How do you find the percent change given the original number is 48 and new number is 60?

Question

How do you find the percent change given the original number is 48 and new number is 60?

1 Answer

Impact of this question

1634 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-15T16:22:02

$41 . \frac{2}{3} %$ $41color(white)(.) 2/3%$

Explanation:

Goes from $48 \to 60$ $48 -> 60$

So this is an increase of $60 - 40 = 20$ $60-40 = 20$

We express this as a change in relation to the original price. So the change expressed as a fraction of the original price is :

$\frac{+ 20}{48}$ $" "color(green)((+20)/48)$

$Using first principles to explain where the \times 100$ $color(purple)("Using first principles to explain where the "xx100)$
$in the shortcut method comes from$ $color(purple)("in the shortcut method comes from")$

$\frac{20}{48} \times 1 = \frac{20}{48} \times \frac{100}{100} = \frac{20 \times 100}{48} \times \frac{1}{100}$ $color(green)(20/48color(red)(xx1)" "=" "20/48color(red)(xx100/100) " "=" "(20color(red)(xx100) )/48color(red)( xx1/100)$

But $\frac{1}{100}$ $1/100$ is the same as % giving:

$= \frac{20 \times 100}{48} %$ $" "=color(green)((20color(red)(xx100) )/48color(red)( %)$

Writing this as in the shortcut method we have:

$= (\frac{20}{48} \times 100) % = 41.6 ¯ 6 %$ $" "=(20/48 xx 100)% = 41.6bar(6)%$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Foot note$ $color(blue)("Foot note")$

The bar over the last 6 indicates that the value 6 repeats for ever.

It is really helpful to remember that $0.333 ¯ 3 is the same as \frac{1}{3}$ $0.333bar3" is the same as "1/3$

So $0.666 ¯ 6$ $0.666bar6$ is the same as $2 \times \frac{1}{3} = \frac{2}{3}$ $2xx1/3=2/3$

Thus: $41.6 ¯ 6 = 41 \frac{2}{3} %$ $41.6bar6 = 41 2/3%$

Science

Math

Humanities

... and beyond

How do you find the percent change given the original number is 48 and new number is 60?

1 Answer

Explanation:

Related questions

Impact of this question