Domain One – Number Sense

Question 1

=

Answer 1

Equal to

Question 2

≠

Answer 2

Not equal to

Question 3

>

Answer 3

Greater than

Answer 4

Less than

Question 5

≥

Answer 5

Greater than or equal to

Question 6

≤

Answer 6

Less than or equal to

Question 7

||

Answer 7

Parallel to

Question 8

Upside down T

Answer 8

Perpendicular to

Question 9

≈

Answer 9

Approximately equal to

Question 10

Natural numbers

Answer 10

Counting numbers (1,2,3,4…); numbers you would naturally count by 
*not 0

Question 11

Whole numbers

Answer 11

All natural numbers and 0

Question 12

Integers

Answer 12

All whole numbers and their opposites (-3,-2,-1,0,1,2,3)

Question 13

Rational numbers

Answer 13

All values that can be expressed in the form a/b, a & b are integers and b ≠ 0, or when they are expressed in decimal form, the expression either terminates or has a repeating pattern

Question 14

Irrational numbers

Answer 14

All values that exist, but are not rational

Example: Pi (does not terminate or repeat), square root of 2 (does not terminate or repeat)

Question 15

Real numbers

Answer 15

All rational and irrational numbers

Question 16

Prime numbers

Answer 16

A natural number greater than 1, and that only has itself and 1 as its divisors (exactly two divisors)

Examples: 2,3,5,7,11,13,17

Question 17

Composite numbers

Answer 17

A natural number greater than 1 that is not a prime number (at least three divisors)

Examples: 4,6,8,9,10,12,14

Question 18

Square numbers

Answer 18

The results of taking integers and raising them to the 2nd power (numbers multiplied by themselves)

Examples: 1,4,9,16,25,36,49

Question 19

Cube numbers

Answer 19

Results of taking integers and raising them to the third power (cubed)

Examples: 1,8,27,64,125,216,343

Question 20

Length

Answer 20

12 inches (in) = 1 foot
3 feet = 1 yard
36 inches = 1 yard
1760 yards = 1 mile
5280 feet = 1 mile

Question 21

Area

Answer 21

144 square inches = 1 square foot

9 square feet = 1 square yard

Question 22

Weight

Answer 22

16 ounces = 1 pound

2,000 pounds = 1 ton (T)

Question 23

Capacity

Answer 23

2 cups = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
4 pecks = 1 bushel

Question 24

Time

Answer 24

365 days = 1 year
52 weeks = 1 year
10 years = 1 decade
100 years = 1 century

Question 25

Weight (gram)

Answer 25

``` Kilogram (kg) 1,000 grams Hectogram (hg) 100 grams Decagram (dag) 10 grams Gram (g) 1 gram Decigram (dg) 0.1 gram Centigram (cg) 0.01 gram Milligram (mg) 0.001 gram ```

Question 26

Volume (Liter)

Answer 26

``` Kiloliter (kl/kL) 1000 liters Hectoliter (hl/hL) 100 liters Decaliter (dal or daL) 10 liters Liter (l/L) 1 liter Deciliter (dl/dL) 0.1 liter Centiliter (cl/cL) 0.01 liter Milliliter (ml/mL) 0.001 liter ```

Question 27

Length (meter)

