multiply and divide rational numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the denominator (q ≠ 0).

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How do you multiply two rational numbers?

Back

To multiply two rational numbers, multiply their numerators together and their denominators together. For example, (a/b) * (c/d) = (a*c)/(b*d).

Front

What is the process for dividing rational numbers?

Back

To divide two rational numbers, multiply the first rational number by the reciprocal of the second. For example, (a/b) ÷ (c/d) = (a/b) * (d/c) = (a*d)/(b*c).

Front

What does it mean to simplify a fraction?

Back

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

Front

What is the reciprocal of a rational number?

Back

The reciprocal of a rational number a/b is b/a, provided that a and b are not zero.

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How do you convert a mixed number to an improper fraction?

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To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 2 1/3 = (2*3 + 1)/3 = 7/3.

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What is the least common denominator (LCD)?

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The least common denominator is the smallest multiple that is common to the denominators of two or more fractions, used to add or subtract fractions.

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How do you add or subtract rational numbers with different denominators?

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To add or subtract rational numbers with different denominators, first find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD, and then add or subtract the numerators.

Front

What is the importance of signs when multiplying or dividing rational numbers?

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The sign of the product or quotient of two rational numbers depends on the signs of the numbers: a positive times a positive is positive, a negative times a negative is positive, and a positive times a negative is negative.

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What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both contain fractions. It can be simplified by finding a common denominator.