Fraction Equivalence and Ordering

a.   Do you agree or disagree with the claim in the headline based on this information? Why or why not?

b.   Determine whether the following fractions are greater or less than $$\frac12$$.

1. $$\frac{5}{12}$$
2. $$\frac35$$

a.   Ishmael says that he knows $$\frac{5}{12}$$ is less than $$\frac35$$ because $$\frac{5}{12}$$ is less than $$\frac12 $$ and $$\frac35$$ is more than $$\frac12$$, so $$\frac{5}{12}$$ must be less than $$\frac35$$. Explain why Ishmael’s reasoning is correct using words or pictures. 

b.   Use Ishmael’s strategy to compare the following pairs of fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

1. $${{4\over10}}$$ and $${{5\over8}}$$

2. $${{7\over12}}$$ and $${{4\over9}}$$

3. $${{1\over3}}$$ and $${{4\over7}}$$

a.   Now Joslyn is comparing $$\frac46$$ and $$\frac58$$. She says that she knows $$\frac46$$ is more than $$\frac58$$ because $$\frac46$$ is $$\frac16$$ more than $$\frac12$$ and $$\frac58$$ is $$\frac18$$ more than $$\frac12$$ and $$\frac16$$ is more than $$\frac18$$. Explain why Jocelyn’s reasoning is correct using words or pictures. 

b.   Use any strategy to compare the following pairs of fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

1. $$\frac{5}{12}$$ and $${{4\over10}}$$
2. $${{3\over5}}$$ and $${{5\over9}}$$

3. $${{1\over3}}$$ and $${{3\over7}}$$

a.   $${{3\over8}}$$  _____  $${{4\over5}}$$

b.   $${{5\over8}}$$  _____  $${{7\over12}}$$