Numbers and Counting
English Basic Vocabulary · 50 lessons
What does “Numerical Order” mean?
Correct Answer (A): Numerical order means arranging numbers following a specific pattern or rule—like smallest to largest, or multiples of 5. There's a logical system to how the numbers are arranged.
Why B is wrong: "Arbitrary or random" is the opposite of numerical order. If numbers were scattered randomly with no pattern, that wouldn't be order at all—it would be chaos. Numerical order requires a deliberate, rule-based system.
What does “Integer” mean?
Why A is correct:
Integers are whole numbers—positive, negative, or zero (like -3, 0, 5, 100). They have no fractional or decimal parts.
Why B is wrong:
That describes a *fraction* or *rational number*—something that represents a part of a whole (like 1/2 or 0.75), which is the opposite of an integer.
What does “Decimal” mean?
Why A is correct:
A decimal is exactly this—a way of writing fractions where the denominator is always 10, 100, 1000, etc. (powers of 10). The digits after the decimal point tell you the numerator. For example, 0.25 means 25/100.
Why B is wrong:
Whole numbers like 5 or 42 have no decimal point and no fractional part, so they're not decimals. A decimal specifically involves the decimal point and digits after it representing a fraction.
What does “Fraction” mean?
Correct Answer: A
A fraction represents a part of a whole—like 1/2 of a pizza or 3/4 of a cup. It's always *less than* a whole number (or sometimes equal to one, like 4/4), but by definition it shows division into parts.
Why B is wrong:
Whole numbers (1, 2, 3, 4...) are complete units with no parts. Fractions are the opposite—they *break* numbers into pieces. While you can write a whole number as a fraction (like 5/1), that's not what "fraction" fundamentally means.
What does “Zero” mean?
A is correct because zero represents the absence of quantity—nothing. It's the baseline starting point in our number system.
B is wrong because it says zero denotes a quantity or existence, which is backwards. Zero means the *lack* of quantity, not the presence of it.
What does “Digit” mean?
A is correct: A digit is a single numerical symbol—0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. These are the building blocks of all numbers. For example, the number 47 has two digits: 4 and 7.
B is wrong: Letters A to Z are called letters or alphabetic characters, not digits. Digits are specifically about numbers, not the alphabet.
What does “Odd Number” mean?
Why A is correct: An odd number cannot be divided evenly by 2—it always leaves a remainder of 1. Examples: 1, 3, 5, 7, 9.
Why B is wrong: This describes an *even* number, not an odd number. Even numbers are multiples of 2 (like 2, 4, 6, 8). Odd and even are opposites.
What does “Even Number” mean?
A is correct: An even number divides evenly by 2 with no remainder. Examples: 2, 4, 6, 8, –2. You can always write an even number as 2×n (where n is any integer).
B is wrong: This describes an *odd* number instead (like 1, 3, 5, 7). Odd numbers have a remainder of 1 when divided by 2.
What does “Prime Number” mean?
Why A is correct:
A prime number has exactly two divisors: 1 and itself. Examples: 2, 3, 5, 7, 11. This is the standard mathematical definition.
Why B is wrong:
This describes a *composite* number (like 6, 12, 15), which is the opposite of prime. Prime numbers have few divisors, not multiple ones.
What does “Negative Number” mean?
A is correct: Negative numbers are any values below zero on the number line (like −5, −0.5, or −100). The minus sign (−) shows they're less than zero.
B is wrong: That describes *positive* numbers, which are greater than zero. Positive and negative are opposites.
What does “Positive Number” mean?
Why A is correct:
A positive number is any real number greater than zero (like 1, 2.5, or 100). The word "positive" literally means "more than zero."
Why B is wrong:
Numbers less than zero are called *negative* numbers, not positive. This is the opposite of what positive means.
What does “Whole Number” mean?
Correct Answer (A): Whole numbers are integers that include zero and all positive integers (0, 1, 2, 3, ...). They have no fractional or decimal parts, making them "whole."
Why B is wrong: This option contradicts the definition by saying whole numbers ARE fractions and can be negative—the opposite of what they actually are. Whole numbers specifically exclude fractions and negative numbers.
What does “Natural Number” mean?
Why A is correct:
Natural numbers are the numbers we use to count: 1, 2, 3, 4... Most modern definitions include 0 as well, making natural numbers {0, 1, 2, 3...}. They're "natural" because they arise naturally from counting.
