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Q&A How can school children intuit why over 100, D is larger? But under 100, D% is larger?

posted 1y ago by Hudjefa‭  ·  edited 1y ago by Hudjefa‭

Answer
#6: Post edited by user avatar Hudjefa‭ · 2023-11-15T10:50:48Z (about 1 year ago)
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}$.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}.
  • **EDIT 1 END**
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}$.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}$.
  • **EDIT 1 END**
#5: Post edited by user avatar Hudjefa‭ · 2023-11-15T06:22:02Z (about 1 year ago)
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}.
  • **EDIT 1 END**
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}$.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}.
  • **EDIT 1 END**
#4: Post edited by user avatar Hudjefa‭ · 2023-11-15T06:20:10Z (about 1 year ago)
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}.
  • **EDIT 1 END*
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}.
  • **EDIT 1 END**
#3: Post edited by user avatar Hudjefa‭ · 2023-11-15T06:19:38Z (about 1 year ago)
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
  • ---
  • **EDIT 1 START**
  • *Intuitively*, we begin where it starts (tautologies are always so out there), which is Discount (as a) percentage (of cost price) = $\frac{c - s}{c} \times 100$, where $c$ = cost price and $s$ is the selling price.
  • Notice that $\frac{c - s}{c} \times 100 = (c - s) \times \frac{100}{c}$. What we've achieved by doing this is that we can compare how the *discount percentage* varies with how $c$ relates to $100$.
  • When $c = 100$, we get $c - s$ which is the absolute discount amount, which is also equal to the discount percentage.
  • When $c < 100$,$c - s$ gets multiplied by an *improper fraction* $\frac{100}{c} > 1$, which means the absolute discount amount $c - s$ will be less than the percentage discount $\frac{c - s}{c} \times 100$ which we saw is the same as $(c - s) \times \frac{100}{c}.
  • When $c > 100$, $c - s$ gets multiplied by an *proper fraction* $\frac{100}{c} < 1$, which means the absolute discount amount $c - s$ will be greater than the percentage discount $\frac{c - s}{s} \times 100$, which we say is the same as $(c - s) \times \frac{100}{c}.
  • **EDIT 1 END*
#2: Post edited by user avatar Hudjefa‭ · 2023-11-14T16:59:27Z (about 1 year ago)
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • If $c < 100$, discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • If $c > 100$, absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • If cost is $c$, sold for $s$, discount, $d = c - s$
  • Discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$
  • Absolute discount = $c - s$
  • As you can see ...
  • 1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.
  • 2. When $c > 100$, $\frac{100}{c} < 1$, and so $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.
  • 3. When $c = 100$, The absolute discount = The percentage discount. $\frac{100}{c} = \frac{100}{100} = 1$
#1: Initial revision by user avatar Hudjefa‭ · 2023-11-14T16:56:31Z (about 1 year ago) 
If cost is $c$, sold for $s$, discount, $d = c - s$

If $c < 100$, discount percentage = $\frac{c - s}{c} \times 100 = (c - s)\times \frac{100}{c}$  

If $c > 100$, absolute discount = $c - s$ 



As you can see ...

1. When $c < 100$, $\frac{100}{c} >1$, and so, $(c - s)\times \frac{100}{c} > (c - s)$. The percentage discount > The absolute discount.   

2. When $c > 100$, $\frac{100}{c} < 1$, and so  $(c - s) \times \frac{100}{c} < (c -s)$. The absolute discount > The percentage discount.