Mathematics
Grade 10
15 min
Add and subtract fractions with unlike denominators: word problems
Add and subtract fractions with unlike denominators: word problems
What you'll learn
- Identify the fractions with unlike denominators in a word problem and rewrite them with a common denominator with 80% accuracy.
- Solve word problems involving addition and subtraction of fractions with unlike denominators, showing all steps, and arriving at the correct answer in at least 3 out of 4 problems.
- Explain the steps taken to solve a word problem involving adding or subtracting fractions with unlike denominators, using mathematical vocabulary, in a written response of at least 3 sentences.
- Apply the skill of adding and subtracting fractions with unlike denominators to create their own word problem, which can be solved by a classmate, with all necessary information provided.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate geometric word problems involving congruent figures into mathematical expressions with fractions.
Identify corresponding parts of congruent figures to correctly set up fraction addition and subtraction problems.
Calculate the least common denominator (LCD) for fractions derived from geometric measurements.
Accurately add and subtract fractions with unlike denominators to determine unknown lengths and perimeters in geometric figures.
Formulate a concluding statement that correctly interprets the fractional answer in the context of the original geometric word problem.
Verify solutions by applying the properties of congruent figures, such as the equality of corresponding side lengths.
If two congruent, triangular steel plates must fit together perf...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresGeometric figures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.If triangle ABC is congruent to triangle DEF (written as ΔABC ≅ ΔDEF), then side AB = DE, side BC = EF, side AC = DF, and ∠A = ∠D, ∠B = ∠E, ∠C = ∠F.
Corresponding PartsThe sides or angles of congruent figures that are in the same relative position. The principle 'Corresponding Parts of Congruent Triangles are Congruent' (CPCTC) is a key tool in proofs.In the statement QUAD ≅ REXS, the corresponding vertices are Q→R, U→E, A→X, D→S. Therefore, the corresponding side to QU is RE.
Unlike DenominatorsThe bottom numbers (denominators) of two or more fractions that are not the same value, indicating the wholes are divided into a di...
3
Core Formulas
Addition of Fractions with Unlike Denominators
\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
To add fractions with different denominators, find a common denominator (ideally the LCD), convert each fraction to an equivalent fraction with that denominator, and then add the numerators.
Subtraction of Fractions with Unlike Denominators
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
To subtract fractions with different denominators, find a common denominator, convert each fraction to an equivalent fraction, and then subtract the numerators.
Property of Congruence
If Figure A ≅ Figure B, then any side length in Figure A is equal to its corresponding side length in Figure B.
This geometric rule allows you to set up an equation. If you can calculate a length on one figure,...
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Sign Up Free to ContinueSample Practice Questions
Easy
Given the congruence statement ΔPQR ≅ ΔSTU, if the length of side PQ is 1/3 meters and the length of side QR is 1/4 meters, what is the sum of the lengths of the corresponding sides ST and TU?
A.2/7 meters
B.1/12 meters
C.7/12 meters
D.1/7 meters
Easy
Quadrilateral ABCD ≅ Quadrilateral WXYZ. The length of side AB is 7/8 inches and the length of side BC is 2/3 inches. What is the difference in length between side WX and side XY?
A.5/5 inches
B.5/24 inches
C.1/2 inches
D.37/24 inches
Easy
Given the congruence statement ΔCAT ≅ ΔDOG, and the length of side AT is 3/5 units. Which side in ΔDOG must also have a length of 3/5 units?
A.DO
B.OG
C.OD
D.DG
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Frequently asked questions
What grade level is "Add and subtract fractions with unlike denominators: word problems"?
Add and subtract fractions with unlike denominators: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract fractions with unlike denominators: word problems?
You'll be able to: Identify the fractions with unlike denominators in a word problem and rewrite them with a common denominator with 80% accuracy; Solve word problems involving addition and subtraction of fractions with unlike denominators….
Is "Add and subtract fractions with unlike denominators: word problems" free to practice?
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How many practice questions are included with Add and subtract fractions with unlike denominators: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.