Posted incompare

How to Use Cross Multiplication When Comparing Fractions

No Comments

COMPARE.EDU.VN clarifies How To Use Cross Multiplication When Comparing Fractions, offering a straightforward method to determine their relationship. This technique simplifies fraction comparison and solving for unknowns, making it easier to work with ratios and proportions. Discover efficient fraction comparison techniques with compare.edu.vn.

1. Understanding Cross Multiplication for Fraction Comparison

Cross multiplication is a valuable shortcut in mathematics, especially when dealing with fractions. It provides a quick way to compare fractions and solve for unknowns, streamlining various mathematical problems. This method is particularly useful when comparing two fractions to determine if they are equal or which one is larger. The procedure involves multiplying the numerator of one fraction by the denominator of the other and comparing the resulting products. This technique simplifies the comparison of fractions and is widely applicable in algebra and arithmetic. Learning how to use cross multiplication effectively can significantly enhance problem-solving skills in mathematics.

1.1. What is Cross Multiplication?

Cross multiplication is a mathematical technique used to simplify and solve equations involving fractions. The primary use of cross multiplication is to determine the equality or inequality of two fractions. When comparing two fractions, (frac{a}{b}) and (frac{c}{d}), cross multiplication involves multiplying a by d and b by c. The results, ad and bc, are then compared. If ad equals bc, the fractions are equivalent. If ad is greater than bc, then (frac{a}{b}) is greater than (frac{c}{d}). Conversely, if ad is less than bc, then (frac{a}{b}) is less than (frac{c}{d}). This method is a shortcut for clearing denominators when solving equations, making it easier to find unknown variables.

1.2. Why Use Cross Multiplication to Compare Fractions?

Using cross multiplication to compare fractions offers several advantages:

  • Efficiency: Cross multiplication is faster than finding a common denominator, especially with large or complex fractions.
  • Simplicity: The method is straightforward and requires only basic multiplication skills.
  • Accuracy: It reduces the chances of errors compared to other methods, providing a reliable way to compare fractions.
  • Versatility: Cross multiplication can also solve for unknown variables in equations involving fractions, extending its utility beyond simple comparisons.
  • Convenience: It eliminates the need to find the least common denominator, simplifying calculations.

Overall, cross multiplication streamlines fraction comparisons, making it a valuable tool in mathematics.

1.3. Basic Principle Behind Cross Multiplication

The principle behind cross multiplication is rooted in the properties of equality and fractions. To understand this better, let’s consider two fractions, (frac{a}{b}) and (frac{c}{d}), that are set equal to each other:

(frac{a}{b} = frac{c}{d})

The goal is to eliminate the denominators to easily compare or solve for variables. To do this, we can multiply both sides of the equation by the product of the denominators, which is bd:

(bd cdot frac{a}{b} = bd cdot frac{c}{d})

This simplifies to:

(ad = bc)

This resulting equation, ad = bc, is the core of cross multiplication. By comparing the products ad and bc, we can determine the relationship between the original fractions without dealing with the denominators. This is especially useful when a, b, c, or d are large numbers or variables.

1.4. Key Terms and Definitions

To effectively use cross multiplication, understanding the following key terms is essential:

  • Fraction: A number representing a part of a whole, expressed as (frac{a}{b}), where a is the numerator and b is the denominator.
  • Numerator: The top number in a fraction, indicating how many parts of the whole are being considered.
  • Denominator: The bottom number in a fraction, indicating the total number of equal parts the whole is divided into.
  • Cross Product: The result of multiplying the numerator of one fraction by the denominator of another fraction. For fractions (frac{a}{b}) and (frac{c}{d}), the cross products are ad and bc.
  • Equivalent Fractions: Fractions that represent the same value, even though they may have different numerators and denominators (e.g., (frac{1}{2}) and (frac{2}{4})).

Having a clear grasp of these terms ensures accurate and confident application of cross multiplication.

2. Step-by-Step Guide to Cross Multiplying Fractions

Cross multiplication is a straightforward process that simplifies fraction comparisons and equation-solving. Here’s a step-by-step guide to effectively use this method:

2.1. Setting Up the Fractions

  1. Write Down the Fractions: Begin by clearly writing down the two fractions you want to compare or the equation you want to solve. Ensure each fraction is in its simplest form if possible, although it’s not mandatory.

  2. Equality or Inequality: Determine whether you are comparing the fractions for equality or inequality. If comparing, write the fractions side by side. If solving an equation, ensure the fractions are set equal to each other with an equal sign (=).

  3. Example Setup:

    • Comparing: (frac{2}{3}) vs. (frac{3}{4})
    • Equation: (frac{x}{5} = frac{4}{7})

    Setting up the fractions correctly is crucial for accurate cross multiplication.

