Точные дроби и операции с смешанными числами · Базовый уровень
Введено| English | Значение |
|---|---|
| improper fraction/ɪmˈprɒpə ˈfrækʃn/ | неправильная дробь |
Can we keep the recipe exact?
- A recipe uses 1½ cups for one batch. How much remains after using ¾ of a cup, and why should the answer stay exact?
- This lesson studies improper fraction 假分数: A fraction whose numerator is at least as large as its positive denominator.
Choose the mathematical structure
- Convert mixed numbers to improper fractions. Add or subtract using a common denominator; multiply numerators and denominators; divide by a nonzero fraction by multiplying its reciprocal. Cancel common factors, not added terms. These rules also apply to negative fractions.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Почему 1/2+1/3 не равно 2/5?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Пятые и третьи — это части разного размера. Переписывание в виде 3/6+2/6 сохраняет размер единицы измерения и дает 5/6; ложная упрощенная формула 2/5 не проходит ни одну проверку на оценку.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
1½-¾=6/4-3/4=3/4. Also (-2/3)×(9/4)=-18/12=-3/2 and (3/4)÷(5/8)=(3/4)×(8/5)=6/5. A common denominator gives 5/6+3/4=10/12+9/12=19/12. Check division by multiplying 6/5 by 5/8 to recover 3/4. Exact multiples of π follow ordinary arithmetic: 3π+2π=5π and 6π/3=2π. Leave an answer such as 5π exact when requested; π≈3.14 would introduce approximation. For subtraction, 5/6-3/4=10/12-9/12=1/12; for a negative mixed number, -1½ means -(1+1/2)=-3/2.
Точные дроби и операции с смешанными числами
Преобразование смешанных чисел в неправильные дроби
Сравните модель с разобраным примером и объясните одно изменение.
Найдите значение выражения 1^(½-¾).
Difficulty 2/5 · 140 coins + a small bonus on first completion today
6/4-3/4=3/4=0.75.
Test a tempting shortcut
- Adding denominators does not preserve the unit size: 1/2+1/3 is not 2/5. Cancel only factors of a whole numerator and denominator. A division by zero is undefined.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
To add two fractions, add their numerators and add their denominators. This claim is false. Explain which definition or assumption it violates.
Найдите (−2/3) × (9/4).
Difficulty 2/5 · 140 coins + a small bonus on first completion today
(-2×9)/(3×4)=-18/12=-1.5.
Чтобы сложить две дроби, сложите их числители и знаменатели.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Сложение знаменателей не сохраняет размер единицы: 1/2 + 1/3 не равно 2/5. Сокращайте только множители целого числителя и знаменателя. Деление на ноль не определено.
Interpret a new situation
- For a non-calculator question show the common denominator or reciprocal step. Convert 19/12 to 1 7/12 if a mixed number is requested; round only when the question explicitly needs a decimal.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Найдите (3/4) ÷ (5/8).
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Умножьте на 8/5: 24/20 = 6/5 = 1.2.
Соотнесите каждую операцию с дробями с соответствующим правилом.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
У каждой операции есть свое правило; деление на дробь заменяется умножением на обратную дробь, так как обратная дробь отменяет деление.
Use this in your course
- 8300 · Foundation · 3.1. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A fraction whose numerator is at least as large as its positive denominator. Choose the relationship, show the method, check its assumptions and interpret the result.