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Калькулятор отношений и пропорций

Simplify a ratio, solve a proportion a : b = c : x for the missing term, scale a ratio to a target, or split an amount in a given ratio, exactly.

Обновлено Проверенные примеры: 8

Terms separated by colons; decimals and fractions are fine (1.5 : 2.5, 1/2 : 3/4)
Попробовать
Результат
2 : 3
Результат: 2 : 3
Scale factor
6
First term ÷ second term
0.666667

12 : 18 simplifies to 2 : 3; each original term is 6 times the matching term of the simple form.

Parts of the whole

Term 12Term 23
Как выполняется расчёт S

  1. Greatest common divisor

    gcd⁡(12,18)=6\gcd(12, 18) = 6

  2. Divide every term by it

    126:186=2:3\frac{12}{6} : \frac{18}{6} = 2 : 3

О калькуляторе: Калькулятор отношений и пропорций

A ratio compares quantities by division, so 12 : 18 and 2 : 3 describe the same proportion. Simplifying divides every term by their greatest common divisor, after multiplying through by the least common multiple of any denominators so that decimal and fraction terms become whole numbers. A proportion a : b = c : d holds exactly when a × d = b × c, which is how cross-multiplication finds a missing term; splitting an amount divides it by the sum of the terms to get the size of one share.

Recipes, paint and concrete mixes, map scales and dividing money between partners are the usual uses. Split 1,000 in the ratio 2 : 3 : 5 and the 10 shares are worth 100 each, giving 200, 300 and 500; solve 3 : 4 = 9 : x and x = 4 × 9 ÷ 3 = 12.

Answers stay exact: shares that do not divide evenly appear as fractions such as 100/3 rather than rounded decimals. Terms must be zero or positive.

Примеры с решением

Simplify 12 : 18

I want to
Simplify a ratio
Ratio
12 : 18
Результат
2 : 3
Scale factor
6
First term ÷ second term
0.666667

Источник проверки: gcd(12, 18) = 6 (Python math.gcd)

Decimal terms 1.5 : 2.5

I want to
Simplify a ratio
Ratio
1.5 : 2.5
Результат
3 : 5
Scale factor
0.5

Источник проверки: ×10 → 15 : 25, gcd 5 (Python fractions)

Fraction terms 1/2 : 3/4 : 5/6

I want to
Simplify a ratio
Ratio
1/2 : 3/4 : 5/6
Результат
6 : 9 : 10

Источник проверки: LCD 12 → 6 : 9 : 10, gcd 1 (Python fractions)

Scale 2 : 3 so the first term is 30

I want to
Scale a ratio to a target
Ratio
2 : 3
Target value for that term
30
Результат
30 : 45
Scale factor
15

Источник проверки: 30 / 2 = 15; 3 × 15 = 45

Вопросы

How do you simplify a ratio?

Divide every term by the greatest common divisor of the terms. For 12 : 18 the GCD is 6, giving 2 : 3. Decimals and fractions are cleared first by multiplying every term by the same number: 1.5 : 2.5 × 2 = 3 : 5, and 1/2 : 3/4 : 5/6 × 12 = 6 : 9 : 10, which is already in simplest form because its GCD is 1.

How do you solve a proportion for x?

Cross-multiply, then divide. In 3 : 4 = 9 : x the products of the diagonal terms are equal, so 3x = 4 × 9 = 36 and x = 12. The unknown can sit in any position: in x : 5 = 6 : 15, 15x = 5 × 6 = 30, so x = 2. If the term diagonally opposite x is 0, there is no single answer.

How do you divide an amount in a ratio?

Add the ratio terms, divide the amount by that total to get one share, then multiply each term by the share. For 1,000 split 2 : 3 : 5 the terms add to 10, one share is 100, and the parts are 200, 300 and 500. The parts always add back to the amount; 100 split 1 : 2 gives 100/3 and 200/3, about 33.33 and 66.67.

What is the difference between a ratio and a fraction?

A ratio compares parts with each other; a fraction compares a part with the whole. In a class of 12 girls and 18 boys the ratio of girls to boys is 12 : 18 = 2 : 3, but girls make up 12/30 = 2/5 of the class. A two-term ratio a : b becomes the fraction a/(a + b) of the whole.

How do you scale a ratio up or down?

Multiply or divide every term by the same factor. To make the first term of 2 : 3 equal 30, the factor is 30 ÷ 2 = 15, so the scaled ratio is 30 : 45. Scaling a recipe works the same way: a 2 : 3 mix made 15 times larger needs 30 and 45 units of the two ingredients, and the proportions stay 40% and 60%.

Насколько точен «Калькулятор отношений и пропорций»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 8. Например, «Simplify 12 : 18» проверяется по источнику gcd(12, 18) = 6 (Python math.gcd).

Откуда взята методика?

Khan Academy — Ratios, rates and proportions; Wolfram MathWorld — Proportional.

Об этом калькуляторе

ab=cd  ⟺  ad=bcsharei=T⋅ri∑jrj\begin{gathered} \frac{a}{b} = \frac{c}{d} \iff a d = b c \\[10pt] \text{share}_i = T \cdot \frac{r_i}{\sum_j r_j} \end{gathered}

Источники

  1. Khan Academy — Ratios, rates and proportions
  2. Wolfram MathWorld — Proportional

Проверено по источникам

В калькулятор включены решённые примеры с ответами из независимых источников. Их количество: 8. Они входят в набор тестов, и вы также можете запустить их здесь.

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