4.3B Decomposing Fractions

The two models are shaded to represent the same fraction,

 $\frac{6}{9}$  .
Which equation shows that the two models represent the same fraction?

•  $\frac{5}{9}+\frac{1}{9}=\frac{4}{9}+\frac{2}{9}$  

•  $\frac{5}{9}+\frac{1}{9}=\frac{4}{9}+\frac{1}{9}$  

•  $\frac{5}{4}+\frac{1}{8}=\frac{4}{5}+\frac{2}{7}$  

•  $\frac{1}{2}+\frac{1}{3}=\frac{2}{3}+\frac{4}{5}$  

The two models are shaded to represent the same fraction

 $\frac{4}{8}$  .
Which equation shows that the two models are the same fraction?

•  $\frac{3}{4}+\frac{1}{4}=\frac{2}{4}+\frac{2}{4}$  

•  $\frac{3}{8}+\frac{1}{8}=\frac{2}{8}+\frac{2}{8}$  

•  $\frac{3}{8}+\frac{2}{8}=\frac{2}{8}+\frac{2}{8}$  

•  $\frac{4}{8}+\frac{1}{8}=\frac{4}{8}+\frac{2}{8}$  

This model can be shaded to represent

 $\frac{8}{5}$  .

Which number sentence represents two different ways that  $\frac{8}{5}$  can be represented with shaded fractions on the model?

•  $\frac{2}{5}+\frac{3}{5}+\frac{3}{5}=\frac{4}{5}+\frac{4}{5}$  

•  $\frac{5}{5}+\frac{3}{5}=\frac{1}{5}+\frac{1}{5}+\frac{4}{5}$  

•  $\frac{1}{5}+\frac{1}{5}+\frac{2}{5}=\frac{2}{5}+\frac{3}{5}$  

•  $\frac{2}{5}+\frac{6}{5}=\frac{2}{5}+\frac{1}{5}+\frac{3}{5}$  

This model can be shaded to represent

 $\frac{7}{6}$  .

Which number sentence represents two different ways that  $\frac{7}{6}$  can be represented with shaded fractions on the model?

•  $\frac{1}{6}+\frac{6}{6}=\frac{5}{6}+\frac{3}{6}$  
  

•  $\frac{1}{6}+\frac{1}{6}+\frac{4}{6}=\frac{4}{6}+\frac{3}{6}$  
  

•  $\frac{3}{6}+\frac{3}{6}=\frac{1}{6}+\frac{2}{6}+\frac{4}{6}$  
  

•  $\frac{3}{6}+\frac{4}{6}=\frac{2}{6}+\frac{5}{6}$  
  

Which expression CANNOT be used to represent thhis number?

• $\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$

• $\frac{2}{3}+\frac{2}{3}$

• $\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$

• $\frac{3}{3}+\frac{1}{3}$

Which expression CANNOT be used to represent this number?

• $\frac{3}{7}+\frac{3}{7}+\frac{3}{7}$

• $\frac{6}{7}+\frac{6}{7}$

• $\frac{4}{7}+\frac{4}{7}+\frac{1}{7}$

• $\frac{5}{7}+\frac{4}{7}$