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secondary 2 | Maths
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Date Posted: 2 years ago
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We can say the ribbon is cut into two pieces, one is p units long and one is q units long.
Total length = (p + q) units
This equals x
1 unit = x/(p + q)
Since p > q, length of the longer piece = p units
= x/(p + q) × p
= px/(p + q)
length of the shorter piece = q units
= x/(p + q) × q
= qx/(p + q)
Difference = length of longer piece - length of shorter piece
= px/(p + q) - qx/(p + q)
= (px - qx)/(p + q)
= x(p - q)/(p + q)
Total length = (p + q) units
This equals x
1 unit = x/(p + q)
Since p > q, length of the longer piece = p units
= x/(p + q) × p
= px/(p + q)
length of the shorter piece = q units
= x/(p + q) × q
= qx/(p + q)
Difference = length of longer piece - length of shorter piece
= px/(p + q) - qx/(p + q)
= (px - qx)/(p + q)
= x(p - q)/(p + q)
Alternatively,
Total length = (p + q) units
This equals x
1 unit = x/(p + q)
Since p > q, length of the longer piece = p units
length of the shorter piece = q units
Difference = length of longer piece - length of shorter piece
p units - q units
= (p - q) units
The difference as a fraction of the total ribbon length = (p - q)/(p + q)
Since the ribbon is x metres long,
Difference in length = x × (p - q)/(p + q)
= (p - q)x / (p + q)
Total length = (p + q) units
This equals x
1 unit = x/(p + q)
Since p > q, length of the longer piece = p units
length of the shorter piece = q units
Difference = length of longer piece - length of shorter piece
p units - q units
= (p - q) units
The difference as a fraction of the total ribbon length = (p - q)/(p + q)
Since the ribbon is x metres long,
Difference in length = x × (p - q)/(p + q)
= (p - q)x / (p + q)
Example : lets say p = 5, q = 3, x = 10
We can say longer piece is 5 units, shorter piece is 3 units
Total = 8 units
The longer piece is ⅝ of the total.
The shorter piece is ⅜ of the total.
Length of longer piece
= 10 m × ⅝
= 50/8 m
= 25/4 m
= 6¼ m
= 6.25 m
But this is just equal to 10m × 5/(5 + 3)
Likewise, the length of the shorter piece
= 10 m × 3/(5 + 3)
= 3.75 m or 3¾ m
Difference = 6.25m - 3.75m = 2.5 m
But this is just equal to :
10(5 - 3)/(5 + 3) m
= 10(2) / 8 m
= 10/4 m
= 2¼ m = 2.5 m
We can say longer piece is 5 units, shorter piece is 3 units
Total = 8 units
The longer piece is ⅝ of the total.
The shorter piece is ⅜ of the total.
Length of longer piece
= 10 m × ⅝
= 50/8 m
= 25/4 m
= 6¼ m
= 6.25 m
But this is just equal to 10m × 5/(5 + 3)
Likewise, the length of the shorter piece
= 10 m × 3/(5 + 3)
= 3.75 m or 3¾ m
Difference = 6.25m - 3.75m = 2.5 m
But this is just equal to :
10(5 - 3)/(5 + 3) m
= 10(2) / 8 m
= 10/4 m
= 2¼ m = 2.5 m
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