Answer 27

``` Kilometer (km) 1000 meters Hectometer (hm) 100 meters Decameter (dam) 10 meters Meter (m) 1 meter Decimeter (dm) 0.1 meter Centimeter (cm) 0.01 meter Millimeter (mm) 0.001 meter ```

Question 28

Metric system

Answer 28

Milli - 1/1000 Centi - 1/100 Deci - 1/10 Basic unit: deca = 10, hecto = 100, kilo = 1000

Question 29

Commutative property

Answer 29

The order in which addition or multiplication is done does not affect the answer A+B=B+A Ab=ba

Question 30

Associative property

Answer 30

The grouping, without changing the order, does not affect the answer A+(b+c)=(a+b)+c A(bc)=(ab)c

Question 31

Distributive property

Answer 31

Multiplication outside parentheses distributing over either addition or subtraction inside parentheses does not affect the answer In general: A(b+c)=ab+ac A(b-c)=ab-ac *cannot be used with only one operation (example: 3(4x5)≠3(4)x3(5) = 60≠80

Question 32

Special properties of 0 and 1

Answer 32

Identity number: value that when added or multiplied with another number does not change the value of that number Addition: 0; any number added to 0 gives that same number; 0+3=3+0=3 (additive identity) Multiplication: 1; any number multiplied by 1, gives that number; 1(3)=3(1)=3 (multiplicative identity)

Question 33

Inverses

Answer 33

The additive inverse of a number (the opposite) is a value that when added to any number equals 0 ** any number added to its additive inverse equals zero 7 + (-7) = 0 The multiplicative inverse of a number (the reciprocal). is a value that when multiplied with any non-zero number equals 1; any non-zero number multiplied with its multiplicative inverse equals 1 4/5 x 5/4 = 1

Question 34

Fractions

Answer 34

Two numbers separated by a bar which indicates division | Numerator(above the bar) and denominator (below the bar)

Question 35

Proper fractions

Answer 35

The numerator is smaller than the denominator Have a value of less than 1 Example: 3/5

Question 36

Improper fractions

Answer 36

Numerator is the same or more than the denominator Have a value equal to or more than 1 6/6 = 1, 5/4 = 1 1/4

Question 37

Mixed numbers

Answer 37

Whole number combined with a proper fraction Improper fraction -> divide the demonization into the numerator To change from a mixed number back to an improper fraction: multiply the whole number by the denominator, add the numerator, and then place that value over the denominator (6 2/5 —> 32/5)

Question 38

Reducing/ simplifying fractions

Answer 38

Find the GCF (greatest common factor) for both the numerator and denominator and then divide them both by that value

Question 39

Adding fractions

Answer 39

Denominators must be changed to their LCM (least common multiple) or their LCD (least common denominator) Smallest value that can be divided into the denominators without a remainder, then multiple the numerator by the number needed to multiply by to get the LCD

Question 40

Adding mixed numbers

Answer 40

Same rule as adding fractions, just make sure to add the whole numbers to arrive at a final answer

Question 41

Subtracting fractions

Answer 41

Find the LCD, and then subtract the numerators

Question 42

Subtracting mixed numbers

Answer 42

May have to borrow from the whole number just like when you subtract ordinary numbers

Question 43

Multiplying fractions

Answer 43

Multiply the numerators and then the denominators, reduce if necessary **can reduce early in the operations, only when multiplying NOT adding or subtracting

Question 44

Multiplying mixed numbers

Answer 44

First change the mixed number to an improper fraction, then multiply Changing Mixed to Improper Fraction: 1. Multiply the whole number by the denominator of the fraction 2. Add this to the numerator of the fraction 3. This is the new numerator 4. The denominator remains the same 5. Change answer back to a mixed number if necessary and then reduce

Question 45

Dividing fractions

Answer 45

Invert the second fraction, multiply, and then reduce if necessary

Question 46

Simplifying fractions

Answer 46

If the numerator or denominator contains several numbers, then these must be combined into one, and then reduced if necessary

Question 47

Place value

Answer 47

The position of a number written in decimal form 109,876,543,210.12345 Hundred billions, ten billions, billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones, tenths, hundredths, thousandths, ten thousandths, hundred thousandths

Question 48

Rounding off

Answer 48

1. Underline the place value being rounded off to 2. Look to the immediate right (One place) to the right of the underlined value 3. If the number is 5 or higher, you round up that place by one. If it is four or less, it will be the same, and everything to the right is now 0

