Mathematics
Grade 8
15 min
Add 3 or more fractions with like denominators
Add 3 or more fractions with like denominators
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify fractions with like denominators.
State the rule for adding fractions with like denominators.
Accurately add three or more fractions with like denominators.
Simplify sums of fractions to their lowest terms.
Convert improper fraction sums to mixed numbers.
Solve real-world problems involving the addition of multiple fractions with like denominators.
Ever tried to combine ingredients for a super-sized recipe, like adding 🍰 1/4 cup of sugar, 2/4 cup of flour, and 3/4 cup of oats? What if you have several parts of a whole to put together?
In this lesson, you'll master how to add three or more fractions that share the same denominator. This skill is fundamental for understanding rational numbers and solving practical problems involving parts of...
2
Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, expressed as a ratio of two integers.1/2, 3/4, 5/8
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In the fraction 3/5, 3 is the numerator.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In the fraction 3/5, 5 is the denominator.
Like DenominatorsFractions that have the same denominator, meaning they represent parts of a whole divided into the same number of equal pieces.1/7, 3/7, 5/7 are fractions with like denominators.
Improper FractionA fraction where the numerator is greater than or equal to the denominator, representing a value of one or more whole units.7/4, 5/5, 11/3
Mixed NumberA number consisti...
3
Core Formulas
Rule for Adding Fractions with Like Denominators
$\frac{a}{c} + \frac{b}{c} + \frac{d}{c} = \frac{a+b+d}{c}$
To add three or more fractions that have the same denominator, simply add their numerators together and keep the denominator the same. The denominator represents the size of the parts, which does not change when you combine them.
Simplifying Fractions
$\frac{N}{D} = \frac{N \div \text{GCF}(N,D)}{D \div \text{GCF}(N,D)}$
After adding fractions, always check if the resulting fraction can be simplified. To simplify, divide both the numerator and the denominator by their greatest common factor (GCF). This expresses the fraction in its lowest terms.
Converting Improper Fractions to Mixed Numbers
$\frac{N}{D} = Q \frac{R}{D}$ where $Q$ is the quotient and $R$ is the r...
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Find the value of the missing numerator, N: $\frac{3}{11} + \frac{N}{11} + \frac{5}{11} = 1 \frac{1}{11}$
A.1
B.4
C.12
D.3
Challenging
A gas tank was full at the beginning of a trip. The first leg of the trip used $\frac{3}{16}$ of the tank, the second leg used $\frac{5}{16}$, and the third leg used $\frac{7}{16}$. What fraction of the gas remains in the tank?
A.$\frac{15}{16}$
B.$\frac{15}{48}$
C.$\frac{1}{4}$
D.$\frac{1}{16}$
Challenging
A student claims that the sum of any three proper fractions with the same odd denominator will always result in a proper fraction. Evaluate the sum $\frac{4}{7} + \frac{5}{7} + \frac{2}{7}$ to determine if this claim is true or false.
A.False, because the sum is $1 \frac{4}{7}$, which is a mixed number.
B.True, because the sum is $\frac{11}{21}$, which is a proper fraction.
C.True, because the sum is $\frac{11}{7}$, and the numerator is odd.
D.False, because the denominator is odd, the sum must be odd.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free