Mathematics
Grade 10
15 min
Subtract fractions with unlike denominators
Subtract fractions with unlike denominators
What you'll learn
- Identify the least common denominator (LCD) for two fractions with unlike denominators with 80% accuracy.
- Rewrite fractions with unlike denominators as equivalent fractions with a common denominator in order to prepare to subtract them, achieving 70% accuracy on a worksheet.
- Solve subtraction problems involving fractions with unlike denominators, expressing the answer in simplest form, with 75% accuracy on a quiz.
- Explain the steps involved in subtracting fractions with unlike denominators to a partner, using mathematical vocabulary (e.g., denominator, numerator, equivalent fraction, simplest form).
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the Least Common Denominator (LCD) for any two fractions.
Convert fractions to equivalent forms with a common denominator to facilitate subtraction.
Accurately subtract fractions with unlike denominators and express the result in simplest form.
Set up ratios of corresponding sides from two geometric figures.
Apply fraction subtraction to analyze and compare geometric ratios, providing evidence for or against congruence.
Interpret the result of a fractional difference in the context of a geometric comparison.
How can subtracting simple fractions help us prove that two complex shapes are definitively NOT congruent? 🤔 Let's find out!
This tutorial revisits the fundamental skill of subtracting fractions with unlike denominators, but frames it...
2
Key Concepts & Vocabulary
TermDefinitionExample
RatioA comparison of two quantities by division. In geometry, we often use ratios to compare the lengths of corresponding sides of two figures.In a triangle with sides a=3 and b=4, the ratio of side a to side b is 3/4.
Corresponding SidesSides that are in the same relative position in two different geometric figures.In two triangles, ΔABC and ΔXYZ, side AB corresponds to side XY.
Unlike DenominatorsThe bottom numbers (denominators) of two or more fractions are different, meaning the fractions represent parts of differently sized wholes.The fractions 2/3 and 3/5 have unlike denominators (3 and 5).
Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators of a set of fractions. It's the smallest 'whole' that all f...
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Core Formulas
Finding the Least Common Denominator (LCD)
LCD(b, d) = LCM(b, d)
The Least Common Denominator (LCD) of two fractions is the Least Common Multiple (LCM) of their denominators. Use this to find the common 'unit' for comparison before subtracting.
Formula for Subtracting Fractions
\frac{a}{b} - \frac{c}{d} = \frac{a \cdot (\frac{LCD}{b}) - c \cdot (\frac{LCD}{d})}{LCD}
To subtract fractions with unlike denominators, first find the LCD. Then, convert each fraction to an equivalent fraction with the LCD as its denominator. Finally, subtract the new numerators and place the result over the LCD.
The Cross-Multiplication Method
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
A shortcut for subtracting two fractions. Multiply the numerator of the first fraction by th...
4 more steps in this tutorial
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Challenging
Two quadrilaterals are being compared for congruence. The ratio of a diagonal to a side in the first is (x+2)/3. The corresponding ratio in the second is x/2. If the difference between the first and second ratio is exactly 1/6, what is the value of x?
A.1
B.2
C.5
D.3
Challenging
A geometer claims two isosceles triangles are congruent because their base-to-leg ratios of 2/3 and 4/5 are 'close'. To formally disprove that the triangles are even similar, what is the exact, non-zero difference between these ratios?
A.2/2
B.2/15
C.1/15
D.2/8
Challenging
A sculptor creates two similar rectangular prisms. For Prism A, the ratio of its surface area to its volume is 7/10. For the larger Prism B, the corresponding ratio is 3/5. What is the difference between the ratio for Prism A and Prism B?
A.1/10
B.4/5
C.13/10
D.4/10
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What grade level is "Subtract fractions with unlike denominators"?
Subtract fractions with unlike denominators is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Subtract fractions with unlike denominators?
You'll be able to: Identify the least common denominator (LCD) for two fractions with unlike denominators with 80% accuracy; Rewrite fractions with unlike denominators as equivalent fractions with a common denominator in order to prepare to….
Is "Subtract fractions with unlike denominators" free to practice?
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How many practice questions are included with Subtract fractions with unlike denominators?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.