Mathematics
Grade 6
15 min
Add and subtract fractions with like denominators
Add and subtract fractions with like denominators
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1
Introduction & Learning Objectives
Learning Objectives
Identify fractions with like denominators.
Add two or more fractions with like denominators.
Subtract one fraction from another with like denominators.
Simplify sums and differences of fractions to their simplest form.
Convert improper fractions to mixed numbers when adding or subtracting.
Solve word problems involving addition and subtraction of fractions with like denominators.
Ever shared a pizza 🍕 or a cake 🎂? What if you ate 2 slices and your friend ate 3 slices from a pizza cut into 8 equal pieces? How much did you eat together?
In this lesson, you'll learn how to combine and take away parts of a whole when those parts are the same size. This skill is super important for understanding how quantities relate to each other in everyday life and...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing part of a whole, written as a numerator over a denominator.$ rac{3}{4}$ means 3 out of 4 equal parts.
NumeratorThe top number in a fraction, indicating how many parts are being considered.In $ rac{3}{4}$, 3 is the numerator.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts in the whole.In $ rac{3}{4}$, 4 is the denominator.
Like DenominatorsFractions that have the same denominator.$ rac{1}{5}$ and $ rac{3}{5}$ have like denominators.
Simplest Form (or Reduced Form)A fraction where the numerator and denominator have no common factors other than 1.$ rac{2}{4}$ simplifies to $ rac{1}{2}$.
Improper FractionA fraction where the numerator is greater than or equal to the denominator.$ rac{7}{4}$ is an impro...
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Core Formulas
Adding Fractions with Like Denominators
$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$
To add fractions with the same denominator, add the numerators and keep the denominator the same.
Subtracting Fractions with Like Denominators
$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$
To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same.
Simplifying Fractions
$\frac{a}{b} = \frac{a \div \text{GCF}(a,b)}{b \div \text{GCF}(a,b)}$
To simplify a fraction, divide both the numerator and the denominator by their Greatest Common Factor (GCF).
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Challenging
A student was asked to compute 5/12 + 9/12 and simplify. Their work was: Step 1: 5/12 + 9/12 = 14/12. Step 2: 14/12 = 1 2/12. Step 3: 1 2/12 = 1 1/6. Another student said there was an error. In which step was the first error made?
A.Step 1
B.Step 2
C.Step 3
D.There is no error.
Challenging
After a party, 3/8 of a cake is left. The next day, you eat some cake, and then there is only 1/8 of the original cake remaining. What fraction of the *original* cake did you eat the next day?
A.4/8
B.2/16
C.1/4
D.1/8
Challenging
Three friends are painting a fence. Alex paints 3/14 of the fence. Ben paints 5/14 of the fence. What fraction must their friend Carla paint to finish the fence exactly?
A.8/14
B.6/14
C.3/7
D.8/28
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