Mathematics
Grade 9
15 min
Add and subtract fractions with like denominators using number lines
Add and subtract fractions with like denominators using number lines
What you'll learn
- Identify congruent polygons by analyzing corresponding sides and angles and verifying their equality using geometric reasoning and measurement tools with 80% accuracy.
- Apply the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS) congruence postulates to prove the congruence of triangles in geometric diagrams and written proofs, demonstrating understanding in at least 3 out of 4 attempts.
- Explain the relationship between congruence and rigid transformations (translations, rotations, reflections) by describing how these transformations preserve size and shape, justifying their explanations with specific examples in a written response assessed using a rubric with a score of 3 or higher out of 4.
- Differentiate between congruent and similar figures, justifying their reasoning by comparing corresponding side lengths and angle measures, achieving a score of at least 75% on a formative assessment.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Accurately represent fractions with like denominators as points on a number line.
Model the addition of two fractions with like denominators as a movement on a number line.
Model the subtraction of two fractions with like denominators as a movement on a number line.
Determine the sum or difference of fractions with like denominators by interpreting the final position on a number line.
Explain why the denominator remains unchanged during addition and subtraction using the number line model.
Simplify the resulting fraction after performing addition or subtraction on the number line.
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Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberAny number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. All fractions are rational numbers.5/9, -2/3, and 7 (which is 7/1) are all rational numbers.
Like DenominatorsTwo or more fractions that have the exact same integer in their denominator (the bottom number).The fractions 3/8 and 5/8 have like denominators because both have a denominator of 8.
NumeratorThe top number in a fraction. It represents how many parts of the whole you have.In the fraction 7/10, the numerator is 7.
DenominatorThe bottom number in a fraction. It represents the total number of equal parts the whole has been divided into.In the fraction 7/10, the denominator is 10.
Unit FractionA fraction where the numerator is 1. It represents a single...
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Core Formulas
Addition Rule for Like Denominators
\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}
To add fractions with the same denominator, add the numerators together and place the sum over the common denominator. On a number line, this is represented by starting at the first fraction and moving to the right by the amount of the second fraction.
Subtraction Rule for Like Denominators
\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}
To subtract fractions with the same denominator, subtract the second numerator from the first and place the difference over the common denominator. On a number line, this is represented by starting at the first fraction and moving to the left by the amount of the second fraction.
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Challenging
A number line is divided into 'n' equal segments between 0 and 1. An operation is described as starting at point x/n and moving y units to the right. Which expression represents the final position?
A.(x+y)/2n
B.(x-y)/n
C.(x+y)/n
D.xy/n
Challenging
A process is described: 'Start at an unknown fraction. Add 5/12. Then subtract 9/12.' The final position on the number line is 2/12. What was the starting fraction?
A.6/12
B.-2/12
C.16/12
D.4/12
Challenging
A baker has a bag of flour that is 7/8 full. She uses 2/8 of the bag for a cake, and then another 3/8 of the bag for bread. Which number line operation correctly finds the fraction of the flour remaining in the bag?
A.Start at 7/8, move 2 units right, then 3 units right.
B.Start at 7/8, move 2 units left, then 3 units left.
C.Start at 1, move 7/8 units left, then 2/8 units right.
D.Start at 7/8, move 2 units left, then 3 units right.
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Add and subtract fractions with like denominators using number lines is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract fractions with like denominators using number lines?
You'll be able to: Identify congruent polygons by analyzing corresponding sides and angles and verifying their equality using geometric reasoning and measurement tools with 80% accuracy; Apply the Side-Side-Side (SSS), Side-Angle-Side (SAS)….
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This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.