Why B is wrong:
This describes negative integers, which are the opposite of natural numbers. Natural numbers are positive (or zero), never negative. Also, natural numbers are *for* counting, not "non-counting."
What does “Composite Number” mean?
Why A is correct:
A composite number is a whole number greater than 1 that can be divided evenly by at least one number besides 1 and itself. For example, 6 is composite because it's divisible by 2 and 3, not just 1 and 6.
Why B is wrong:
- Composite numbers are *positive*, not negative
- The definition in B describes a prime number (has no divisors except 1 and itself), not a composite number
- Negative integers aren't classified as composite or prime in standard math
What does “Real Number” mean?
Correct answer (A):
Real numbers form a continuous spectrum that includes all integers, fractions, and decimals (like π or √2). They can be placed on a number line at any position, representing actual distances—this is the defining feature of real numbers.
Why B is wrong:
Real numbers are *continuous*, not discrete. Discrete quantities are separate, individual values (like counting people). Real numbers fill every point on a number line with no gaps, and they *do* represent distances along a line—the opposite of what B claims.
What does “Imaginary Number” mean?
Correct Answer (A):
An imaginary number is defined as any real number times *i* (where *i* = √-1). For example, 3*i* or 5*i* are imaginary numbers. This is the standard mathematical definition.
Why B is wrong:
Option B contradicts itself—it says a real number "cannot" be multiplied by *i*, which is backwards. Also, real numbers alone (like 2 or 7) aren't imaginary numbers; they're just real. Imaginary numbers specifically require the *i* component.
What does “Rational Number” mean?
Correct Answer (A): A rational number is literally "ratio-nal"—it comes from the word "ratio." It's any number you can write as a fraction with two integers (like 3/4, 5/1, or -2/7). Examples: 0.5 = 1/2, and 3 = 3/1.
Why B is wrong: That's the definition of an *irrational* number (like π or √2). The prefix "ir-" means "not," so irrational means "not rational."
What does “Irrational Number” mean?
Why A is correct:
An irrational number literally cannot be written as a fraction of two whole numbers (like 3/4 or 22/7). Examples include π, √2, and e—they go on forever without repeating, so there's no simple fraction that equals them exactly.
Why B is wrong:
That's actually the definition of a *rational* number, not irrational. Numbers like 1/2, 5/3, and 0.25 can be expressed as ratios—these are the opposite of what we're looking for.
What does “Absolute Value” mean?
Correct Answer: A
Absolute value measures the distance a number is from zero on a number line—always as a positive amount. For example, both -5 and +5 are 5 units away from zero, so they both have an absolute value of 5.
Why B is wrong:
"Associates with" is vague and doesn't describe what absolute value actually does. Absolute value isn't about connection or relationship—it's about measuring distance.
What does “Counting Numbers” mean?
Correct Answer (A): Counting numbers are the numbers we naturally use to count things—1, 2, 3, 4, and so on. They're called "counting" numbers because that's their primary purpose.
Why B is wrong: This is the opposite of the definition. Numbers we *don't* use to count objects (like 0, negative numbers, or fractions) are NOT counting numbers.
What does “Numerical Value” mean?
A is correct. Numerical value (also called absolute value) measures *how far* a number is from zero on a number line—only the size matters, not whether it's positive or negative. For example, both 5 and -5 have a numerical value of 5.
B is wrong because it describes a *signed* number, which keeps the positive or negative sign. That's just a regular number, not its numerical value. If we cared about the sign, we wouldn't need a special term like "numerical value."
What does “Sum” mean?
Correct Answer: A
"Sum" specifically refers to the result when you add numbers together. For example, the sum of 3 + 5 is 8.
Why B is wrong: The result of subtraction is called the "difference," not the sum. For example, 5 − 3 = 2 is a difference, not a sum.
What does “Difference” mean?
A is correct. "Difference" is the mathematical term for the result you get when you subtract one number from another. For example, the difference between 10 and 3 is 7 (because 10 − 3 = 7).
B is wrong. Adding numbers together gives you a "sum," not a difference. That's the opposite operation.
What does “Product” mean?
A is correct: When you multiply numbers together, the answer you get is called the product. For example, 3 × 4 = 12, so 12 is the product.
B is wrong: The result of dividing one number by another is called the *quotient*, not a product. For example, 12 ÷ 3 = 4, where 4 is the quotient.
