Hellloooo
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Can someone please tell me what I have done wrong as x= 1/3
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Muttley79
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(Original post by Hellloooo)
Can someone please tell me what I have done wrong as x= 1/3
It went wrong when you x by 15. The 15 cancels the denominator but does not multiply the numerator in the second term - it should still be 1(6 - 3x)
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simon0
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For the line immediately after:

"x15",

I do not understand how you came up with the middle term.

If you multiplied by 15, then your middle term would be:

 6-3x ,

since the 15 (you multiplied by) cancels out the 15 in the denominator (of the middle term).
Last edited by simon0; 4 weeks ago
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Hellloooo
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(Original post by simon0)
For the line immediately after:

"x15",

I do not understand how you came up with the middle term.

If you multiplied by 15, then your middle term would be:

 6-3x ,

since the 15 (you multiplied by) cancels out the 15 in the denominator (of the middle term).
I followed this example of cancelling denominator
I'm extremely confused now.
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simon0
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(Original post by Hellloooo)
I followed this example of cancelling denominator
I'm extremely confused now.
The example is fine as after both sides were multiplied by 65, the fractions were then broken down (to their simplest form) as necessary.

For example in second line, first term:

 65/5, breaks down to  13 , since  65 = 13 ^{\ast} 5 .

Getting back to the original question, you had:

 2x + \frac{1}{3} \big( \frac{6-3x}{5} \big) = 1 .

This works out as:

 2x + \frac{1}{15} ( 6-3x ) = 1 .

Can you now see why multiplying by 15 would cancel out the denominator of the middle term?
Spoiler:
Show
 15 \big( 2x + \frac{1}{15} (6-3x) \big) = 15 (1),

 \Rightarrow (15 ^{\ast} 2) x + \frac{15}{15} (6-3x) = 30x + (6-3x) = 15.
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simon0
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The corrected formula is:

 30x + (6-3x) = 15 .

Can you carry on from there?
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Hellloooo
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(Original post by simon0)
The corrected formula is:

 30x + (6-3x) = 15 .

Can you carry on from there?
I can see how the 15 cancels out in the middle part of this question however I don't understand why we do it that way? As I thought with fractions you must cross multiply? So for the fractions I'd do 5x1 and (3×6-3x) ...?

HOWEVER, is it because the fractions are written next to each other in this question and you can multiply top to bottom first to give you a denominator of 15 and then you can cancel out? So you multiplied the brackets out first?
Last edited by Hellloooo; 4 weeks ago
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simon0
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(Original post by Hellloooo)
I can see how the 15 cancels out in the middle part of this question however I don't understand why we do it that way? As I thought with fractions you must cross multiply? So for the fractions I'd do 5x1 and (3×6-3x) ...?

HOWEVER, is it because the fractions are written next to each other in this question and you can multiply top to bottom first to give you a denominator of 15 and then you can cancel out? So you multiplied the brackets out first?
When multiplying fractions, generally terms of the numerators are multiplied together and terms of the denomiators are multiplied together as well.
i.e.

 \displaystyle \big( \frac{a}{b} \big) \ast \big( \frac{c}{d} \big) = \frac{a * c}{b * d}.

For more information, try: https://www.mathsisfun.com/fractions...plication.html

----------------------------------------------------------------------------------------------------------------------------

As for cross mulitplying, are you thinking of dividing fractions?

More information on dividing fractions:

https://www.mathsisfun.com/fractions_division.html
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