Operations With Fractions
边玩边学
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课程笔记
Adding & Subtracting Fractions
- Find the lowest common denominator (LCD) of the fractions.
- Rewrite each fraction as an equivalent fraction with the LCD.
- Add or subtract the numerators only; keep the denominator the same.
- Simplify the result by cancelling common factors.
- If a fraction is a mixed number, convert it to an improper fraction first.
- After calculation, convert back to a mixed number if required.
Multiplying Fractions
- Cancel any common factors between numerators and denominators before multiplying.
- Multiply the numerators together and the denominators together.
- If a fraction is a mixed number, convert it to an improper fraction first.
- Simplify the final fraction by cancelling any remaining common factors.
- Convert improper fractions back to mixed numbers if needed.
Dividing Fractions
- Flip the second fraction (find its reciprocal) and change ÷ to ×.
- This is often remembered as 'flip and times'.
- Cancel common factors before multiplying.
- Multiply the numerators together and the denominators together.
- If a fraction is a mixed number, convert it to an improper fraction first.
- Simplify and convert back to a mixed number if required.
Working with Mixed Numbers
- Convert mixed numbers to improper fractions: multiply the whole part by the denominator, add the numerator, write over the denominator.
- Perform the operation (add, subtract, multiply, divide) using the improper fractions.
- Convert the final answer back to a mixed number if the question asks for it or if it's an improper fraction.
Simplifying Fractions
- Always give your final answer in simplest form.
- Cancel common factors by dividing numerator and denominator by the same number.
- Check for common factors at every step to keep numbers small.
- A fraction is in simplest form when the numerator and denominator have no common factors other than 1.
Common Mistakes to Avoid
- Do not add or subtract denominators; only numerators.
- Always find a common denominator before adding or subtracting.
- Remember to convert mixed numbers before performing operations.
- When dividing, flip only the second fraction, not the first.
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练习题
免费预览——60 题中的 8 题。注册即可查看全部。
1.Work out \frac{5}{6} + \frac{2}{3}. Give your answer as a mixed number in its simplest form.
Medium- A1\frac{1}{2}
- B1\frac{1}{3}
- C\frac{7}{9}
- D1\frac{1}{6}
2.Giulio's reaction times are \frac{1}{3} second and \frac{1}{8} second. Find the difference between the two reaction times.
Medium- A\frac{5}{24} seconds
- B\frac{11}{24} seconds
- C\frac{1}{5} seconds
- D\frac{1}{24} seconds
3.Work out \frac{12}{35} \times \frac{7}{9}. Give your answer as a fraction in its simplest form.
Medium- A\frac{4}{15}
- B\frac{84}{315}
- C\frac{12}{45}
- D\frac{4}{45}
4.Write down a fraction that completes \frac{13}{11} \times \ldots = 1.
Easy- A\frac{11}{13}
- B\frac{13}{11}
- C\frac{1}{11}
- D\frac{1}{13}
5.Work out \frac{7}{8} + \frac{1}{6}. Give your answer as a mixed number in its simplest form.
Medium- A1\frac{1}{24}
- B\frac{25}{24}
- C1\frac{1}{12}
- D\frac{8}{14}
6.Work out 1\frac{3}{4} - \frac{11}{12}. Give your answer as a fraction in its simplest form.
Medium- A\frac{5}{6}
- B\frac{7}{12}
- C\frac{1}{2}
- D\frac{11}{12}
7.Work out \frac{15}{28} \div \frac{4}{7}. Give your answer as a fraction in its simplest form.
Medium- A\frac{15}{16}
- B\frac{105}{112}
- C\frac{15}{49}
- D\frac{60}{28}
8.Work out 1\frac{7}{12} + \frac{13}{20}. Give your answer as a mixed number in its simplest form.
Hard- A2\frac{7}{30}
- B2\frac{1}{15}
- C1\frac{59}{60}
- D2\frac{1}{2}