Question 49

Decimals

Answer 49

Numbers to the left of the decimal: whole numbers | Numbers to the right: fractions with the denominators of 10,100,1000,10000, etc.

Question 50

Adding and subtracting decimals

Answer 50

Line up the decimal points, and add or subtract like normal *adding 0’s can help make the problem more approachable; whole numbers can add a decimal point to their right and add any amount of zeros

Question 51

Multiplying decimals

Answer 51

Multiply as usual, count the total number of digits above the line which are to the right of all decimal points. Add the decimal point in your answer so there is the same number of digits to the right as there were above the line.

Question 52

Dividing decimals

Answer 52

If the divisor has a decimal, move it to the right as many places as necessary until it is a whole number. Then move the decimal point in the dividend (the number being divided into) the same number of places *sometimes you have to add zeros to the dividend (the number inside the division sign)

Question 53

Decimals to percents

Answer 53

1. Move the decimal point two places to the right | 2. Insert a percent sign

Question 54

Percents to decimals

Answer 54

1. Eliminate the percent sign | 2. Move the decimal point two places to the left (sometimes adding zeros will be necessary)

Question 55

Fractions to percents

Answer 55

1. Multiply by 100%

Question 56

Percents to fractions

Answer 56

1. Divide the percent by 100 2. Eliminate the percent sign 3. Reduce if necessary

Question 57

Fractions to decimals

Answer 57

Do what the operation says | 13/20 = 13 divided by 20

Question 58

Decimals to fractions

Answer 58

1. Read it (0.8 = eight-tenths) 2. Write it (8/10) 3. Reduce it (4/5)

Question 59

Finding percentage

Answer 59

Change the percentage to a fraction or a decimal and then multiply ** of = multiply Example: What is 20% of 80? (20/100) x 80 = 1600/10 = 16 OR .20 x 80 = 16.00 = 16

Question 60

Percentage increase/decrease

Answer 60

Change/starting point x 100% = percentage change Example: Percent increase of salary from $150-$200: $50 change; 50/150 x 100% = 1/3 x 100% = 33 1/3% increase

Question 61

Square/square root

Answer 61

To square: multiply it by itself *perfect squares: square of a whole number Square roots of nonperfect squares can be approximated: square root of 2 ≈ 1.4, square root of 3 ≈ 1.7 Square Root Rules: - two numbers multiplied under a radical (square root) sign equal the product of the two square roots and same with division - adding and subtracting under a radical sign requires that the numbers must be combined under the radical before any computation can be done Approximating: - utilize the perfect squares closest to it

Question 62

Simplifying square roots

Answer 62

1. Factor the number into two numbers, one (or more) of which is a perfect square 2. Take the square root of the perfect square(s) 3. Leave the others under the radical sign

Question 63

Scientific notation

Answer 63

Very small or large numbers Begins with a positive number that is greater to or equal to one, but less than 10, multiplied by an integer power of 10. If the original value is larger than one, the exponent by 10 will be positive, if less than one, the exponent will be negative, for values between 0 and 1 the exponent is negative

Question 64

Adding signed numbers

Answer 64

When two numbers have the same sign, add the absolute values (pure) and keep the same sign. * if no sign, assumed to be positive If they have different signs, subtract the absolute and then keep the sign of the larger pure number value

Question 65

Subtracting signed numbers

Answer 65

Add the opposite; change the sign of the number being subtracted and then proceed like an addition problem

Question 66

Multiplying or dividing signed numbers

Answer 66

Product of two numbers with the same sign will produce a positive answer Product of two numbers with different signs will produce a negative answer

Question 67

Parentheses

Answer 67

Grouping symbols Evaluate everything inside of the parentheses before doing any other operations * if multiple, start with the most inside parentheses first and work your way out

Question 68

Order of operations

Answer 68

PEMDAS: Please Excuse My Dear Aunt Sally Parentheses (simplify all expressions) Exponents (apply exponents to their appropriate bases) Multiplication or Division (multiplication or division in the order from left to right) Addition or Subtraction (order from left to right)