Exercices corrigés sur les nombres relatifs (5ème) : règles de calcul et fiche de révision

Page 2: Multiplication and Division of Relative Numbers

This page covers the rules for multiplying and dividing relative numbers, with particular emphasis on sign rules for these operations.

Definition: The product or quotient of two relative numbers follows specific sign rules.

Highlight: Two numbers with the same sign multiply to give a positive result, while different signs yield a negative result.

Example: $+4$ × $+2$ = +8 demonstrates multiplication of positive numbers.

Quote: "Le produit (ou le quotient) de deux nombres relatifs de même signe est positif."

Page 3: Operations with Fractions - Part 1

This page introduces basic operations with fractions, focusing on addition and subtraction rules.

Definition: To add or subtract fractions, denominators must be the same or need to be converted to a common denominator.

Example: 13/5 - 4/10 = 22/10 = 11/5 demonstrates fraction subtraction with different denominators.

Highlight: When subtracting a positive fraction from a negative fraction, add their opposites.

Page 4: Operations with Fractions - Part 2

This page continues with fraction operations, focusing on multiplication and division.

Definition: The inverse of a fractional number a/b is b/a (for non-zero a and b).

Highlight: To divide fractions, multiply the first fraction by the inverse of the second.

Example: 8/42 ÷ 64/49 = 7/48 demonstrates division of fractions.

Page 5: Equal Fractions and Cross Products

This page explores the relationship between equal fractions and cross multiplication.

Definition: If a/b = c/d, then a×d = b×c (cross product rule).

Example: For x/60 = 12/7, solving gives x = 1.4.

Highlight: Cross multiplication is a key technique for determining fraction equality.

Quote: "Si a×d = b×c alors a/b = c/d" (If the cross products are equal, the fractions are equal).

Page 1: Addition and Subtraction of Relative Numbers

This page introduces fundamental concepts of addition de nombres relatifs and subtraction operations. The content explains how to handle numbers with same and different signs.

Definition: Two numbers are considered opposites when their sum equals zero.

Highlight: For adding relative numbers with the same sign, add the distances from zero and keep the same sign.

Example: $-27$ + $-8$ = -35 demonstrates adding numbers with same signs.

Vocabulary: Distance to zero refers to the absolute value of a number.

Quote: "Soustraire un nombre relatif revient à additionner son opposé" (Subtracting a relative number is equivalent to adding its opposite).