What does “Quotient” mean?
Why A is correct:
"Quotient" is the mathematical term for the answer you get when you divide one number by another. For example, in 12 ÷ 3 = 4, the quotient is 4.
Why B is wrong:
The result of multiplying numbers is called a "product," not a quotient. For example, 3 × 4 = 12, where 12 is the product.
What does “Exponent” mean?
Correct Answer (A): An exponent tells you how many times to multiply a base number by itself. For example, 2³ means 2 × 2 × 2 (multiply 2 three times), which equals 8.
Why B is wrong: Division is not what exponents do. If we used division instead, 2³ wouldn't make mathematical sense and wouldn't follow the rules of exponents we use in math.
What does “Square Root” mean?
A is correct: The square root of a number is what you multiply by itself to get that number back. For example, √9 = 3 because 3 × 3 = 9.
B is wrong: Dividing a number by itself always gives 1, not the original number. So this doesn't describe square roots at all.
What does “Percentage” mean?
Correct Answer (A):
A percentage literally means "per cent" (per 100). It shows how many parts out of 100 something represents. For example, 50% means 50 out of 100 parts.
Why B is wrong:
If you multiplied by 100, you'd get a much larger number going in the wrong direction. For instance, 0.5 multiplied by 100 gives you 50, but that's the final percentage—you actually *divide* the original amount by 100 to convert it into a percentage form.
What does “Factorial” mean?
Why A is correct:
Factorial means multiplying all positive integers from 1 up to a given number. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
Why B is wrong:
That describes a *sum*, not a factorial. Summing 1 + 2 + 3 + 4 + 5 = 15, which is completely different from multiplying them together.
What does “Dividend” mean?
Correct Answer: A number to be divided by another number.
In division, the dividend is the number being split up or divided. For example, in 12 ÷ 3 = 4, the 12 is the dividend because it's the number we're dividing.
Why B is wrong: Multiplication uses factors, not dividends. A dividend specifically relates to division, not multiplication.
What does “Divisor” mean?
Correct Answer: A
A divisor is the number you divide *by* in a division problem. For example, in 12 ÷ 3 = 4, the number 3 is the divisor because you're dividing 12 by it.
Why B is wrong:
That describes a multiplier, not a divisor. Multiplication and division are opposite operations, so this confuses the two concepts.
What does “Multiple” mean?
A is correct: "Multiple" literally means more than one—it describes something made up of several or many parts, items, or instances combined together.
B is wrong: This describes the opposite meaning. "Single" or "isolated" means one thing alone, not multiple things. That contradicts what "multiple" actually means.
What does “Subtraction” mean?
A is correct: Subtraction means taking away or removing a quantity from another. When you subtract, you're finding the difference by removing one amount from another (e.g., 10 − 3 = 7).
B is wrong: That describes *addition*, not subtraction. Adding puts amounts together, while subtraction takes them apart.
What does “Addition” mean?
A is correct: Addition means combining things together to make more. The word itself comes from "add," so it's about putting amounts or items together.
B is wrong: This describes subtraction or removal, which is the opposite of addition. Addition increases a total, while removal decreases it.
What does “Greater Than” mean?
A is correct. "Greater than" means something is bigger, more, or higher in value—like 10 is greater than 5 because 10 is larger.
B is wrong. This describes "less than," which is the opposite. If something is smaller or lower, it's *less* than something else, not greater than.
What does “Less Than” mean?
A is correct. "Less than" means something is smaller in amount, size, or value—for example, 3 is less than 5, or a cup holds less water than a gallon.
B is wrong. This describes "more than" or "greater than," which is the opposite of "less than."
What does “Equal To” mean?
Correct answer: A
"Equal to" means things are the same in some way—whether that's size, amount, value, or ability. For example, 5 + 5 is equal to 10 because they have the same value.
Why B is wrong: It says "different," which is the opposite of equal. If things are different, they're *not* equal to each other—they're unequal.
What does “Infinity” mean?
A is correct. "Infinity" literally means something without limits or boundaries—it goes on forever. Think of it like an endless number line that never stops.
B is wrong because it describes the opposite concept. "Finite" and "bounded" mean something HAS limits and ends, which is the complete opposite of infinity.
What does “Factor” mean?
A is correct: A factor divides evenly into a number with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder left over.
