Mathematics
Grade 10
15 min
Add and subtract fractions with like denominators: word problems
Add and subtract fractions with like denominators: word problems
What you'll learn
- Solve word problems involving addition of fractions with like denominators and express the answer in simplest form in at least 8 out of 10 problems.
- Solve word problems involving subtraction of fractions with like denominators and express the answer in simplest form in at least 8 out of 10 problems.
- Identify the operation (addition or subtraction) needed to solve a word problem involving fractions with like denominators with 100% accuracy.
- Explain the steps taken to solve a word problem involving addition or subtraction of fractions with like denominators, using mathematical vocabulary, in at least 2 out of 3 problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate word problems involving congruent figures into mathematical expressions with fractions.
Apply the rules of adding and subtracting fractions with like denominators to solve for unknown lengths or angle measures.
Use the properties of congruent figures to establish a 'whole' or common unit for fractional parts.
Construct a logical argument or justification for a solution that involves fractional quantities in a geometric context.
Simplify fractional answers and relate them back to the original geometric problem.
Analyze and deconstruct multi-step geometry problems where fractional parts of congruent segments or angles are combined or compared.
If two identical puzzle pieces are each missing a fraction of their area, how can you calculate...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresFigures that have the exact same size and shape. All corresponding sides and corresponding angles are equal in measure.If triangle ABC is congruent to triangle XYZ (written as ΔABC ≅ ΔXYZ), then segment AB = segment XY, angle B = angle Y, and so on for all corresponding parts.
Corresponding PartsThe sides and angles that are in the same relative position on two congruent figures. The properties of congruence guarantee these parts are equal.In ΔABC ≅ ΔXYZ, angle A corresponds to angle X, and side BC corresponds to side YZ. Their measures are identical.
Like DenominatorsThe bottom number (denominator) of two or more fractions is the same. This indicates that the 'whole' has been divided into the same number of equal parts.The fractions 3/11 a...
3
Core Formulas
Addition of Fractions with Like Denominators
\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}
To add fractions that have the same denominator, add the numerators together and place the sum over the common denominator. This is used when combining fractional parts of the same whole, such as joining two adjacent segments of a line.
Subtraction of Fractions with Like Denominators
\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}
To subtract fractions that have the same denominator, subtract the second numerator from the first and place the difference over the common denominator. This is used to find the difference between two fractional parts or to find a remaining fractional part.
4 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
Two congruent regular pentagons, PENTA ≅ GRMTH, have a side length of S. A path starts at P, travels along PE, then EN, and stops at a point X on NT such that NX is 3/11 of S. A second path starts at G, travels along GR, RM, MT, and stops at a point Y on TH such that TY is 5/11 of S. What is the difference between the length of segment XT and the length of segment YH, expressed as a fraction of S?
A.2/11
B.8/11
C.3/11
D.6/11
Challenging
Given two congruent segments AB ≅ CD of length L. Let x and y be positive integers where x+y < z. A point P on AB is located such that AP = x/z of L. A point Q on CD is located such that CQ = y/z of L. Which expression represents the length of segment PB minus the length of segment DQ, as a fraction of L?
A.(z - x - y) / z
B.(x - y) / z
C.(z - x + y) / z
D.(y - x) / z
Challenging
Two congruent squares, S1 and S2, have side length L. S1 is partitioned into 17 vertical strips of equal area. S2 is partitioned into 17 horizontal strips of equal area. If you take 5 vertical strips from S1 and add them to 9 horizontal strips from S2, what is the fundamental reason, based on the tutorial, that the resulting total area can be calculated as 14/17 of the area of one square?
A.Because the strips are all congruent rectangles.
B.Because the 'whole' (the area of a square) is the same for both fractions, as S1 ≅ S2.
C.Because the numerators (5 and 9) are less than the denominator (17).
D.Because adding vertical and horizontal strips always results in a valid sum.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Introduction to congruent figures
Mathematics for other grades
Frequently asked questions
What grade level is "Add and subtract fractions with like denominators: word problems"?
Add and subtract fractions with like denominators: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract fractions with like denominators: word problems?
You'll be able to: Solve word problems involving addition of fractions with like denominators and express the answer in simplest form in at least 8 out of 10 problems; Solve word problems involving subtraction of fractions with like denominators….
Is "Add and subtract fractions with like denominators: word problems" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Add and subtract fractions with like denominators: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.