Question

unit 3, lesson 16 - finding the percentage
lets find percentages in general.
warm - up: true or false: percentages
is each statement true or false? be prepared to explain your reasoning.

1. 25% of 512 is equal to \\(\frac{1}{4}\cdot500\\).
2. 90% of 133 is equal to (0.9)·133.
3. 30% of 44 is equal to 3% of 440.
4. the percentage 21 is of 28 is equal to the percentage 30 is of 40.

Explanation:

Step1: Evaluate left side of statement 1

$25\% \times 512 = \frac{1}{4} \times 512 = 128$

Step2: Evaluate right side of statement 1

$\frac{1}{4} \times 500 = 125$

Step3: Compare values for statement 1

$128
eq 125$, so statement 1 is False.

Step4: Convert 90% to decimal for statement 2

$90\% = 0.9$, so $90\% \times 133 = 0.9 \times 133$. Statement 2 is True.

Step5: Evaluate left side of statement 3

$30\% \times 44 = 0.3 \times 44 = 13.2$

Step6: Evaluate right side of statement 3

$3\% \times 440 = 0.03 \times 440 = 13.2$

Step7: Compare values for statement 3

$13.2 = 13.2$, so statement 3 is True.

Step8: Calculate percentage for statement 4 left

$\frac{21}{28} \times 100\% = 75\%$

Step9: Calculate percentage for statement 4 right

$\frac{30}{40} \times 100\% = 75\%$

Step10: Compare values for statement 4

$75\% = 75\%$, so statement 4 is True.

Answer:

1. False
2. True
3. True
4. True