Number Sense Quiz

Example 1) 2:3 is read as "two to three," but the fractional values are $$\frac{2}{5}$$  and $$\frac{3}{5}$$  , since 5 is the total.

Example 2) 3:5:8 is read as "three to five to eight," but the fractional values are $$\frac{3}{16},\ \frac{5}{16},\ \text{and}\ \frac{1}{2}$$  , since 16 is the total

Distance cannot be negative.

Distance on the number line (1 dimension) can be found by subtracting the smaller number FROM the larger number. This is called the difference of two values and is signified by the symbol $$\Delta$$  (delta).

Distance on a coordinate plane (2 dimensions) is given by pythagorean theorem:

$$D=\sqrt{\left(\Delta x\right)^2+\left(\Delta y\right)^2}$$   

Distance in physical space (3 dimensions) is

$$D=\sqrt{\left(\Delta x\right)^2+\left(\Delta y\right)^2+\left(\Delta z\right)^2}$$   

Check out this tool to help understand: https://www.desmos.com/calculator/7fpqcivft7

'of' means multiply:

$$\frac{3}{8}\cdot\frac{2}{3}\Longrightarrow\frac{6}{24}\Longrightarrow\frac{1}{4}$$  

"how many a's are in b" means "b divided by a."

Ex: how many 2's are in 10?

$$\frac{10}{2}=5$$  

Ex: how many halves are in three fourths?

$$\frac{3}{4}\div\frac{1}{2}$$  "

To divide by a fraction, use Keep Change Flip: Keep the first fraction, Change the division into multiplication, Flip the second fraction.

$$\frac{3}{4}\div\frac{1}{2}\Longrightarrow\frac{3}{4}\cdot\frac{2}{1}\Longrightarrow\frac{6}{4}\Longrightarrow\frac{3}{2}\Longrightarrow1\frac{1}{2}$$  

% percent - 'per' means division, 'cent' means 100, so percent means "divided by 100" or "out of 100" or "over 100"

$$40\%=\frac{40}{100}=\frac{2}{5}$$

% percent - 'per' means division, 'cent' means 100, so percent means "divided by 100" or "out of 100" or "over 100"

'of' means multiply

56% of 250 means $$\frac{56}{100}\cdot250=140$$  

Base: Number being multiplied by itself

Exponent: number of times you multiply the base by itself

$$a^2\cdot b^2=a\cdot a\cdot b\cdot b=a\cdot b\cdot a\cdot b=\left(a\cdot b\right)^2$$  

$$\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$$  

$$10^4=10\cdot10\cdot10\cdot10=10,000$$   $$10^3=10\cdot10\cdot10=1,000$$   $$10^2=10\cdot10=100$$   $$10^1=10$$   $$10^0=1$$   $$10^{-1}=\frac{1}{10^1}=\frac{1}{10}=0.1$$   $$10^{-2}=\frac{1}{10^2}=\frac{1}{10\cdot10}=\frac{1}{100}=0.01$$   $$10^{-3}=\frac{1}{10^3}=\frac{1}{10\cdot10\cdot10}=\frac{1}{10}\cdot\frac{1}{10}\cdot\frac{1}{10}=\frac{1}{1000}=0.001$$