Mathematics
Grade 8
15 min
Add and subtract fractions with like denominators using number lines
Add and subtract fractions with like denominators using number lines
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1
Introduction & Learning Objectives
Learning Objectives
Identify and locate fractions with like denominators on a number line.
Model the addition of fractions with like denominators using forward movement on a number line.
Model the subtraction of fractions with like denominators using backward movement on a number line.
Accurately solve addition problems involving fractions with like denominators by interpreting number line movements.
Accurately solve subtraction problems involving fractions with like denominators by interpreting number line movements.
Interpret the final position on a number line as the sum or difference of fractions.
Simplify fraction answers obtained from number line operations.
Ever wondered how to visually combine or take away parts of a whole, like sharing a pizza or measuring ingredi...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, expressed as a ratio of two integers, where the numerator is divided by the 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 or taken.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 into which the whole has been divided.In $\frac{5}{8}$, the denominator is 8, meaning the whole is divided into 8 equal parts.
Like DenominatorsFractions that have the same denominator, meaning they represent parts of a whole divided into the same number of equal pieces.$\frac{1}{6}$ and $\...
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Core Formulas
Rule for 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. On a number line, this means starting at the first fraction and moving forward (to the right) by the amount of the second fraction.
Rule for 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. On a number line, this means starting at the first fraction and moving backward (to the left) by the amount of the second fraction.
Representing Fractions on a Number Line
Divide the segment between two whole numbers (e.g., 0 and 1) into 'c'...
5 more steps in this tutorial
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Challenging
A point on a number line is at 13/9. An operation is performed, and the point ends up at 5/9. A second, identical operation is performed from the new position. Where is the final position?
A.1/9
B.-3/9
C.21/9
D.8/9
Challenging
A robot starts at 1/10 meters on a track. It moves forward 7/10 meters, then backward 4/10 meters, then forward 3/10 meters, then backward 8/10 meters. Which number line model correctly shows the robot's final position relative to its starting point?
A.The robot ends at the origin (0).
B.The robot ends at 1/10, its starting point.
C.The robot ends at -1/10 meters.
D.The robot ends at 23/10 meters.
Challenging
A number line is scaled in sevenths. An arrow starts at Point A, moves to the right a distance of 6/7, and ends at Point B, which is 4/7. What is the equation that correctly identifies Point A?
A.4/7 + 6/7 = A
B.- 6/7 = 4/7
C.4/7 - 6/7 = A
D.6/7 - 4/7 = A
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