Students have learned earlier that equivalent fractions are fractions that represent the same point on a number line.

In this lesson, they learn to write a fraction that is equivalent to another fraction, when the denominator of the new fraction is larger than the denominator of the original fraction. This is done without the aid of a number line, and is defined as expanding a fraction.

Students learn to determine the numerator by first determining the factor by which the original denominator is multiplied to get the new denominator. The original numerator is then multiplied by the same factor to get the numerator of the expanded fraction.

In solving problems in this lesson, students must show the number they used to multiply the numerator of the original fraction by in order to find the numerator of the expanded fraction.

In this lesson, students find the numerator of an expanded fraction that is equivalent to a specified fraction, but they are not required to show the factors used to multiply the numerator and denominator of the original fraction by.

They are only required to show the numerator of the equivalent fraction.

In this lesson, students find the numerator of an expanded fraction that is equivalent to a specified fraction, but they are not required to show the factors used to multiply the numerator and denominator of the original fraction by.

They are only required to show the numerator of the equivalent fraction.

In this lesson, students learn to write the numerator of a fraction that is equivalent to another fraction, just as they did in the first lesson in this series. The only difference is that the denominator of the new fraction is smaller than the denominator of the original fraction. This is done without the aid of a number line, and is defined as simplifying, or reducing, a fraction.

In solving problems in this lesson, students must show the number they used to multiply the numerator of the original fraction by in order to find the numerator of the expanded fraction.

In this lesson, students find the numerator of a simplified, or reduced, fraction that is equivalent to a specified fraction, but they are not required to show the factors used to multiply the numerator and denominator of the original fraction by.

They are only required to show the numerator of the equivalent fraction.

In earlier lessons, students learn that fractions are numbers and that their size can be compared using a number line. Fractions that are farther to the right on a number line than another number or fraction is larger than that number or fraction.

Students have also learned to use this knowledge to compare fractions that have different denominators when the numerators are equal to 1 (unit fractions) and to compare fractions that have the same numerator and different denominators.

In this lesson, students apply that knowledge to compare the size of fractions that have both different numerators and different denominators. They compare these fractions by placing each fraction on a number line, then determining which fraction is farther to the right.

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