Sets & Venn Diagrams
Negative Numbers & Absolute Value
Ratios & Proportions
Fractions & Decimals
100

Let  `A=` {perfect squares} and  `B=` {nonpositive integers}.

Find  `A\capB` 

`A\capB={0}`

100

Simplify. 

`-2(2.14)-\abs{-2(2.14)`

`-8.56`

100

Write & solve a proportion:

The tax on a $24 restaurant meal was $1.44. Find the tax on a restaurant meal costing $35.

`\frac{1.44}{24}=\frac{x}{35}`

`50.4=24x`

 `2.1=x` 

The tax on a $35 meal is $2.10.

100

Express 56.0768 as a mixed number in lowest terms.

 `56.0768` 

`=56\frac{768}{10000`

`=56\frac{48}{625}`

200

In a group of 100 people, everyone speaks English and/or French but no other languages. 72 people can speak English and 43 can speak French. How many people speak English only?

`72+43-100=15`

speak both languages

`72-15=57`

speak only English. 

200

True or false? Be prepared to explain!

For any real number x,

`\abs x=x`

False! Example: any negative number. 

200

Express the following ratio in lowest terms:

`0.62 : \frac{1}{500}`

`0.62 : \frac{1}{500}`

`=310:1`

200

Express in scientific notation. 

`(3.8\times 10^11)\times (6.2\times 10^-89)`

`(3.8\times 10^11)\times (6.2\times 10^-89)`

`=23.56\times 10^-78`

`=2.356\times10^-77`

300

Order using `\subset:`

`\bbbQ, \bbbN, \bbbR, \bbbZ`

`\bbbN\sub\bbbZ\sub\bbbQ\sub\bbbR`

300

Solve. 

`\abs{-p}+\abs{p}=\abs{3.2-9.7}`

`2\abs{p}=\abs{-6.5}`

`2\abs{p}=6.5`

`\abs{p}=3.25`

`p\in{-3.25,3.25}`

300

Solve. 

`42/(3-2x)=-28/(2x+1)`

`x=-4.5`

300

Express `6.2\overline{15}` as a mixed number in lowest terms. 

`6.2\overline{15}=6\frac{71}{330}`

400

Is the following set empty? If so, explain. If not, find at least one element in the set.  

`\bbbQ^c\cap\bbbR`

Not empty! Any irrational number, for example:

`\pi, e,\sqrt 2,\cdots `

400

Solve.

`-\abs{x}=\abs{-x}`

`-\abs{x}=\abs{-x}`

`-\abs{x}=\abs{x}`

`x=0`

400

Daisy had $66 in savings, while her older brother Oliver had $82. One day, Daisy & Oliver each donated the same amount of money to charity. The ratio of their savings became 3:7. How much money do they each have left?

Let  x= amount donated. Then,

\frac{66-x}{82-x}=\frac{3}{7}

(66-x)(7)=(82-x)(3)

462-7x=246-3x

462=246+4x

216=4x

54=x

Daisy has  66-54= $12 left, while Oliver has  82-54= $28 left.

400

Does the fraction  `\frac 121{34375}` have a terminating or repeating decimal representation? Be prepared to explain!

Terminating! We have 

`\frac{121}{34375}`

`=\frac{11}{3125}`

`=\frac{11}{5^5}`

 

500

Fill in the blank with always, sometimes, or never. Be prepared to explain!

If  `A, B` are non-empty sets,  `A\cupB` is ____ a subset of `A` 

sometimes! true exactly when 

`B\subsetA`

500

Solve. 

`\abs{5x+8}=\abs{2x-2}`

`5x+8=2x-2`

or

`5x+8=-(2x-2)`

`x\in{-3\frac{1}{3}, -\frac{6}{7}}`

500

Answer using a proportion:

The ratio of the sum of two numbers to the difference between them is 5:1. What is the ratio of the two numbers?

`\frac{a+b){a-b}=\frac{5}{1}` 

`5(a-b)=a+b`

`5a-5b=a+b`

`4a=6b`

`\frac{a}{b}=\frac{6}{4}`

`\frac{a}{b}=\frac{3}{2}`

500

True or false? A proper fraction with a denominator of 765 will have a repeating decimal representation. 

(Be prepared to explain.)

False! 

`\frac{153}{765}=\frac 1 5 = 0.2`