Subtraction of Fractions

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What is the process of subtracting fractions with like denominators?

Back

To subtract fractions with like denominators, keep the denominator the same and subtract the numerators. For example, \( \frac{a}{c} - \frac{b}{c} = \frac{a-b}{c} \).

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How do you subtract fractions with unlike denominators?

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To subtract fractions with unlike denominators, first find a common denominator, convert each fraction, and then subtract the numerators. For example, \( \frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - c \cdot b}{b \cdot d} \).

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What is a mixed number and how can it be converted to an improper fraction?

Back

A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, \( 3 \frac{2}{5} = \frac{3 \cdot 5 + 2}{5} = \frac{17}{5} \).

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What is the importance of simplifying fractions after subtraction?

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Simplifying fractions after subtraction is important to express the answer in its simplest form, making it easier to understand and use in further calculations.

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How do you handle subtraction when the result is a negative fraction?

Back

If subtracting fractions results in a negative fraction, it indicates that the second fraction is larger than the first. The answer can be expressed as a negative fraction or converted to a mixed number with a negative sign.

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What is the relationship between addition and subtraction of fractions?

Back

Subtraction of fractions can be viewed as adding the negative of a fraction. For example, \( a - b = a + (-b) \). This means that understanding addition helps in understanding subtraction.

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What is the first step in solving a word problem involving the subtraction of fractions?

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The first step is to identify the quantities involved and translate the word problem into a mathematical expression or equation.

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How can you check your answer after subtracting fractions?

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You can check your answer by adding the result to the fraction you subtracted. If the sum equals the original fraction, your subtraction is correct.

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What is a common mistake when subtracting fractions?

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A common mistake is to subtract the denominators instead of keeping them the same when the fractions have like denominators.

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How do you convert a fraction to a decimal?

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To convert a fraction to a decimal, divide the numerator by the denominator. For example, \( \frac{3}{4} = 3 \div 4 = 0.75 \).