Anna likes working with fractions and understands the equality and inequality lessons with Fraction Bars.

Question

After class she asks her teacher how to tell which is greater, g or ½, because she does not have a Fraction Bar for 4. Devise a way to help her using the Fraction Bars model she understands.

Answer 1

One way to help Anna compare g and ½ using the Fraction Bars model is to create equivalent fractions for both sides using the same denominator.

First, let's determine a common denominator for g and ½. Since ½ already has a denominator of 2, we can choose 2 as the common denominator.

Now, let's create equivalent fractions for both g and ½ using the denominator of 2:
- g is equivalent to (2/2)g
- ½ is equivalent to 1/2

Since both fractions now have the same denominator of 2, we can easily compare their numerators. If the numerator of g is greater than the numerator of ½, then g is greater. If the numerator of g is smaller than the numerator of ½, then ½ is greater.

For example, let's say g is equal to 3. In the equivalent fraction form, g becomes (2/2)g = (2/2)3 = 6/2. Now, we can compare the numerators:
- g = 6/2
- ½ = 1/2

Since the numerator of g (6) is greater than the numerator of ½ (1), we can conclude that g is greater than ½.

By using this method, Anna can compare any value of g to ½ using the Fraction Bars model she understands.