Mathematics
Grade 10
15 min
Complete addition and subtraction sentences with mixed numbers
Complete addition and subtraction sentences with mixed numbers
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1
Introduction & Learning Objectives
Learning Objectives
Translate geometric relationships, like the Segment Addition Postulate, into addition and subtraction sentences involving mixed numbers.
Convert mixed numbers to improper fractions to facilitate accurate calculations for segment lengths.
Solve for an unknown segment length by completing addition or subtraction sentences with mixed numbers.
Apply the concept of congruence to set up equations with mixed numbers.
Verify geometric properties by accurately adding and subtracting segment lengths expressed as mixed numbers.
Perform regrouping (borrowing) when subtracting mixed numbers in the context of finding a partial segment length.
An architect is designing a frame where one side is 15 3/4 inches long, composed of two smaller pieces. If one piece is 8 7/8 in...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.The length 5 1/2 inches is a mixed number, representing 5 whole inches and an additional 1/2 inch.
Improper FractionA fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number).The mixed number 5 1/2 can be converted to the improper fraction 11/2.
Congruent SegmentsLine segments that have the exact same length. If segment AB is congruent to segment CD, we write AB ≅ CD, which implies their measures are equal (AB = CD).If side XY of △XYZ has a length of 7 1/4 cm and side PQ of congruent △PQR corresponds to XY, then PQ must also have a length of 7 1/4 cm.
Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and...
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Core Formulas
Addition of Mixed Numbers (via Improper Fractions)
A \frac{b}{c} + D \frac{e}{f} = \frac{Ac+b}{c} + \frac{Df+e}{f}
To add mixed numbers, first convert them into improper fractions. Then, find a common denominator, add the numerators, and simplify the result, converting back to a mixed number if necessary. This method is the most reliable for complex problems found in geometry.
Subtraction of Mixed Numbers (via Improper Fractions)
A \frac{b}{c} - D \frac{e}{f} = \frac{Ac+b}{c} - \frac{Df+e}{f}
Similar to addition, convert both mixed numbers to improper fractions. Find a common denominator, subtract the numerators, and simplify. This avoids common errors with borrowing across the whole number and the fraction.
Segment Addition Postulate Formula
m(\overline{AB}) + m(\over...
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Challenging
On a line, point B is between A and C. The length of AC is 15 1/2 units. The length of AB is 2 3/4 units longer than the length of BC. What is the length of BC?
A.6 3/8 units
B.9 1/8 units
C.12 3/4 units
D.7 3/4 units
Challenging
You are given that segment AB ≅ segment DE. You measure sub-segments and find AC = 4 2/3, CB = 5 1/2, DF = 6 1/4, and FE = 3 5/6. Based on these measurements, is the statement AB ≅ DE true? Complete the necessary addition sentences to verify.
A.Yes, because 10 1/6 = 10 1/12.
B.No, because 10 1/6 ≠ 10 1/12.
C.Yes, because 10 1/6 = 10 1/6.
D.No, because 10 1/6 ≠ 10 1/12.
Challenging
The perimeter of rectangle QRST is 50 units. The length of side QR is 14 2/3 units. What is the length of the adjacent side RS?
A.35 1/3 units
B.20 2/3 units
C.10 1/3 units
D.11 1/3 units
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