Percent in everyday life

Percent, ratio and scale, grade 6 Lesson 5 of 11Learning

Percent in everyday life

A discount

Another way: after a 20% discount you pay

\displaystyle {100\%-20\%}={80\%}

of the price, and 80% of 150 is 120 ₪.

A discount is an amount taken off the price.
A pair of shoes costs 150 ₪, and there is a 20% discount on it: 20% of the price is taken off.

The discount: $\displaystyle {20\%}={\frac{1}{5}}$ , and $\displaystyle \frac{1}{5}$ of 150 is 30 ₪.
The price after the discount: $\displaystyle {150-30}={120}$ ₪.

A price rise

When a price rises, something is added to it.
A cinema ticket cost 40 ₪, and its price rose by 10%.
10% of 40 is 4 ₪, so the new price is $\displaystyle {40+4}={44}$ ₪.

Reduced and enlarged copies

On a photocopier you choose the size of the copy as a percent of the original:

100% – the copy is the size of the original.
50% – every length in the copy is half the length in the original: a drawing 20 cm wide comes out 10 cm wide.
150% – every length in the copy grows by a half: a drawing 20 cm wide comes out 30 cm wide.

Percents in the news

“5% cheese”: every 100 grams of the cheese hold 5 grams of fat.
“Road accidents fell by 3% this year”: for every 100 accidents last year, there were 97 this year.

Exercise 1

A shirt costs 80 ₪.
There is a 25% discount on it.

How many shekels is the discount?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

What is the price after the discount?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Exercise 2

A youth movement’s branch has 200 members this year.
Last year it had 15% fewer members than this year.
How many members did the branch have last year?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Exercise 3

A picture 12 cm wide was copied enlarged, at 150%.
How wide is the copy?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Exercise 4

Can this be?
If it can – give an example. If not – explain why.

Everything in a shop is 50% off.
Rachel bought two things: on one of them she got a discount of 20 ₪, and on the other a discount of 25 ₪.

In a stationery shop, Amichai bought a pen and Doron bought a pencil case.
Each of them got a discount of 2 ₪, but the percent of the discount was different for each.

Formulas: percent, ratio and scale, grade 6

Open as a page

A percent is a hundredth

$\displaystyle a$ percent are $\displaystyle a$ hundredths
$\displaystyle a\%$ $\displaystyle =$ $\displaystyle \frac{a}{100}$
The whole
$\displaystyle 100\%$ $\displaystyle =$ $\displaystyle 1$
A half
$\displaystyle 50\%$ $\displaystyle =$ $\displaystyle \frac{1}{2}$
A quarter
$\displaystyle 25\%$ $\displaystyle =$ $\displaystyle \frac{1}{4}$
Three quarters
$\displaystyle 75\%$ $\displaystyle =$ $\displaystyle \frac{3}{4}$
A tenth
$\displaystyle 10\%$ $\displaystyle =$ $\displaystyle \frac{1}{10}$
A fifth
$\displaystyle 20\%$ $\displaystyle =$ $\displaystyle \frac{1}{5}$
An eighth
$\displaystyle 12\frac{1}{2}\%$ $\displaystyle =$ $\displaystyle \frac{1}{8}$

The value of a percent

$\displaystyle a\%$ of the whole quantity $\displaystyle b$
$\displaystyle a\%\times b$ $\displaystyle =$ $\displaystyle \frac{a}{100}\times b$
The percent and the quantity can change places: 18% of 50 is 50% of 18
$\displaystyle a\%\times b$ $\displaystyle =$ $\displaystyle b\%\times a$

Finding the percent

What percent $\displaystyle a$ is of $\displaystyle b$ – reduce or expand to the denominator 100; the numerator $\displaystyle p$ is the number of percent
$\displaystyle \frac{a}{b}=\frac{p}{100}=p\%$

Ratio

A ratio is a quotient – it can be written as a fraction
$\displaystyle a:b$ $\displaystyle =$ $\displaystyle \frac{a}{b}$
Equal ratios – both numbers multiplied or divided by the same number $\displaystyle k$
$\displaystyle a:b$ $\displaystyle =$ $\displaystyle (a\times k):(b\times k)$ $\displaystyle k\neq0$
A quantity $\displaystyle c$ shared in the ratio $\displaystyle a:b$ – the first share ( $\displaystyle a$ parts out of $\displaystyle a+b$ )
$\displaystyle \frac{c}{a+b}\times a$
A quantity $\displaystyle c$ shared in the ratio $\displaystyle a:b$ – the second share ( $\displaystyle b$ parts out of $\displaystyle a+b$ )
$\displaystyle \frac{c}{a+b}\times b$

Scale

At the scale $\displaystyle 1:n$ – $\displaystyle a$ the length in the drawing, $\displaystyle b$ the real length, in the same unit
$\displaystyle b$ $\displaystyle =$ $\displaystyle a\times n$