الكسور الدقيقة وعمليات الكسور المختلطة · المستوى الأساسي
مُقدَّم| English | المعنى |
|---|---|
| improper fraction/ɪmˈprɒpə ˈfrækʃn/ | كسر غير صحيح |
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.
لماذا 1/2+1/3 لا يساوي 2/5؟
Difficulty 1/5 · 100 coins + a small bonus on first completion today
الخمسيات والثلاثيات هي أجزاء مختلفة الحجم. إعادة الكتابة كـ 3/6+2/6 تحافظ على حجم الوحدة وتعطي 5/6؛ بينما يفشل الاختصار الخاطئ 2/5 في كل فحص للتقدير.
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.
الكسور الدقيقة وعمليات الكسور المختلطة
تحويل الكسور المختلطة إلى كسور غير عادية
قارن النموذج بالحالة المحلولة واشرح تغييراً واحداً.
أوجد 1½-¾.
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.
أوجد (-2/3)×(9/4).
Difficulty 2/5 · 140 coins + a small bonus on first completion today
(-2×9)/(3×4)=-18/12=-1.5.
لجمع كسرين، اجمع البسط مع البسط والمقام مع المقام.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
جمع المقامات لا يحافظ على حجم الوحدة: 1/2+1/3 لا يساوي 2/5. اختصر فقط عوامل البسط والمقام الصحيحين. القسمة على الصفر غير معرفة.
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.
أوجد (3/4)÷(5/8).
Difficulty 2/5 · 140 coins + a small bonus on first completion today
اضرب في 8/5: 24/20=6/5=1.2.
طابق كل عملية كسر بقاعدتها.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
لكل عملية قاعدة خاصة بها؛ القسمة على كسر هي ضرب في مقلوبه لأن المقلوب يلغي عملية القسمة.
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.