51 terms

Equivalent ratios

Ratios that have the same value; for example, 1:3, 2:6, and 3:9 are equivalent ratios.

Quantities

Amounts, or measurements, such as length, area, volume, and speed.

Quotient

The answer to a division problem.

Ratio

A statement of how two (nonzero) numbers compare. They can be written as A:B or A to B.

Ratio relationship

The relationship between two quantities in a given setting; for example, sugar to butter in a recipe or paws to tails in the monkey house at the zoo. It is also the set of all ratios that are the same (equivalent). A ratio of 1:4, for example, can be used to describe ratio relationships (1:4, 2:8, 3:12) and can be represented by various models (ratio tables, double number line diagrams, and by equations and their graphs) as shown in the Models section.

Value of the ratio

For the ratio A:B, the value of the ratio is the quotient A/B where B ≠ 0. For example, the ratio 6:10 has a value of 6/10 or 0.6.

Unit rate

The numerical part of a rate measurement; for example, in the rate 45 mph, the unit rate is 45.

Percent

One part in every hundred. One out of 100 is written as 1/100 For example, 30% of a quantity means 30/100 times the quantity.

Dividend

The number that is divided by another number. For example, in the expression 32 ÷ 4, the number 32.

Divisor

The number by which another number is divided. In the problem 36 ÷ 9 = 4, 9 is the divisor.

Multiplicative Inverse

When multiplying a number by its multiplicative inverse, the product (answer) is one. For example, 3/4 and 4/3 are multiplicative inverses because ¾ × 4/3 = 1.

Unit form

Place value counting. For example, 34 can be stated as 3 tens 4 ones.

Unit language

Using the unit (e.g., thirds, fifths, tenths) to describe a number. For example, 0.4 is 4 tenths and 1/5 is 1 fifth.

Difference

The answer to a subtraction problem.

Distributive property

Allows the numbers in a multiplication problem to be broken down into partial products (i.e., partial answers) to make the mental math simpler. The partial products can then be combined to find the end product (the answer to the original multiplication problem). For example, consider the problem 6 × 27. The number 27 can be broken down into (20 + 7), so 6 × 27 = (6 × 20) + (6 × 7) = 120 + 42 = 162.

Factors

Numbers that are multiplied together to get other numbers. For example, 2 and 3 are factors of 6 because 2 × 3 = 6; 4 and 5 are factors of 20 because 4 × 5 = 20.

Standard algorithm

Step-by-step procedures used to solve a particular type of problem. Students will use the standard algorithms for adding, subtracting, multiplying, and dividing decimals, whole numbers, and fractions.

Product

The answer to a multiplication problem.

Sum

The answer to an addition problem.

Divisible

When one number can be divided by another and the result (quotient) is an exact whole number, we can say that number is divisible by the other number. For example, 36 is divisible by 9 because 36 ÷ 9 = 4.

Multiple

The product of a given number and any other whole number. For example, 5, 10, 15, 20, and 25 are all multiples of 5 because 5 can be multiplied by a whole number to equal each of these numbers.

Common factors

Factors shared by two or more numbers. For example, 3 is a common factor of 6, 9, and 12.

Common multiples

Multiples shared by two or more numbers. For example, 30 is a common multiple of 3, 6, and 10.

Divisibility rules

Ways to tell whether one whole number is divisible by another.

Greatest common factor (GCF)

The largest number that divides evenly into all numbers in a group of two or more numbers. To determine the greatest common factor of two numbers—for example, 12 and 16—list all the whole number factors of 12 (1, 2, 3, 4, 6, 12) and all the whole number factors of 16 (1, 2, 4, 8, 16). The greatest whole number that appears on both lists is 4, so 4 is the greatest common factor of 12 and 16.

Least common multiple (LCM)

The smallest whole number multiple shared by all numbers in a group of two or more numbers. To nd the least common multiple of two numbers—for example, 5 and 6—list the rst few multiples of each number: 5, 10, 15, 20, 25, 30, and so on for 5, and 6, 12, 18, 24, 30, and so on for 6. The first (and, thus, least) multiple they share is the least common multiple (30).

Units digit

The number in the ones place. For example, the units digit for 2,981 is 1, the units digit for 570 is 0, and the units digit for 19,823.4 is 3.

Equation

A statement indicating that two expressions are equal (e.g., 3 × 4 = 6 × 2 and 5 + x = 20).

Equivalent expressions

Expressions that have the same value (e.g., 2 × 6 is equivalent to 4a if a = 3).

Expression

A group of numbers, symbols, and operators such as + and − with no equal sign that evaluates to a number (e.g., 2 × 4 and 9n + 7).

Number sentence

A statement indicating that two numerical expressions are equal (e.g., 8 − 2 = 5 + 1).

Variable

A symbol, such as a letter, that is a placeholder for a number.

Algebraic expression

An expression containing numbers, variables, and operators (such as + and −) that represents a single value and does not contain equal signs or inequality symbols (e.g., 2m or 9a + 3).

Base

In the term y6, the y is the base, or repeating factor, and may be a variable or a number.

Cubed

When a base is raised to the third power. For example, 53 can be read as five cubed.

Evaluate

To evaluate an expression means to find the answer.

Exponential notation for whole number exponents

A way to write numbers using exponents. For example, the number 3,125 (standard form) can be written as 5 × 5 × 5 × 5 × 5 (expanded form) or 55 (exponential form). It provides a simpler alternative to expanded form when indicating that a number should be multiplied by itself repeatedly. We can read 55 as five to the fifth power.

Exponent

In the term 3y6, the 6 is the exponent. The exponent tells you how many times to use the base (y) as a factor.

Numerical expression

A group of numbers, symbols, and operators (such as + and −) that represents a single value and does not contain equal signs or inequality symbols (e.g., 2 × 4 or 9(5 + 1)).

Squared

When a base is raised to the second power. For example, 52 can be read as five squared.

Value of a numerical expression

The number found by evaluating the expression, or, in other words, by simplifying the expression to a single value. For example, the value of the expression 3 × 8 is 24.

Additive identity

By definition, the number zero. (See additive identity property of zero below.)

Additive identity property of zero

The additive identity (zero) can be added to any number without changing the identity of the number (e.g., 11 + 0 = 11 and a + 0 = a).

Commutative property

The order of an addition or multiplication problem may change, but the sum or product will remain the same.

Multiplicative identity

By definition, the number one. (See multiplicative identity property of one below.)

Multiplicative identity property of one

The multiplicative identity (one) can be multiplied by any number without changing the identity of the number (e.g., 4 × 1 = 4 and a × 1 = a).

Coefficient

A constant factor (not to be confused with a constant) in a variable term. For example, in the term 4m, 4 is the coefficient, and it is multiplied by the variable m.

Term

Part of an expression that can be added to or subtracted from the rest of the expression. In the expression 7g + 8h + 3, the terms are 7g, 8h, and 3.

Inequality

An inequality is a statement comparing expressions that are unequal or not strictly equal. The symbol used to compare the expressions reveals the type of inequality: < (less than), ≤ (less than or equal to), > (greater than), ≥ (greater than or equal to), or ≠ (not equal).

Dependent variable

A variable whose value depends on the value of another variable. For example, if x represents the number of hours spent studying and y represents the test score, the value of y might change according to the value of x.

Independent variable

A variable (e.g., age) whose value is not affected by the values of other variables.