Convert between improper fractions and mixed numbers

Learning Objectives Identify improper fractions and mixed numbers. Convert any improper fraction into an equivalent mixed number. Convert any mixed number into an equivalent improper fraction. Explain the relationship between division and converting improper fractions to mixed numbers. Represent improper fractions and mixed numbers visually. Solve simple word problems involving conversions between improper fractions and mixed numbers. Have you ever ordered a pizza and ended up with more than a whole pizza, like one and a half pizzas? 🍕 Or maybe you've shared cookies and had 7 halves of cookies left over? 🤔 In this lesson, you'll learn how to switch between two different ways of writing fractions: improper fractions and mixed numbers. Understanding these conversi...

TermDefinitionExample FractionA number that represents a part of a whole or a part of a collection. It is written as a numerator over a denominator.1/2 (one half of a pizza) NumeratorThe top number in a fraction, which tells you how many parts you have.In 3/4, the numerator is 3, meaning you have 3 parts. DenominatorThe bottom number in a fraction, which tells you how many equal parts the whole is divided into.In 3/4, the denominator is 4, meaning the whole is divided into 4 equal parts. Proper FractionA fraction where the numerator is smaller than the denominator, representing a value less than one whole.2/3, 5/8, 1/4 Improper FractionA fraction where the numerator is equal to or larger than the denominator, representing a value equal to or greater than one whole.7/4, 5/5, 10/3 Mixed Num...

Converting Improper Fractions to Mixed Numbers $$\text{Whole Number} = \text{Numerator} \div \text{Denominator}$$ $$\text{Remainder} = \text{Numerator} \pmod{\text{Denominator}}$$ $$\text{Mixed Number} = \text{Whole Number} \frac{\text{Remainder}}{\text{Denominator}}$$ To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient (the answer to the division) becomes the whole number part. The remainder becomes the new numerator, and the denominator stays the same. Converting Mixed Numbers to Improper Fractions $$\text{Improper Numerator} = (\text{Whole Number} \times \text{Denominator}) + \text{Numerator of fraction part}$$ $$\text{Improper Denominator} = \text{Denominator of fraction part}$$ To convert a mixed number to an improper...