Mixed Numbers and Their Conversions

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a proper fraction, such as 2 \frac{1}{2}.

Front

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

Back

Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}.

Front

What is the process to convert an improper fraction to a mixed number?

Back

Divide the numerator by the denominator. The quotient is the whole number, and the remainder over the original denominator is the fraction. For example, \frac{9}{4} = 2 \frac{1}{4}.

Front

How do you add mixed numbers?

Back

Convert to improper fractions, add them, and convert back to a mixed number if necessary. For example, 1 \frac{1}{2} + 2 \frac{2}{3} = \frac{3}{2} + \frac{8}{3} = \frac{17}{6} = 2 \frac{5}{6}.

Front

How do you subtract mixed numbers?

Back

Convert to improper fractions, subtract them, and convert back to a mixed number if necessary. For example, 3 \frac{1}{4} - 1 \frac{2}{3} = \frac{13}{4} - \frac{5}{3} = \frac{7}{12}.

Front

What is the rule for multiplying mixed numbers?

Back

Convert both mixed numbers to improper fractions, multiply the fractions, and simplify if necessary. For example, 1 \frac{1}{2} \times 2 \frac{1}{3} = \frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = 3 \frac{1}{2}.

Front

What is the rule for dividing mixed numbers?

Back

Convert both mixed numbers to improper fractions, multiply by the reciprocal of the second fraction, and simplify if necessary. For example, 2 \frac{1}{2} \div 1 \frac{1}{4} = \frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5} = 2.

Front

What is the importance of finding a common denominator when adding or subtracting fractions?

Back

A common denominator allows you to combine fractions easily. Without it, you cannot directly add or subtract the fractions.

Front

How do you simplify a fraction?

Back

Divide the numerator and the denominator by their greatest common divisor (GCD). For example, \frac{8}{12} simplifies to \frac{2}{3}.

Front

What is the greatest common divisor (GCD)?

Back

The GCD is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 8 and 12 is 4.