Mathematics
Grade 8
15 min
Subtract fractions with like denominators using number lines
Subtract fractions with like denominators using number lines
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1
Introduction & Learning Objectives
Learning Objectives
Define and identify fractions with like denominators.
Accurately represent fractions on a number line.
Model the subtraction of fractions with like denominators using a number line.
Calculate the difference between two fractions with like denominators.
Simplify fractional answers to their lowest terms.
Explain the steps involved in subtracting fractions using a number line.
Ever wonder how much pizza is left after your friends eat some slices? 🍕 Understanding how to subtract fractions helps us figure out exactly that!
In this lesson, we'll explore how to subtract fractions that share the same denominator. We'll use number lines as a visual tool to make this process clear and intuitive, building a strong foundation for working with rational num...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, expressed as a ratio of two integers, a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{5}{8}$, the numerator is 5, meaning we have 5 out of 8 equal parts.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts that make up the whole.In $\frac{2}{3}$, the denominator is 3, meaning the whole is divided into 3 equal parts.
Like DenominatorsFractions that have the same denominator, meaning they refer to parts of a whole that are divided into the same number of equal pieces.$\frac{1}{5}$ and $\frac{3}{5}$ have like denominators...
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Core Formulas
Rule for Subtracting Fractions with Like Denominators
$\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$
When subtracting fractions with the same denominator, subtract only the numerators and keep the denominator the same. The result should then be simplified if possible.
Representing Fractions on a Number Line
To represent $\frac{a}{c}$ on a number line, divide the segment from 0 to 1 into $c$ equal parts. The fraction $\frac{a}{c}$ is located at the $a$-th mark from 0.
This rule helps visualize the magnitude of a fraction and sets up the starting point for subtraction.
Subtracting on a Number Line
To subtract $\frac{b}{c}$ from $\frac{a}{c}$ on a number line, start at the position of $\frac{a}{c}$ and move $b$ units to the left, where each unit represents $\frac{1}{c}$....
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
A point is at $\frac{13}{14}$ on a number line. First, you move 5 units (of $\frac{1}{14}$) to the left. From that new point, you move another 4 units to the left. What is the final position, in simplest form?
A.$\frac{4}{14}$
B.$\frac{2}{7}$
C.$\frac{9}{14}$
D.$\frac{1}{2}$
Challenging
If $\frac{a}{c} - \frac{b}{c} = \frac{d}{c}$ where a, b, c, d are positive integers, which statement accurately describes the relationship between the points $\frac{a}{c}$ and $\frac{d}{c}$ on a number line?
A.The point $\frac{d}{c}$ is located 'b' units of size $\frac{1}{c}$ to the left of $\frac{a}{c}$.
B.The point $\frac{a}{c}$ is located 'd' units of size $\frac{1}{c}$ to the left of $\frac{b}{c}$.
C.The distance between 0 and $\frac{d}{c}$ is greater than the distance between 0 and $\frac{a}{c}$.
D.The points $\frac{a}{c}$ and $\frac{d}{c}$ are in the same location.
Challenging
A student attempts to solve $\frac{11}{10} - \frac{7}{10}$. They start at $\frac{11}{10}$ and move 7 units to the right, ending at $\frac{18}{10}$. They simplify this to $\frac{9}{5}$. Which two common pitfalls did this student fall into?
A.Subtracting denominators and miscounting segments.
B.Forgetting to simplify and subtracting denominators.
C.Miscounting segments and moving in the incorrect direction.
D.Moving in the incorrect direction and forgetting to simplify (for the correct answer).
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