This is the part of Dai's homework:

Question:

Write these expressions in their simplest form.

$a.2x+8+6x-4$                      $b.3bc+5bd-2bc+3db$

Solution:

$a.2x+8+6x-4=8x+4=12x$

$b.3bc+5bd-2bc+3db=5bc+5bd+3db$

Dai has made several mistakes. Explain what Dai has done wrong. Work out the correct answers.

 

Copy and complete this algebraic pyramid. Remember that you find the expression in each block by adding the expressions in the two blocks below it:

Marcus is trying to complete this algebraic pyramid:

Is Marcus correct? Explain your answer.

Copy this pyramid and fill in as many blocks as you can.

This is the method Giovanna uses to simplify the expression $\frac{3a}{4}+\frac{5a}{12}$

To work out $\frac{3a}{4}+\frac{5a}{12},$ I need to use a common denominator of $12$.

$\frac{3a}{4}=\frac{3\times 3a}{3\times 4}=\frac{9a}{12}$, So, $\frac{9a}{12}+\frac{5a}{12}=\frac{14a}{12}$

I can now write $\frac{14a}{12}$ in its simplest form as$\frac{7a}{6}$.

Critique Giovanna's method. Is it easy to follow.

Do you think it is the best method to use to answer this type of question or you can improve the method?

Simplify the expression. 

Write your answer in its simplest form and as an improper fraction.

$\frac{3a}{4}+\frac{a}{2}$

Simplify the expression. 

Write your answer in its simplest form and as an improper fraction.

$\frac{3b}{5}+\frac{7b}{15}$