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secondary 4 | E Maths
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Hi my qn is why can’t I reduce the fraction with (y)? I’m really confused how it can be reduced with (x) but not (y) pls explain to me thank u so much
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Date Posted: 3 years ago
Views: 445
We can always cancel a numerator and denominator if there is a common factor.
Eg. 3/9
= (1×3)/(3×3)
= 1/3 × 3/3
= 1/3 × 1
= 1/3
(The simpler way taught in primary school is just to divide by 3 immediately to simplify)
Sub in some values to see why we can't cancel the y.
Let's say x = 5 and y = 7
2/x × xy/(3y + 4x)
= 2/5 × (5×7)/(3×7 + 4×5)
Here, denominator on the left is 5 and numerator on the right has a 5 . So you can cancel them as it is as good as dividing both by 5 to simplify.
= 2/1 × 7/(3×7 + 4×5)
= (2 × 7)/(3 × 7 + 4 × 5)
= (2 × 7)/41
Here, we cannot cancel the 7 in the numerator and the denominator immediately since we need to simplify the denominator first by adding 3×7 to 4×5)
If you can factor out a 7 in the denominator then yes you can cancel.
Eg. 3/9
= (1×3)/(3×3)
= 1/3 × 3/3
= 1/3 × 1
= 1/3
(The simpler way taught in primary school is just to divide by 3 immediately to simplify)
Sub in some values to see why we can't cancel the y.
Let's say x = 5 and y = 7
2/x × xy/(3y + 4x)
= 2/5 × (5×7)/(3×7 + 4×5)
Here, denominator on the left is 5 and numerator on the right has a 5 . So you can cancel them as it is as good as dividing both by 5 to simplify.
= 2/1 × 7/(3×7 + 4×5)
= (2 × 7)/(3 × 7 + 4 × 5)
= (2 × 7)/41
Here, we cannot cancel the 7 in the numerator and the denominator immediately since we need to simplify the denominator first by adding 3×7 to 4×5)
If you can factor out a 7 in the denominator then yes you can cancel.
When you divide the denominator, you need to divide the whole thing and not just the 3y portion.
i.e
2y/x × xy/(3y + 4x)
= 2/1 × y/(3y + 4x)
= 2y/(3y + 4x) ★
If you continue to divide by y here,
= 2/((3y + 4x)/y)
= 2 / (3y/y + 4x/y)
= 2 / (3 + 4x/y)
In order to leave in the most simple or elegant form, we stop at ★
i.e
2y/x × xy/(3y + 4x)
= 2/1 × y/(3y + 4x)
= 2y/(3y + 4x) ★
If you continue to divide by y here,
= 2/((3y + 4x)/y)
= 2 / (3y/y + 4x/y)
= 2 / (3 + 4x/y)
In order to leave in the most simple or elegant form, we stop at ★
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done
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Hope you can see the difference between x and y.
Date Posted:
3 years ago
Only if the 2 algebraic expression in the denominator was multiplying each other, you can cancel them off. Otherwise you have to leave them as it is since they are adding to each other.
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