Glossary

How to read this glossary

The words of this volume, from A to Z

The chapter where each word is settled is stated at the end of its definition.

Bracket

Give the two consecutive whole numbers between which a fraction lies. The bracket is obtained by dividing the numerator by the denominator. Introduced in chapter 2.

Check

Set a result obtained against the estimate made before calculating. A result outside the announced bounds is wrong, without any need to do the calculation again. Introduced in chapter 9.

Common denominator

A denominator that suits several fractions at once. A common multiple of their denominators always suits, and the product of the denominators supplies one. Introduced in chapter 5, and used for every addition in chapter 6.

Compare

Say which of two fractions is the larger, that is to say which one lies further to the right on a number line. Introduced in chapter 5.

Counting unit

The part chosen for counting, fixed by the denominator. With a denominator of 5, we count in fifths, and every quantity in the problem is said in that unit. Introduced in chapter 2.

Decimal fraction

A fraction whose denominator is ten, one hundred, one thousand, and so on. Every decimal fraction can be written with a decimal point and a finite number of digits, and other fractions can be too as soon as they can be rewritten as a decimal fraction: 1/2 is worth 50/100, therefore 0.5. Introduced in chapter 8.

Denominator

The number written under the fraction bar, or after the slash. It says into how many equal parts the whole is shared, and it therefore gives the part its name. Its name means the one that names. Introduced in chapter 1.

Divisor

A number that divides another one with no remainder: 6 is a divisor of 18 and of 24. To simplify a fraction is to divide its two terms by a common divisor. Introduced in chapter 4.

Equivalent fractions

Two fractions that point to the same number, therefore to the same point on a number line. We go from one to the other by multiplying or dividing both terms by one and the same number other than zero. Introduced in chapter 4.

Estimate

Give an order of magnitude of the result before calculating it, leaning on the benchmarks 1/2 and 1. Estimating is not guessing: it is bracketing the result between two safe bounds. Introduced in chapter 9.

Fraction

The report of two gestures: sharing a whole into equal parts, then taking a certain number of those parts. It is one number, and not two numbers written one above the other. Introduced in chapter 1.

Fraction greater than the whole

A fraction whose numerator is larger than its denominator: more than one whole was needed in order to take those parts, so it is worth more than 1. Introduced in chapter 2.

Fraction smaller than the whole

A fraction whose numerator is smaller than its denominator: not all the parts of the sharing have been taken, so it is worth less than 1. Introduced in chapter 2.

Hundredth

One unit shared into a hundred equal parts, or one tenth shared into ten. Ten hundredths are worth one tenth, and a hundred hundredths are worth one unit. Introduced in chapter 8.

Multiple

A number obtained by multiplying a number by a whole number: 15, 20 and 100 are multiples of 5. An imposed denominator has to be a multiple of the denominator of the simplest form of the fraction. Introduced in chapter 4.

Number line

A line on which a point 0 has been marked, then the whole numbers at equal intervals. Placing a fraction on it gives the fraction its standing as a number. Introduced in chapter 3.

Numerator

The number written above the fraction bar, or before the slash. It says how many parts are taken out of those of the sharing. Its name means the one that counts. Introduced in chapter 1.

Operator

The use of a fraction that acts on a number in order to produce another one: three quarters of 40 are worth 30. The result is a quantity, not a fraction. The notion is settled in chapter 7, and the word in chapter 9.

Part

One of the pieces obtained by a sharing. All the parts of one and the same sharing have the same size, and it is that equality which allows them to be named. Introduced in chapter 1.

Simplify

Divide the numerator and the denominator by one and the same number, so as to obtain a shorter writing of the same number. Simplifying never changes the value. Introduced in chapter 4.

Tenth

One unit shared into ten equal parts. Ten tenths are worth one unit, and one tenth is worth ten hundredths. Introduced in chapter 8.

Thousandth

One unit shared into a thousand equal parts, or one hundredth shared into ten. Ten thousandths are worth one hundredth. Introduced in chapter 8.

Unit fraction

A fraction whose numerator is 1, that is to say a single part of the sharing. It is the brick every other fraction is made of. Introduced in chapter 1.

Whole

What is shared, and what the fraction relates to: an object, a collection, a length, a duration, a sum of money. A fraction says nothing as long as its whole is not named. Introduced in chapter 1.