B is wrong: This describes a *multiplier*, not a factor. While factors and multipliers are related (if 3 is a factor of 12, then 3 is multiplied by 4 to get 12), the definition focuses on the wrong action—multiplying rather than dividing.
What does “Multiplication” mean?
A is correct because multiplication is literally defined as the process of multiplying numbers together—like combining groups to find a total (e.g., 3 × 4 = 12).
B is wrong because that describes subtraction, which is taking away or finding the difference between numbers. Subtraction and multiplication are completely different math operations.
What does “Cube Root” mean?
Correct Answer (A): A quantity of which a given quantity is the cube.
The cube root is the opposite of cubing. If you cube a number (multiply it by itself three times), the cube root finds the original number. For example, the cube root of 8 is 2, because 2³ = 8.
Why B is wrong:
"Inversely proportional to the cube" describes a completely different mathematical relationship (like 1/x³), not the cube root operation at all.
What does “Base Number” mean?
Why A is correct:
A "base number" is a foundational reference value used across multiple mathematical contexts—most notably in number systems (like base 10 or binary) and in logarithms (where you have a base like log₁₀). It's a broad, versatile concept.
Why B is wrong:
Base numbers aren't limited to geometry at all. While bases can appear in some geometric contexts, they're primarily used in number systems and logarithms, making this option far too narrow and inaccurate.
What does “Integer Division” mean?
Correct Answer: A
Integer division keeps only the whole number part of a division result. For example, 7 ÷ 2 = 3 (not 3.5), because the remainder of 1 is thrown away. This is useful in programming when you only need whole units.
Why B is wrong:
Option B describes regular division or operations that *keep* the remainder—the exact opposite of integer division. Integer division specifically *ignores* remainders, not includes them.
What does “Decimal Place” mean?
A is correct: When we talk about "decimal places," we mean the digits *after* the decimal point. For example, in 3.14, the "1" is in the first decimal place and the "4" is in the second decimal place. These places show fractions (tenths, hundredths, etc.).
B is wrong: Digits to the left of the decimal point are called "place values" (like ones, tens, hundreds), not "decimal places." The term "decimal place" specifically refers to positions *after* the decimal point.
What does “Ordinal Number” mean?
Correct answer (A): Ordinal numbers tell you the *position or rank* of something in a sequence. Words like "first," "second," "third," "21st," or "last" all show where something falls in an order—this is what "ordinal" means.
Why B is wrong: That describes a *cardinal* number, which counts quantity (1, 2, 3, 5 apples). Cardinal numbers answer "how many," while ordinal numbers answer "which position."
What does “Cardinal Number” mean?
Correct Answer (A):
Cardinal numbers tell you *how many* things there are—they measure quantity. Examples: one apple, two cats, three books.
Why B is wrong:
That describes *ordinal* numbers, which show position or order in a sequence (1st, 2nd, 3rd, first place, second place, etc.). These are a different category entirely.
What does “Arithmetic Sequence” mean?
Why A is correct:
An arithmetic sequence has a constant *difference* (called the common difference) between each pair of consecutive terms. For example: 2, 5, 8, 11 (difference of +3 each time).
Why B is wrong:
That describes a *geometric* sequence, not an arithmetic one. A geometric sequence has a constant *ratio* between consecutive terms—like 2, 6, 18, 54 (ratio of ×3 each time). These are two different types of sequences.
What does “Geometric Sequence” mean?
Why A is correct:
In a geometric sequence, each term is multiplied by the same number (called the common ratio) to get the next term. For example: 2, 6, 18, 54 — each term is 3 times the previous one. The word "geometric" refers to this multiplicative pattern.
Why B is wrong:
That describes an *arithmetic* sequence, not a geometric one. An arithmetic sequence uses addition/subtraction (constant difference), like 2, 5, 8, 11. These are two different types of sequences.
What does “Unit Digit” mean?
Correct Answer (A): The unit digit is the rightmost digit in a number because it represents the "ones place" in our number system. For example, in 347, the unit digit is 7 because it's in the ones position.
Why B is wrong: The first digit to the left is called the leading digit or leftmost digit—it represents the highest place value. In 347, that would be 3 (the hundreds place), not the unit digit.
What does “Decimal Expansion” mean?
A is correct: Decimal expansion means writing a number in base-10 (our everyday number system), like how 1/4 becomes 0.25 or π becomes 3.14159...
B is wrong: Binary is base-2 (using only 0s and 1s)—that's a completely different number system, not decimal expansion.
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