# Math Glossary

**base ten number system ** The common number

system we use . Our number system is based on the

number 10 because we have ten fingers with which to

group. Each group represents ten of the previous

group, so we can write numbers efficiently. By

extending the place value system to include places

that represent fractions with 10 or powers of 10 in

the denominator, we can easily represent very large

and very small quantities. Below is a graphic

representation of counting in the base ten number

system. (Figure 1)

**benchmark **A reference number that can be used to

estimate the size of other numbers. For work with

fractions, 0, 1/2, and 1 are good benchmarks. We often

estimate fractions or decimals with benchmarks

because it is easier to do arithmetic with them , and

estimates often give enough accuracy for the

situation. For example, many fractions and

decimals—such as 37/50, 5/8, 0.43, and 0.55—can be

thought of as being close to 1/2.You might say 5/8 is

between 1/2 and 1 but closer to 1/2, so you can estimate 5/8

to be about 1/2 .We also use benchmarks to help

compare fractions and decimals. For example, we

could say that 5/8 is greater than 0.43 because 5/8 is

greater than 1/2 and 0.43 is less than 1/2 .

**decimal **A special form of a fraction. Decimals, or

decimal fractions, are based on the base ten

place-value system. To write numbers as decimals, we

use only 10 and powers of 10 as denominators .

Writing fractions in this way saves us from writing

the denominators because they are understood. When

we write as a decimal (0.375) the denominator

of is understood. The digits to the left of
the

decimal point show whole units. The digits to the

right of the decimal point show a portion of a whole

unit. The diagram shows the place value for each

digit of the number 5,620.301.

**denominator** The number written below the line in

a fraction. In the fraction 3/4, 4 is the denominator. In

the part-whole interpretation of fractions, the

denominator shows the number of equal-size parts

into which the whole has been split.

** equivalent fractions ** Fractions that are equal in

value, but may have different numerators and

denominators . For example, 2/3 and 14/21 are equivalent

fractions. The shaded part of this rectangle represents

both 2/3 and 14/21.

**fraction **A number (quantity) of the form a/b where
a

and b are whole numbers. A fraction can indicate a

part of a whole object, set, or measurement unit; a

ratio of two quantities ; or a division. For the picture

below, the fraction 3/4 shows the part of the rectangle

that is shaded. The denominator 4 indicates the

number of equal-size pieces. The numerator 3

indicates the number of pieces that are shaded.

The fraction 3/4 could also represent three of a group

of four items meeting a particular criteria. For

example, when 12 students enjoyed a particular

activity and 16 students did not, the ratio is 3 to 4.

Another example is the amount of pizza each person

receives when three pizzas are shared equally among

four people (3 ÷ 4 or 3/4 of a pizza per person).

**improper fraction** A fraction in which the

numerator is larger than the denominator. An

improper fraction is a fraction that is greater than 1.

The fraction 5/2 is an improper fraction. The fraction 5/2

means 5 halves and is equivalent to , which is

greater than 1.

**mixed number** A number that is written with both

a whole number and a fraction. A mixed number is

the sum of the whole number and the fraction. The

number represents two wholes and one half and

can be thought of as 2 + 1/2.

**numerator** The number written above the line in a

fraction. In the fraction 5/8, 5 is the numerator. When

you interpret the fraction 5/8 as a part of a whole, the

numerator 5 represents 5 of 8 equal parts.

**percent** “Out of 100.”A percent is a special decimal

fraction in which the denominator is 100.When we

write 68%, we mean 68 out of 100, 68/100, or 0.68.We

write the percent sign (%) after a number to indicate

percent. The shaded part of this square is 68%.

**ratio **A number, often expressed as a fraction, used

to make comparisons between two quanitities. Ratios

may also be expressed as equivalent decimals or

percents. 3/5, 0.6, and 60% are all ratios. A phrase such

as “120 out of 200” is another way to represent a ratio.

**rational number** A number that can be written as a

quotient of two positive or negative whole numbers.

You are familiar with positive rational numbers like

3/4, 107/5,and . Some examples of the
negative

rational numbers you will see in the future are –3,

–2/5, and –20. Both positive and negative rational numbers

can be used to represent real -life situations. For

example, temperatures or yardage during a football

game can be positive, negative, or 0.There are other

numbers, such as pi, that are not rational numbers.

**unit fraction** A fraction with a numerator of 1. In

the unit fraction 1/13, the denominator 13 indicates

the number of equal-size parts into which the whole

has been split. The fraction represents the quantity of

1 of those parts.

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