Estimating Percentages

Lesson

A lot of the time it's hard for us to accurately calculate percentages of amounts in real life, so we'll have to estimate! Because percentages are expressed as something out of a hundred, we can also express them in diagrams of $5,10,100$5,10,100 things or more!

Now it's your turn!

Example

Someone has been eating the brand new $10\times10$10×10 square block of chocolate! Can you figure out how much of the original chocolate block is left in percentages?

Think about the chocolate block as a fraction first

Do :We can see that there used to $10\times10=100$10×10=100 blocks of chocolate here, and now there are $67$67 blocks. So the fraction that represents how much is left of the original is $\frac{67}{100}$67100 . This is easily translated into a percentage as the denominator is already $100$100 , so the answer is $67%$67% .

Worked Examples

QUESTION 1

Which point on the line is closest to $56%$56%?

A horizontal number line ranging from 0% on the far left to 100% on the far right. This number line is divided into equal segments, each representing a 10% interval, but only the 0% and 100% markers are labeled. Four arrows, labeled A, B, C, and D, are positioned above the line, each pointing downwards to specific intervals on the scale. (The arrow labeled A points between 20% and 30%, B's arrow points between 30% and 40%, C's arrow is between 50% and 60%, and D's arrow is between 80% and 90%. The location of the arrows is not explicitly given, so just use them as hints for the students. Remember that the students are asked which of the letters is closest to the given number.)

$A$A
A
$C$C
B
$D$D
C
$B$B
D

QUESTION 2

$Ellie$ bought a $454$454 mL drink that claimed to be orange juice. In the ingredients list it said that orange juice made up $17%$17% of the drink. To estimate the amount of orange juice in the drink, which of the following would give the closest answer?

$10%\times454$10%×454
A
$20%\times454$20%×454
B
$10%\times400$10%×400
C

QUESTION 3

In a census, people are asked their gender and age. The graph shows the results: the percentage of females and males in each age group.

To the nearest $1%$1%, what percentage of females are between $5$5 and $9$9 years of age?
$7%$7%
A
$2%$2%
B
$11%$11%
C
To the nearest $1%$1%, what percentage of males are between $30$30 and $34$34 years of age?
$7%$7%
A
$4%$4%
B
$2%$2%
C
The percentage of females between the ages of $20$20 and $29$29 is about:
$15%$15%
A
$7%$7%
B
$25%$25%
C
The percentage of males below $20$20 years of age is about:
$15%$15%
A
$10%$10%
B
$30%$30%
C
$50%$50%
D