Mathematics
Grade 5
15 min
Add 3 or more fractions with unlike denominators
Add 3 or more fractions with unlike denominators
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1
Introduction & Learning Objectives
Learning Objectives
Identify fractions with unlike denominators.
Determine the Least Common Denominator (LCD) for three or more fractions.
Convert fractions into equivalent fractions with a common denominator.
Add three or more fractions once they have a common denominator.
Simplify the sum of fractions to its simplest form.
Solve real-world problems involving the addition of three or more fractions with unlike denominators.
Ever tried to combine ingredients for a super-duper cake, like 1/2 cup flour, 1/3 cup sugar, and 1/4 cup cocoa, and wondered how much total dry ingredients you have? 🍰
In this lesson, you'll learn a super useful skill: how to add three or more fractions that have different bottom numbers (denominators). This skill helps you combine different parts...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, written as a numerator over a denominator.The fraction `\frac{3}{4}` means 3 out of 4 equal parts.
NumeratorThe top number in a fraction, showing how many parts are being considered.In `\frac{3}{4}`, 3 is the numerator.
DenominatorThe bottom number in a fraction, showing the total number of equal parts the whole is divided into.In `\frac{3}{4}`, 4 is the denominator.
Unlike DenominatorsFractions that have different bottom numbers.`\frac{1}{2}`, `\frac{1}{3}`, and `\frac{1}{4}` have unlike denominators.
Least Common Denominator (LCD)The smallest common multiple of the denominators of two or more fractions.For `\frac{1}{2}`, `\frac{1}{3}`, and `\frac{1}{4}`, the LCD is 12.
Equivalent FractionsFractions that look differen...
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Core Formulas
Finding the Least Common Denominator (LCD)
To find the LCD of two or more fractions, list the multiples of each denominator until you find the smallest multiple that all denominators share.
This rule helps you find the smallest common bottom number so you can add fractions with unlike denominators.
Creating Equivalent Fractions
To change a fraction `\frac{a}{b}` to an equivalent fraction with a new denominator `c`, multiply both the numerator `a` and the denominator `b` by the same number `k` such that `b \times k = c`. The new fraction is `\frac{a \times k}{b \times k}`.
This rule allows you to rewrite fractions so they all have the same denominator (the LCD) without changing their value.
Adding Fractions with Common Denominators
To add fractions with the same denomin...
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
A project requires three pieces of wood measuring `1/2` foot, `2/3` foot, and `1/4` foot. If these pieces are cut from a board that is 2 feet long, what fraction of a foot is left over?
A.1 5/12
B.17/12
C.5/12
D.7/12
Challenging
To solve `1/6 + 3/8 + 1/4`, which of the following is the most efficient Least Common Denominator (LCD) to use?
A.48
B.24
C.192
D.72
Challenging
In a school garden, `1/5` of the plots are used for tomatoes, `1/4` for cucumbers, and `1/6` for peppers. The rest of the plots are for flowers. What fraction of the garden is used for flowers?
A.37/60
B.1/3
C.23/60
D.1/2
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