MHB Fractions/brackets/parentheses and powers.

[Jackie In Italy]

My daughter has some maths homework for the Christmas holidays and with a test when she returns next week but I really don't understand how to do this kind of maths and she doesn't understand it either. She has a page of exercises to do but if someone could please help me with one by explaining how to do it, I would be most grateful.
Here is one of the exercises:

(- 1/2 - 1/3)^2 . (2/5 -2)^2 +[(7/9 - 2/3) : (1/2 - 9/22) ] - 5/6 (2+ 2/5)

Sorry I couldn't type the fractions on my computer any better than above. ^2 is to the power of 2 as I couldn't put a small 2 high up.
The dot . is actually in the middle not at the baseline in the exercise.

 

[anemone]

Re: Help needed with fractions/brackets/parentheses and powers.

My daughter has some maths homework for the Christmas holidays and with a test when she returns next week but I really don't understand how to do this kind of maths and she doesn't understand it either. She has a page of exercises to do but if someone could please help me with one by explaining how to do it, I would be most grateful.
Here is one of the exercises:

(- 1/2 - 1/3)^2 . (2/5 -2)^2 +[(7/9 - 2/3) : (1/2 - 9/22) ] - 5/6 (2+ 2/5)

Sorry I couldn't type the fractions on my computer any better than above. ^2 is to the power of 2 as I couldn't put a small 2 high up.
The dot . is actually in the middle not at the baseline in the exercise.

Hi Jackie from Italy! Welcome to MHB!

For starters, do you mean to simplify:

$\left(-\frac{1}{2}-\frac{1}{3}\right)^2 \cdot \left(\frac{2}{5}-2\right)^2 +\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{2}-\frac{9}{22}}- \frac{5}{6\left(2+\frac{2}{5}\right)}$

or

$\left(-\frac{1}{2}-\frac{1}{3}\right)^2 \cdot \left(\frac{2}{5}-2\right)^2 +\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{2}-\frac{9}{22}}- \frac{5\left(2+\frac{2}{5}\right)}{6}$

P.S. You can quote my reply to see how to formulate the mathematics expressions in latex. :D

 

[Jackie In Italy]

Re: Help needed with fractions/brackets/parentheses and powers.

Hi Jackie from Italy! Welcome to MHB!

For starters, do you mean to simplify:

$\left(-\frac{1}{2}-\frac{1}{3}\right)^2 \cdot \left(\frac{2}{5}-2\right)^2 +\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{2}-\frac{9}{22}}- \frac{5}{6\left(2+\frac{2}{5}\right)}$

or

$\left(-\frac{1}{2}-\frac{1}{3}\right)^2 \cdot \left(\frac{2}{5}-2\right)^2 +\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{2}-\frac{9}{22}}- \frac{5\left(2+\frac{2}{5}\right)}{6}$

P.S. You can quote my reply to see how to formulate the mathematics expressions in latex. :D

Hi,

Thanks for your reply.

I am not sure as it is just written as you wrote except the ending

- - - Updated - - -

Hi,

Thanks for your reply.

I am not sure as it is just written as you wrote except the ending

$\left(-\frac{1}{2}-\frac{1}{3}\right)^2 \cdot \left(\frac{2}{5}-2\right)^2 +\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{2}-\frac{9}{22}}-\frac{5}{6} (2+\frac{2}{5} )$

- - - Updated - - -

ps. thanks for your help with the latex!

 

[anemone]

Re: Help needed with fractions/brackets/parentheses and powers.

$\left(-\frac{1}{2}-\frac{1}{3}\right)^2 \cdot \left(\frac{2}{5}-2\right)^2 +\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{2}-\frac{9}{22}}-\frac{5}{6} (2+\frac{2}{5} )$

In this case, what you've to exercise cautious with is all about the order of operations. It's a standard that defines the order in which you should simplify the given expression with a combination of different operations.

First, we should always simplify the inside of parentheses before dealing with the exponent of the set of parentheses.

Second, we simplify the exponent of a set of parentheses before we multiply, divide, add, or subtract it.

Next, we simplify multiplication and division in the order that they appear from left to right.

Last, we simplify addition and subtraction in the order that they appear from left to right.

$=\color{red}\left(-\dfrac{1}{2}-\dfrac{1}{3}\right)^2 \cdot \left(\dfrac{2}{5}-2\right)^2 \color{black}+\dfrac{\dfrac{7}{9}-\dfrac{2}{3}}{\dfrac{1}{2}-\dfrac{9}{22}}-\dfrac{5}{6} \color{red}(2+\dfrac{2}{5} )$

$=\color{red}\left(-\dfrac{5}{6}\right)^2 \cdot \left(-\dfrac{8}{5}\right)^2 \color{black}+\dfrac{\dfrac{7}{9}-\dfrac{2}{3}}{\dfrac{1}{2}-\dfrac{9}{22}}-\dfrac{5}{6} \color{red}(\dfrac{12}{5} )$

$=\color{red}\left(\dfrac{5}{6}\right)\left(\dfrac{5}{6}\right) \cdot \left(\dfrac{8}{5}\right)\left(\dfrac{8}{5}\right) \color{black}+\dfrac{\dfrac{7}{9}-\dfrac{2}{3}}{\dfrac{1}{2}-\dfrac{9}{22}}-\dfrac{\cancel{5}^1}{\cancel{6}} \color{red}(\dfrac{\cancel{12}^2}{\cancel{5}} )$

$=\color{red}\left(\dfrac{\cancel{5}}{\cancel{6}^3}\right)\left(\dfrac{\cancel{5}}{\cancel{6}^3}\right) \cdot \left(\dfrac{\cancel{8}^4}{\cancel{5}}\right)\left(\dfrac{\cancel{8}^4}{\cancel{5}}\right) \color{black}+\dfrac{\dfrac{7}{9}-\dfrac{2}{3}}{\dfrac{1}{2}-\dfrac{9}{22}}-\color{red}\dfrac{2}{1}$

$=\color{red}\left(\dfrac{4\cdot 4}{3\cdot 3}\right) \color{black}+\dfrac{\dfrac{7}{9}-\dfrac{2}{3}}{\dfrac{1}{2}-\dfrac{9}{22}}-\color{red}2$

$=\color{red}\dfrac{16}{9} \color{black}+\color{blue}\dfrac{\dfrac{1}{9}}{\dfrac{1}{11}}-\color{red}2$

$=\color{red}\dfrac{16}{9} \color{black}+\color{blue}\dfrac{1}{9}\div\dfrac{1}{11}-\color{red}2$

$=\color{red}\dfrac{16}{9} \color{black}+\color{blue}\dfrac{1}{9}\times\dfrac{11}{1}-\color{red}2$

$=\color{red}\dfrac{16}{9} \color{black}+\color{blue}\dfrac{11}{9}-\color{red}2$

$=\color{red}\dfrac{16+11}{9} \color{black}-\color{red}2$

$=\color{red}\dfrac{27}{9} \color{black}-\color{red}2$

$=\color{red}3 \color{black}-\color{red}2$

$=1$