Question

ДАЮ 15 БАЛЛОВ! Объясните правила умножения, деления, сложения и вычитания рациональных чисел с примерами! Прошу!

Answer 1

Сложение рациональных чисел

Так как рациональные числа содержат натуральные числа, то смысл сложения рациональных чисел, должен быть согласован со смыслом сложения натуральных чисел. К примеру, сумма рациональных чисел вида 2+1/3 может означать такое действие: к 2 целым предметам добавили одну третью часть такого предмета, и теперь они рассматриваются совместно.

Теперь можно переходить к правилам сложения рациональных чисел, и к рассмотрению примеров применения этих правил.

Answer 2

Rules of Operations with Rational Numbers

When dealing with rational numbers, which include both integers and fractions, there are specific rules for addition, subtraction, multiplication, and division. Let's go through each operation with examples.

Addition of Rational Numbers

Addition of rational numbers involves adding the numerators when the denominators are the same. If the denominators are different, the fractions need to be converted to equivalent fractions with the same denominator before adding.

For example, to add 3/4 and 1/2: 3/4 + 1/2 = (3*2)/(4*2) + 4/8 = 6/8 + 4/8 = 10/8 = 1 1/4

Subtraction of Rational Numbers

Subtraction of rational numbers follows similar rules to addition. The numerators are subtracted when the denominators are the same. If the denominators are different, the fractions need to be converted to equivalent fractions with the same denominator before subtracting.

For example, to subtract 5/6 from 7/8: 7/8 - 5/6 = (7*3)/(8*3) - 5*4/(6*4) = 21/24 - 20/24 = 1/24

Multiplication of Rational Numbers

Multiplication of rational numbers involves multiplying the numerators and denominators of the fractions.

For example, to multiply 2/3 by 5/7: 2/3 * 5/7 = (2*5)/(3*7) = 10/21

Division of Rational Numbers

Division of rational numbers is similar to multiplication, but it involves multiplying by the reciprocal of the divisor.

For example, to divide 4/5 by 2/3: 4/5 ÷ 2/3 = 4/5 * 3/2 = (4*3)/(5*2) = 12/10 = 6/5

These rules are fundamental to working with rational numbers and are essential for various mathematical operations involving fractions and integers.