Fractions: Addition and Subtraction

Questions and Answers

What is the result of adding two fractions with the same denominator?

The numerators are added together. (correct)

The denominators remain unchanged. (correct)

The denominators are multiplied together.

The result is simplified by subtracting the numerators.

What must be done when adding fractions with different denominators?

Find a common denominator and adjust the fractions. (correct)

Ignore the denominators and only add the numerators.

Use the larger denominator as the new denominator.

Add the denominators directly.

What is the correct formula for subtracting two fractions with different denominators?

$ \frac{a}{b} - \frac{c}{d} = \frac{a - c}{b - d} $

$ \frac{a}{b} - \frac{c}{d} = \frac{a - c}{b + d} $

$ \frac{a}{b} - \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d} $

$ \frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - b \cdot c}{b \cdot d} $ (correct)

Which of the following statements is essential before performing any addition or subtraction with fractions?

<p>The denominators must not be zero.</p> Signup and view all the answers

After performing an operation with fractions, what should you do if the result can be simplified?

<p>Simplify the fraction if possible.</p> Signup and view all the answers

Study Notes

Phân Số

Định nghĩa

Phân số là biểu thức dạng a/b, trong đó a (tử số) và b (mẫu số) là các số nguyên, b khác 0.

Cộng Phân Số

Công thức:
- Cộng hai phân số cùng mẫu:
  ( \frac{a}{b} + \frac{c}{b} = \frac{a+c}{b} )
- Cộng hai phân số khác mẫu:
  ( \frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d} )
Bước thực hiện:
1. Đối với phân số cùng mẫu, cộng tử số.
2. Đối với phân số khác mẫu, tìm mẫu chung (b * d), quy đồng hai phân số, sau đó cộng tử số.

Trừ Phân Số

Công thức:
- Trừ hai phân số cùng mẫu:
  ( \frac{a}{b} - \frac{c}{b} = \frac{a-c}{b} )
- Trừ hai phân số khác mẫu:
  ( \frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - b \cdot c}{b \cdot d} )
Bước thực hiện:
1. Đối với phân số cùng mẫu, trừ tử số.
2. Đối với phân số khác mẫu, tìm mẫu chung (b * d), quy đồng hai phân số, sau đó trừ tử số.

Lưu ý

Khi thực hiện phép cộng và trừ, cần rút gọn phân số kết quả nếu có thể.
Luôn luôn kiểm tra xem mẫu số có khác 0 hay không trước khi thực hiện phép toán.

Definition of Fractions

A fraction is expressed in the form a/b, where a (numerator) and b (denominator) are integers, and b cannot be zero.

Adding Fractions

Formula for Addition:
- For fractions with the same denominator:
  ( \frac{a}{b} + \frac{c}{b} = \frac{a+c}{b} )
- For fractions with different denominators:
  ( \frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d} )
Step-by-Step Process:
- For fractions sharing the same denominator, simply add their numerators.
- For fractions with different denominators, find a common denominator (b * d), rewrite both fractions with this common denominator, then add their numerators.

Subtracting Fractions

Formula for Subtraction:
- For fractions with the same denominator:
  ( \frac{a}{b} - \frac{c}{b} = \frac{a-c}{b} )
- For fractions with different denominators:
  ( \frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - b \cdot c}{b \cdot d} )
Step-by-Step Process:
- For fractions with the same denominator, subtract the numerators.
- For fractions with different denominators, find a common denominator (b * d), rewrite both fractions accordingly, then subtract the numerators.

Important Notes

Always simplify the resulting fraction if possible after addition or subtraction.
Verify that the denominator is not zero before performing any operations.

Description

This quiz covers the basics of fractions, including definitions, addition, and subtraction. You'll learn how to add and subtract fractions with like and unlike denominators. Put your knowledge to the test and see how well you understand the operations with fractions.