From Whole Numbers to Rationals

First, we start with whole numbers, writing them over 1 to make fractions. Then we learn what that bottom number 1 means and what the top number, or numerator, means.

Fractions of All Sizes

We've looked at whole numbers as fractions. Now we'll see that we can model all kinds of fractions—fractions close to 0, fractions close to one half, and fractions close to 1.

Making Fractions Smaller and Larger

Increasing the top number, or numerator, without changing the denominator makes a fraction larger while decreasing it makes it smaller. The opposite is true for the bottom number, or denominator.

Comparing Two Fractions

Now we compare two fractions when the fractions are fractions of the same whole and when they have the same numerator or the same denominator (or both).

Estimating Comparisons with 0 and 1

Fractions can sometimes be compared by estimating. Look at whether the fraction is close to 0, close to 1, less than 1, equal to 1, or greater than 1.

Equal Fractions

Now we learn that if we multiply or divide the numerator and denominator of a fraction by the same number, we produce an equal fraction.

Comparing Using Equal Fractions

Once you know how to make equal fractions, you can compare any two fractions, even those with different numerators and different denominators.

Different Ways to Compare Fractions

A very short and sweet summary of some of the methods for comparing two fractions—including estimation, distance from 1, and comparing numerators or denominators.

Adding Like Fractions

When two fractions have the same denominator, we can add them by adding their numerators and keeping the denominator the same.

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