A mixed number is a representation of a quantity that combines a whole number and a proper fraction. It is a way to express a number that is not a whole number, but also not a simple fraction.
congrats on reading the definition of Mixed Number. now let's actually learn it.
A mixed number can be converted to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and then dividing by the denominator.
Mixed numbers can be added, subtracted, multiplied, and divided, just like whole numbers and fractions.
When adding or subtracting mixed numbers, you must first convert them to either all whole numbers or all fractions.
Multiplying a mixed number by a whole number or another mixed number can be done by multiplying the whole number parts and the fraction parts separately, then combining the results.
Dividing a mixed number by a whole number or another mixed number can be done by converting the mixed numbers to improper fractions and then dividing the numerators and multiplying the denominators.
Review Questions
Explain how to convert a mixed number to an improper fraction.
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction, then add the numerator, and finally divide the result by the denominator. For example, to convert the mixed number $2\frac{3}{4}$ to an improper fraction, you would multiply the whole number 2 by the denominator 4, giving you 8. Then, you would add the numerator 3, giving you 11. Finally, you would divide 11 by the denominator 4, resulting in the improper fraction $\frac{11}{4}$.
Describe the process of adding or subtracting mixed numbers.
When adding or subtracting mixed numbers, you must first convert them to either all whole numbers or all fractions. To add mixed numbers, you would add the whole number parts and the fraction parts separately, then combine the results. For example, to add $3\frac{1}{2}$ and $2\frac{3}{4}$, you would first convert them to improper fractions ($\frac{7}{2}$ and $\frac{11}{4}$, respectively), then add the numerators (7 + 11 = 18) and keep the same denominator (4), resulting in the mixed number $4\frac{2}{4}$ or $4\frac{1}{2}$. The process for subtraction is similar, but you would subtract the numerators instead of adding them.
Analyze the steps involved in multiplying and dividing mixed numbers.
To multiply mixed numbers, you can convert them to improper fractions and then multiply the numerators and the denominators separately. For example, to multiply $2\frac{3}{4}$ by $3\frac{1}{2}$, you would first convert them to improper fractions ($\frac{11}{4}$ and $\frac{7}{2}$, respectively), then multiply the numerators (11 x 7 = 77) and the denominators (4 x 2 = 8), resulting in the mixed number $9\frac{5}{8}$. To divide mixed numbers, you would convert them to improper fractions, divide the numerators, and multiply the denominators. This process allows you to work with the whole number and fraction parts separately to arrive at the final result.
Related terms
Whole Number: A whole number is a positive integer, such as 1, 2, 3, or a negative integer, such as -1, -2, -3.
Proper Fraction: A proper fraction is a fraction where the numerator is less than the denominator, such as $\frac{1}{2}$ or $\frac{3}{4}$.