GED Math

The four operations each have their own vocabulary. In addition the addends combine to form a sum. In subtraction the subtrahend is taken from the minuend to leave a difference. In multiplication, which is repeated addition, factors combine into a product. In division a dividend is split by a divisor into a quotient. "The product of 6 and a number" means 6 × n.

Addition and multiplication are commutative (order does not matter: 5 + 3 = 3 + 5 = 8; 4 × 7 = 7 × 4 = 28) and associative (grouping does not matter: (2 + 3) + 4 = 2 + (3 + 4) = 9; (2 × 3) × 5 = 2 × (3 × 5) = 30). Subtraction and division are neither: 12 ÷ 3 ≠ 3 ÷ 12. Division by zero is undefined: 8 ÷ 0 has no value, although 0 ÷ 8 = 0.

Signed Numbers

Operation	Rule	Examples
Add samesigns ,	Addtheabsolutevaluesandkeepthecommonsign	−4+( −6) =−10
Add differentsigns ,	Subtractthesmallerabsolutevaluefromthelarger;keep	−8 + 5 = −3 (8 − 5 = 3 , and 8 > 5)
	thesignofthelarger
Subtract	Add the opposite: a − b = a + ( −b)	7 − 12 = 7 + ( −12) = −5; −3 − ( −5) = −3 + 5
		=2
Multiply	Same signs positive; different signs negative → →	( −3)×( −4) =12;( −5)×6=−30
Divide	Samesignrulesasmultiplication	( −24)÷( −6) =4;( −35)÷7=−5

Order of Operations

Evaluate expressions in this order, often remembered as PEMDAS: Parentheses and other grouping symbols, Exponents and roots, Multiplication and Division from left to right, then Addition and Subtraction from left to right. In 3 + 4 × 2, multiply first: 4 × 2 = 8, then 3 + 8 = 11.

(5 + 3) × 2 − 4²

= 8 × 2 − 4² parentheses

= 8 × 2 − 16 exponents

= 16 − 16 multiplication

= 0 subtraction

Multiplication and division share one step, as do addition and subtraction: 12 ÷ 3 × 2 = 4 × 2 = 8, not 12 ÷ 6.

Decimals

To add or subtract decimals, line up the decimal points and work as with whole numbers. To multiply, multiply as whole numbers, count the total decimal places in both factors, and place the decimal point that many places from the right: for 2.5 × 1.4, 25 × 14 = 350 and there are 2 decimal places, so the product is 3.50 = 3.5. To divide, move the decimal point in the divisor to make it a whole number and move the dividend's decimal point the same number of places: 4.56 ÷ 1.2 becomes 45.6 ÷ 12 = 3.8.

Fractions

Operation	Procedure	Example
Addorsubtract	Rewritewithacommondenominator thenaddor ,	2/3+1/4=8/12+3/12=11/12
	subtractthenumerators
Multiply	Multiplynumeratorsandmultiplydenominators;	2/3×5/7=10/21
	simplify
Divide	Multiplybythereciprocalofthedivisor	3/4÷2/5=3/4×5/2=15/8=17/8

A recipe uses 2¾ cups of flour. How much for 1½ batches?

2¾ × 1½ = 11/4 × 3/2 = 33/8 = 4⅛ cups convert mixed numbers first

An 8-foot board is cut into pieces 2/3 foot long. How many pieces?

8 ÷ 2/3 = 8 × 3/2 = 24/2 = 12 pieces multiply by the reciprocal

Convert mixed numbers to improper fractions before multiplying or dividing. A common denominator is needed only to add or subtract.

Powers

An exponent tells how many times the base is used as a factor: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. A number to the second power is squared (5² = 25) and to the third power is cubed (4³ = 64). Any nonzero number to the zero power is 1, and a number to the first power is itself. Watch the sign: in (−3)² = (−3)(−3) = 9 the negative is part of the base, but in −3² = −(3 × 3) = −9 the exponent applies only to 3. An even power of a negative number is positive; an odd power is negative: (−2)³ = −8.

Square Roots and Cube Roots

A square root undoes squaring: √49 = 7 because 7² = 49. A cube root undoes cubing: ∛64 = 4 because 4³ = 64, and

• square of an integer; its square root is an integer. Memorizing the table below speeds up Part 1, where no calculator is available.

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
n²	1	4	9	16	25	36	49	64	81	100	121	144	169	196	225
n³	1	8	27	64	125	216	343	512	729	1000 ,

To estimate the square root of a number that is not a perfect square, find the two perfect squares it lies between. Because 49 < 50 < 64, √50 lies between 7 and 8, and because 50 is much closer to 49, √50 is just above 7 (√50 ≈ 7.07).

A square garden has an area of 196 ft². How much fencing surrounds it?

side = √196 = 14 ft 14² = 196

fencing = 4 × 14 = 56 ft perimeter of a square

A cube-shaped box holds 64 in³. How long is each edge?

edge = ∛64 = 4 in 4³ = 64

Area of a square is s², so the side is √(area). Volume of a cube is s³, so the edge is ∛(volume).

Scientific Notation

Very large and very small numbers are written in scientific notation as a × 10ⁿ, where 1 ≤ a < 10: 45,000,000 = 4.5 × 10⁷ and 0.00032 = 3.2 × 10⁻⁴. A positive exponent moves the decimal point right and a negative exponent moves it left. Operations with scientific notation are covered fully in Section 4.

Mental-Math Habits for Part 1

Estimate first: 49 × 21 ≈ 50 × 20 = 1,000, which eliminates answer choices that are far off.

Break numbers apart: 6 × 47 = 6 × 40 + 6 × 7 = 240 + 42 = 282.

Use compatible pairs: 25 × 16 = 25 × 4 × 4 = 100 × 4 = 400.

Shift the decimal for powers of 10: multiplying by 10, 100, or 1,000 moves the decimal point 1, 2, or 3 places right; dividing moves it left.

Know the landmarks: perfect squares, perfect cubes, and common fraction–decimal–percent equivalents let you skip computation.

The TI-30XS MultiView has dedicated keys for squaring, square roots, general powers (the caret key), and powers of ten for scientific notation. Use parentheses when a negative number is raised to a power: typing (−3)² gives 9, while −3² gives −9, exactly as on paper. Use the negation key (−), not the subtraction key, to enter a negative number.

Follow PEMDAS; multiply and divide left to right, then add

Common denominators are needed to add or subtract

and subtract left to right.

fractions, not to multiply or divide.

Subtracting a negative is adding: −3 − (−5) = 2.

Estimate a root by bracketing: 49 < 50 < 64, so 7 < √50 < 8.

(−3)² = 9, but −3² = −9.