1 quarter + 16 dimes + 3 nickels = $200

Female students: \(\dfrac{4}{5}\)

Male students: \(\dfrac{1}{5}\)

The ratio is: \(\dfrac{1}{5}\div\dfrac{4}{5}=\dfrac{1}{4}=1:4\)

First 3 fractions:

2 x 3 = 6 (the 5^th)

3 x 3 = 9 (the 6^th)

4 x 3 = 12 (the 7^th)

Continue with the next 3 fractions:

5 x 6 = 30 (the 8^th)

6 x 6 = 36 (the 9^th)

9 x 6 = 54 (the 10^th)

So \(\dfrac{1}{19}\) is incorrect and should be replaced with \(\dfrac{1}{30}\)

We can also put dot (.): 6.7

The sum of 7 numbers is: \(6\times7\) = 42

The sum of 6 numbers is: \(7\times6\) = 42

The sum of 3 numbers is \(42\times3\) = 126

So the average of these number is: \(\dfrac{42+42+126}{16}=13.125\)

(The average of group A, B, C can't be the average of the average of group A, B, C)

Or if you mean 1 is the denominator, it will be different:

\(A=\dfrac{1}{\dfrac{\sqrt{.1}}{\sqrt{.01}}}=\dfrac{1^2}{\left(\dfrac{\sqrt{.1}}{\sqrt{.01}}\right)^2}=\dfrac{1}{\left(\dfrac{0.1}{0.01}\right)}=\dfrac{1}{10}=0.1\)

\(B=\dfrac{1}{\dfrac{\sqrt{.01}}{\sqrt{.1}}}=\dfrac{1^2}{\left(\dfrac{\sqrt{.01}}{\sqrt{.1}}\right)^2}=\dfrac{1}{\left(\dfrac{0.01}{0.1}\right)}=\dfrac{1}{0.1}=10\)

So A < B

BE CAREFUL WITH WHAT YOU WRITE!

\(\dfrac{\dfrac{1}{\sqrt{.1}}}{\sqrt{.01}}=\dfrac{\left(\dfrac{1}{\sqrt{.1}}\right)^2}{\left(\sqrt{.01}\right)^2}=\dfrac{\dfrac{1}{0.1}}{0.01}=\dfrac{10}{0.01}=1000\)

\(\dfrac{\dfrac{1}{\sqrt{.01}}}{\sqrt{.1}}=\dfrac{\left(\dfrac{1}{\sqrt{.01}}\right)^2}{\left(\sqrt{.1}\right)^2}=\dfrac{\dfrac{1}{0.01}}{0.1}=\dfrac{100}{0.1}=1000\)

Answer: They are equal

Too easy: 3/4 (=0.75) and 5/6 (=0.83333...)

1/3 × 1/3 + 1/2 × 1/2 + 1/5 × 1/5 = 1/9 + 1/4 +1/25 = 361/900

Sorry, I forgot to put ¢ in the end

Can I use "-"?

30.9 - (-21,4) = 52,3

31.4 - (-20.9) = 52.3 (=>)

Not only Sherlockkichi but also others nick, for example: Nobita - Kun, Doraemonchan, Dangnguyen555 nobita, Dragon,  ......

We have: 7p = 30¢ + 5p \(\Rightarrow\) 2p = 30¢ \(\Rightarrow\)p = 15¢

So 8 pencils cost: 15 \(\times\) 8 = 120

a. .0001 means 0.0001

b. \(\dfrac{1}{1000}=0.001\)

c. .100 = 0.1 so -.100² = -0.1² = -0.01

d. \(\dfrac{1}{10^4}=0.0001\)

e. \(\dfrac{1}{10}\div.1=\dfrac{1}{10}\div0.1=1\)

SO e has the largest value

123 + 4 - 5 + 67 - 89 = 100

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 × 9 = 100

(You only ask two so I have two

But there are over 200 ways to make 100 by 0 - 9!!!)

4 x 4 + 4 x 4 + 4 + 4 + 4 \(\div\) 4 + 4 \(\div\)4  = 42

I don't need any luck!

113 = 2 x 7² + 2 x 7¹ + 1 x 7⁰ = 221₇

(How can I get those number?

CLUE: Keep dividing 113 by 7:

113 \(\div\) 7 = 16 (remainder 1)

16 \(\div\) 7 = 2 (remainder 2)

Because 2  \(\div\) 7 = 0, we stop here.

We get three number: 2, 2, 1)

262 = 2 x 5³ + 0 x 5² + 2 x 5¹ + 2 x 5⁰ = 2022₅

Step 1: Change 534 to base 10

534₆ = 5 x 6² + 3 x 6¹ + 4 x 6⁰ = 202

Step 2: Change 202 to base 4

202 = 3 x 4³ + 0 x 4² + 2 x 4¹ + 2 x 4⁰ = 3022₄

1 KOD (Kondlo Dollars) = 4.28466 POD (Ponplos Dollar)

\(\Rightarrow\) \(\dfrac{1}{4.28466}\) KOD = \(\dfrac{4.28466}{4.28466}\) POD

\(\Leftrightarrow\) 0.23339 KOD = 1 POD