Compare mixed numbers and improper fractions

Learning Objectives Convert any mixed number into its equivalent improper fraction. Convert any improper fraction into its equivalent mixed number. Compare two rational numbers, one in mixed number form and one in improper fraction form, by converting them to a common format. Determine the least common denominator (LCD) for two fractions to facilitate comparison. Use inequality symbols (<, >, =) correctly to express the relationship between two mixed numbers or improper fractions. Apply comparison skills to solve contextual word problems involving mixed numbers and improper fractions. Which is a better deal: a plank of wood measuring 4 1/2 feet or one measuring 17/4 feet? 📏 Let's learn the skills to figure it out instantly! This tutorial will refresh your skills...

TermDefinitionExample Mixed NumberA number composed of a whole number and a proper fraction. It represents a value greater than one.3 1/4 (read as 'three and one-fourth') Improper FractionA fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). It represents a value greater than or equal to one.13/4 (read as 'thirteen-fourths') NumeratorThe top number in a fraction, representing how many parts of the whole are being considered.In the fraction 13/4, the numerator is 13. DenominatorThe bottom number in a fraction, representing the total number of equal parts the whole is divided into.In the fraction 13/4, the denominator is 4. Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators...

Converting a Mixed Number to an Improper Fraction a \frac{b}{c} = \frac{(a \times c) + b}{c} To convert, multiply the whole number (a) by the denominator (c), add the numerator (b) to the result, and place this new value over the original denominator (c). Converting an Improper Fraction to a Mixed Number \frac{d}{c} \rightarrow q \frac{r}{c}, \text{ where } d \div c = q \text{ with remainder } r To convert, divide the numerator (d) by the denominator (c). The quotient (q) becomes the whole number, the remainder (r) becomes the new numerator, and the denominator (c) stays the same. Comparing Fractions with a Common Denominator \text{If } c > 0, \text{ then } \frac{a}{c} > \frac{b}{c} \iff a > b When two fractions have the same positive denominator, the fracti...