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Answer:

There is not actually ONE single operation which should be done first in this expression. There are three possible operations which can be done in the first line of working.

Explanation:

There is not actually ONE operation which should be done first in this expression.
There are 4 terms - you can work in any of the terms independently from the others. We have:

#color(magenta)(21)color(blue)( - 5) color(red)(+24 -: 3)color(green)( + 90xx4)#

While the obvious calculations are in the third and the fourth terms, we could also combine the first and second terms already, as there is nothing more that can be done with them.

So the next step could read as:

#16 color(red)(+8)color(green)( + 360)#

However, it is probably better to leave all the additions and subtractions to the LAST step.

#color(magenta)(21)color(blue)( - 5) color(red)(+8)color(green)( + 360)#

It is much less confusing and far easier to do the additions first and then the subtraction.

#color(magenta)(21 color(red)(+8)color(green)( + 360) )color(blue)( - 5)#

=#384#

Answer:

#"males : females " = 6 : 5#

Explanation:

When working with averages (means), remember that we can add sums and numbers, but we cannot add averages.

(An exception would be if there were the same number of males and females - in this case we may add the averages and divide by 2)

Let the number of females be #x#.
Let the number of males be #y#

Let's work with the #color(red)("whole group first:")#
The total number of people at the party is #color(red)(x+y)#
The sum of all their ages is #color(red)((x+y) xx 29)#

Now let's work with #color(blue)("males and females separately.")#
The sum of the ages of all the females = #23 xx x = color(blue)(23x)#
The sum of the ages of all the males = #34xx y = color(blue)(34y)#

The sum of the ages of all the people = #color(blue)(23x + 34y)#

The sum of the ages of all the people = #color(red)(29(x+y))#

We now have 2 different expressions for the same information, so we can make an equation.

#color(red)(29(x+y)) = color(blue)(23x + 34y)#

#29x + 29y = 23x +34y#

#34y -29y =29x-23x#

#5y = 6x " we need to compare " y : x#

#y = (6x)/5#

#y/x = 6/5#

# y:x = 6:5#

Notice that although we do not know the actual number of people at the party, we are able to determine the ratio.

#"males : females " = 6 : 5#

Answer:

#1/5#

Explanation:

We have to find a #color(blue)"common factor"# which will divide into 3 and 15 and reduce the fraction.

This process is referred to as #color(blue)"cancelling"#

The lowest common factor here is #color(red)(3)#

#rArr3/15=(3÷color(red)(3))/(15÷color(red)(3))=1/5#

#" Usually written as" 3/15=cancel(3)^1/cancel(15)^5=1/5larr" simplest form"#

A fraction is in #color(blue)"simplest form"# when no other factor apart from 1 will divide into the numerator/denominator.

Answer:

#27/52#

Explanation:

The method for #color(blue)"division of fractions"# is.

#•" Leave the first fraction"#

#•" Change division to multiplication"#

#•" Invert (turn upside down) the second fraction"#

#•" Cancel factors between numerator/denominator if poss."#

#rArr6/13÷8/9#

#=6/13xx9/8larr" multiply and invert"#

#=cancel(6)^3/13xx9/cancel(8)^4larr" cancelling"#

#=(3xx9)/(13xx4)=27/52larr" in simplest form"#

A fraction is in #color(blue)"simplest form"# when no other factor, apart from 1 will divide into the numerator/denominator.

Answer:

#16#

Explanation:

When we are multiplying 2 fractions together we can #color(blue)"cancel"# any #color(blue)"common factors"# that exist on the numerators/denominators of the fractions.

There is a choice here as 2 and 4 have a common factor of 2 and 32 and 4 have common factors of 2 and 4.

#rArr32/1xxcancel(2)^1/cancel(4)^2=cancel(32)^(16)/1xx1/cancel(2)^1=(16xx1)/(1xx1)=16#

#color(red)"or"#

#cancel(32)^8/1xx2/cancel(4)^1=(8xx2)/(1xx1)=16#

Either method is valid and it depends only on ' how you see it'

Answer:

4

Explanation:

For this problem, we will need to have knowledge of the order of operations.

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction.

In order from top to bottom.

..................................................................................................................

Using the order of operations we know that first we need to solve what is inside the parentheses.

#22- 2( 13- 7+ 3)#

#22- 2( 6+3)#

#22- 2( 9)#

..................................................................................................................

Now, we are going to do the multiplication, because that is before subtraction on our order of operations.

#22- 2( 9)#

#22- 18#

..................................................................................................................

Now, we just have to do basic subtraction.

#22-18=4#

This brings us to our final answer of 4.

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