3}{4}

\frac{2}{2}

to find a fraction that is equivalent to

\frac{3}{4}

\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}

So,

\frac{6}{8}

is equivalent to

\frac{3}{4}

Next, multiply

\frac{3}{4}

\frac{3}{3}

to find another fraction that is equivalent to

\frac{3}{4}

\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}

So,

\frac{9}{12}

is also equivalent to

\frac{3}{4}

Equivalent fractions are equal.

One way to find an equivalent fraction is to divide both
the numerator and denominator by the same number.

Divide the numerator and denominator by 2 to find a fraction that is equivalent to

\frac{6}{12}

\begin{array}{rcl} \frac{6}{12} & = & \frac{6 \div 2}{12 \div 2} \\ = & \frac{3}{6} \end{array}

So,

\frac{3}{6}

is equivalent to

\frac{6}{12}

Next, divide the numerator and denominator by 3 to find a fraction that is equivalent to

\frac{2}{4}

\begin{array}{rcl} \frac{6}{12} & = & \frac{6 \div 3}{12 \div 3} \\ = & \frac{2}{4} \end{array}

So,

\frac{2}{4}

is also equivalent to

\frac{6}{12}

A mixed number can be converted to an improper fraction by thinking
of the mixed number as the sum of a whole number and a fraction.

10 \frac{3}{4} = 10 + \frac{3}{4}

\begin{array}{rcl} 10 + \frac{3}{4} & = & \frac{10}{1} + \frac{3}{4} \\ = & \frac{40}{4} + \frac{3}{4} \\ = & \frac{43}{4} \end{array}

An improper fraction can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction.

Divide each digit of the dividend by the divisor.

Write the remainder with the quotient.

11 R 2 \to 11 \frac{2}{5}

Equivalent Fractions

Texas Essential Knowledge and Skills (TEKS): 5.2.A*

generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3;

Texas Essential Knowledge and Skills (TEKS): 5.2.B*

generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number;

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