Year 7 function machine worksheet answer

[Jignesh77]

Good evening,
My son is in year 7 and they are learning function machines.
I am not sure if answered the question no 17 correctly or not. I want to help him so please guide me through. We don't have the correct answer. I am referring to the question no 17 with the final output 2i+8/3
Thank you in advance.

 

[blamocur]

I am not sure if answered the question no 17 correctly or not.

Why cannot you verify it yourself? Can't you write down the resulting expression after each step of the "machine" in 17) ?

I am referring to the question no 17 with the final output 2i+8/3

The output is (2i+8)/3, not 2i+8/3.

 

[Jignesh77]

Thank you. I think it should be + 4 in the input not 8 and then multiply by 2 followed by /3. Is that correct?

 

[Jignesh77]

Thanks

 

[The Highlander]

Thank you. I think it should be + 4 in the input not 8 and then multiply by 2 followed by /3. Is that correct?

Yes, it should be "+ 4" in the first input followed by "× 2" and then "÷ 3" to get \(\displaystyle \frac{2i+8}{3}\left(or\; \frac{(2i+8)}{3}=(2i+8)/3\right)\)

 

[Jignesh77]

Thank you for clarifying the answer.

 

[The Highlander]

Thank you for clarifying the answer.

YVW

 

[Jignesh77]

Out of curiosity, how do we know when to use brackets as used in my example?
Thank you in advance.

 

[blamocur]

Out of curiosity, how do we know when to use brackets as used in my example?

See order of operations on internet: https://www.mometrix.com/academy/order-of-operations/, https://en.wikipedia.org/wiki/Order_of_operations, https://www.splashlearn.com/math-vocabulary/algebra/order-of-operations.
In case you are referring to [imath]\frac{2i+8}{3}[/imath] you'd compute [imath]2i+8[/imath] first then divide it by 3. But when you write [imath]2i+8/3[/imath] you have to compute [imath]8/3[/imath] first then add it to [imath]2i[/imath].

 

[Dr.Peterson]

Out of curiosity, how do we know when to use brackets as used in my example?

When you want to write a fraction like [imath]\frac{a+b}{c+d}[/imath] on one line, you need to recognize that the fraction bar acts also as a grouping symbol, so it has to be replaced by parentheses around the numerator and denominator: (a+b)/(c+d), not a+b/c+d, to force them to be evaluated first. But the parentheses are not needed when the denominator is a single number or letter (or, for many people a single term like 2c -- but it's safer to use parentheses anyway).

 

[blamocur]

the parentheses are not needed when the denominator is a single number

Do you mean that the parentheses are not needed around a single number ? And wouldn't that apply to both denominator and numerator? E.g. (a+b)/c vs. a+b/c.

 

[Dr.Peterson]

Do you mean that the parentheses are not needed around a single number ? And wouldn't that apply to both denominator and numerator? E.g. (a+b)/c vs. a+b/c.

I hoped it would be clear that the parentheses can be dropped around the part that doesn't need them (either numerator or denominator), not that if one part doesn't need them, you can drop them everywhere. If the numerator has more than one term, then it needs parentheses, as in a+b/c.

So let's rewrite that:

When you want to write a fraction like [imath]\frac{a+b}{c+d}[/imath] on one line, you need to recognize that the fraction bar acts also as a grouping symbol, so it has to be replaced by parentheses around the numerator and denominator: (a+b)/(c+d), not a+b/c+d, to force them to be evaluated first. But the parentheses are not needed around the denominator when it is a single number or letter (or, for many people, a single term like 2c -- but it's safer to use parentheses anyway), as in the current example.

The feedback I was expecting was about whether the parentheses are needed in writing [imath]\frac{a+b}{2c}[/imath] as (a+b)/2c.