Mathematics
Grade 4
15 min
Convert between improper fractions and mixed numbers
Convert between improper fractions and mixed numbers
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define and identify an improper fraction.
Define and identify a mixed number.
Convert an improper fraction to a mixed number using division.
Convert a mixed number to an improper fraction using multiplication and addition.
Visually represent improper fractions and mixed numbers using models.
Explain why an improper fraction and its equivalent mixed number represent the same value.
Imagine you have 9 quarter-pieces of an apple. How many whole apples do you actually have? 🍎
In this lesson, you will learn how to switch between two ways of writing fractions that are greater than one: improper fractions and mixed numbers. Mastering this skill is a key step that will help you add and subtract all kinds of fractions later on.
Real-World Applications
Baking...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It has a numerator (top number) and a denominator (bottom number).1/4 means 1 part out of 4 equal parts.
NumeratorThe top number in a fraction. It tells you how many parts you have.In the fraction 5/8, the numerator is 5.
DenominatorThe bottom number in a fraction. It tells you how many equal parts make up one whole.In the fraction 5/8, the denominator is 8.
Proper FractionA fraction where the numerator is smaller than the denominator. A proper fraction is always less than one whole.3/5 is a proper fraction because 3 is less than 5.
Improper FractionA fraction where the numerator is greater than or equal to the denominator. An improper fraction is equal to or greater than one whole.9/4 is an improper fraction becaus...
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Core Formulas
Converting an Improper Fraction to a Mixed Number
Whole Number = Numerator \div Denominator (the quotient)
New Numerator = The Remainder
To change an improper fraction into a mixed number, you divide the numerator by the denominator. The result of the division (the quotient) is your whole number. The leftover number (the remainder) becomes the new numerator. The denominator stays the same.
Converting a Mixed Number to an Improper Fraction
New Numerator = (Whole Number \times Denominator) + Numerator
To change a mixed number into an improper fraction, you first multiply the whole number by the denominator. Then, you add the original numerator to your result. This new number is the numerator of your improper fraction, and the denominator stays the same.
4 more steps in this tutorial
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Challenging
The mixed number ? 3/4 is equal to the improper fraction 19/4. What is the missing whole number?
A.4
B.3
C.5
D.6
Challenging
The improper fraction ?/5 is equal to the mixed number 6 2/5. What is the missing numerator?
A.13
B.28
C.30
D.32
Challenging
Why does the improper fraction 7/3 represent the same amount as the mixed number 2 1/3?
A.Because 7 minus 3 is 4, and 4 divided by 2 is 2.
B.Because you can make two wholes (which is 6/3) from 7/3, and you have 1/3 left over.
C.Because 7 and 3 are odd numbers, and so are 2 and 1.
D.Because the rule says to divide 7 by 3, and the answer is 2.
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