Mathematics
Grade 10
15 min
Complete addition and subtraction sentences with fractions
Complete addition and subtraction sentences with fractions
What you'll learn
- Solve addition and subtraction problems involving fractions with unlike denominators by finding a common denominator and simplifying the answer.
- Identify missing numerators or denominators in addition and subtraction sentences with fractions to make the equation true.
- Explain the steps used to add or subtract fractions with unlike denominators to a partner, using mathematical vocabulary like 'common denominator' and 'equivalent fraction'.
- Apply knowledge of equivalent fractions to rewrite fractions with different denominators to have a common denominator.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Use the definition of congruent segments to set up addition and subtraction sentences with fractions.
Solve for an unknown fractional length in a geometric figure by completing a number sentence.
Apply the Segment Addition Postulate to verify segment lengths by completing fractional addition sentences.
Determine the length of a sub-segment by completing a fractional subtraction sentence.
Justify steps in a geometric problem using properties of congruence and the rules of fraction arithmetic.
Apply the principle 'Corresponding Parts of Congruent Triangles are Congruent' (CPCTC) to solve problems involving fractional side lengths.
How can an architect ensure two decorative beams are perfectly identical if one beam's length is defined by the s...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent SegmentsTwo or more line segments that have the exact same length. If segment AB is congruent to segment CD, we write \(\overline{AB} \cong \overline{CD}\), which implies their measures are equal (AB = CD).If \(\overline{AB} \cong \overline{CD}\) and the length of AB is \(\frac{3}{4}\) inches, then the length of CD must also be \(\frac{3}{4}\) inches.
Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and C, then the length of segment AB plus the length of segment BC is equal to the length of the entire segment AC.If AB = \(\frac{1}{2}\) cm and BC = \(\frac{1}{3}\) cm, then the total length AC = \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\) cm.
Corresponding PartsIn congruent figures, the sides and angles that are in the sa...
3
Core Formulas
Segment Addition Postulate
If B is between A and C, then \(AB + BC = AC\)
Use this postulate to set up an addition sentence when you have smaller, adjacent segments that form a larger segment. This is the foundation for combining fractional lengths.
Definition of Congruence
If \(\overline{AB} \cong \overline{CD}\), then \(AB = CD\)
Use this definition to equate the measures of two segments. If one length is a known fraction and the other is an expression, this allows you to create an equation to solve.
Subtraction Property of Equality (for Segments)
If \(AB + BC = AC\), then \(AC - AB = BC\)
Use this property to create a subtraction sentence when you know the total length of a segment and one of its parts, and you need to find the other part.
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
If it is given that \(\overline{XY} \cong \overline{MN}\) and the length of XY is \(\frac{5}{8}\) inches, what is the length of MN?
A.It cannot be determined.
B.\(\frac{8}{5}\) inches
C.\(\frac{5}{8}\) inches
D.\(\frac{10}{16}\) inches
Easy
On a line segment \(\overline{DF}\), point E is between D and F. If DF = \(\frac{7}{10}\) and DE = \(\frac{1}{5}\), which subtraction sentence must be completed to find the length of EF?
A.\(\frac{7}{10} - \frac{1}{5} = ?\)
B.\(\frac{1}{5} - \frac{7}{10} = ?\)
C.\(\frac{7}{10} + \frac{1}{5} = ?\)
D.\(\frac{7}{5} - \frac{1}{10} = ?\)
Easy
What is the crucial first step that must be taken before completing the number sentence \(\frac{11}{12} - \frac{1}{4} = ?\) as shown in the tutorial example?
A.Subtract the numerators and then the denominators.
B.Find a common denominator for both fractions.
C.Convert the fractions to decimals.
D.Add the numerators and denominators.
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What grade level is "Complete addition and subtraction sentences with fractions"?
Complete addition and subtraction sentences with fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Complete addition and subtraction sentences with fractions?
You'll be able to: Solve addition and subtraction problems involving fractions with unlike denominators by finding a common denominator and simplifying the answer; Identify missing numerators or denominators in addition and subtraction sentences….
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How many practice questions are included with Complete addition and subtraction sentences with fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.