2.2. Performing the Cross Multiplication

  1. Identify Numerators and Denominators: Clearly identify the numerators and denominators in both fractions.
  2. Multiply Across: Multiply the numerator of the first fraction by the denominator of the second fraction. Then, multiply the numerator of the second fraction by the denominator of the first fraction.
    • For fractions (frac{a}{b}) and (frac{c}{d}), multiply a by d and b by c.
  3. Write Down the Products: Write down the products of these multiplications.
    • ad and bc are the cross products.
  4. Example:
    • For (frac{2}{3}) and (frac{3}{4}):
      • (2 times 4 = 8)
      • (3 times 3 = 9)
    • For (frac{x}{5} = frac{4}{7}):
      • (x times 7 = 7x)
      • (5 times 4 = 20)

2.3. Comparing the Results

  1. Equality: If the products ad and bc are equal, the two fractions are equivalent. This means (frac{a}{b} = frac{c}{d}).
  2. Inequality: If ad is greater than bc, then (frac{a}{b} > frac{c}{d}). If ad is less than bc, then (frac{a}{b} < frac{c}{d}).
  3. Example:
    • For (frac{2}{3}) and (frac{3}{4}):
      • Since 8 < 9, (frac{2}{3} < frac{3}{4})
  4. Interpretation: Understand what the comparison tells you about the relationship between the original fractions.

2.4. Solving for Unknown Variables

  1. Set Up the Equation: After cross multiplying, set up the equation with the products.
    • For (frac{x}{5} = frac{4}{7}), the equation becomes (7x = 20).
  2. Isolate the Variable: Use algebraic manipulation to isolate the variable. This usually involves dividing both sides of the equation by the coefficient of the variable.
    • In the example, divide both sides by 7:
      • (x = frac{20}{7})
  3. Simplify: Simplify the fraction if possible to get the final value of the variable.
  4. Example:
    • (x = frac{20}{7}) is the solution. You can also express it as a mixed number: (x = 2frac{6}{7}).
  5. Check Your Work: Substitute the value back into the original equation to ensure it holds true.

2.5. Examples to Illustrate the Process

Example 1: Comparing Fractions

Compare (frac{5}{8}) and (frac{3}{5}).

  1. Setup: (frac{5}{8}) vs. (frac{3}{5})
  2. Cross Multiply:
    • (5 times 5 = 25)
    • (8 times 3 = 24)
  3. Compare: Since 25 > 24, (frac{5}{8} > frac{3}{5}).

Example 2: Solving for a Variable

Solve (frac{7}{x} = frac{14}{16}).

  1. Setup: (frac{7}{x} = frac{14}{16})
  2. Cross Multiply:
    • (7 times 16 = 112)
    • (x times 14 = 14x)
  3. Equation: (14x = 112)
  4. Solve: Divide both sides by 14:
    • (x = frac{112}{14} = 8)

Alt: Cross multiplication steps: multiply diagonally, then compare to find the larger fraction.

Example 3: Determining Equality

Determine if (frac{4}{6}) and (frac{6}{9}) are equal.

  1. Setup: (frac{4}{6}) vs. (frac{6}{9})
  2. Cross Multiply:
    • (4 times 9 = 36)
    • (6 times 6 = 36)
  3. Compare: Since 36 = 36, (frac{4}{6} = frac{6}{9}).

These examples illustrate how cross multiplication can be applied in different scenarios to compare fractions and solve equations effectively.

3. Common Mistakes to Avoid

While cross multiplication is a straightforward technique, several common mistakes can lead to incorrect results. Being aware of these pitfalls can help ensure accuracy in your calculations.

3.1. Incorrect Multiplication

  1. Multiplying the Wrong Numbers: Ensure you are multiplying the numerator of one fraction by the denominator of the other fraction.
    • Mistake: Multiplying numerators together or denominators together.
    • Correct: Multiply diagonally (numerator of the first fraction by the denominator of the second, and vice versa).
  2. Simple Arithmetic Errors: Double-check your multiplication to avoid basic calculation mistakes.
    • Mistake: Incorrectly calculating (7 times 8) as 54 instead of 56.
    • Correct: Use a calculator or mental math techniques to verify each multiplication.

3.2. Misinterpreting the Results

  1. Reversing the Inequality: When comparing fractions, ensure you correctly interpret the inequality. If ad > bc, then (frac{a}{b} > frac{c}{d}).
    • Mistake: Concluding that (frac{a}{b} < frac{c}{d}) when ad > bc.
    • Correct: Double-check which cross product is larger to correctly determine the greater fraction.
  2. Incorrectly Applying the Equal Sign: When solving for a variable, remember that the cross products form an equation.
    • Mistake: Not setting the cross products equal to each other, leading to an incorrect equation.
    • Correct: Ensure that after cross multiplying, you set the products equal to each other (e.g., (ad = bc)).

3.3. Forgetting to Simplify

  1. Not Simplifying Fractions Before Cross Multiplying: While not always necessary, simplifying fractions before cross multiplying can make calculations easier.
    • Mistake: Working with large, unsimplified fractions, increasing the chance of arithmetic errors.
    • Correct: Simplify fractions to their lowest terms before cross multiplying to reduce the size of the numbers.
  2. Not Simplifying the Final Answer: After solving for a variable, make sure to simplify the resulting fraction.
    • Mistake: Leaving the answer as an unsimplified fraction, such as (frac{14}{16}) instead of (frac{7}{8}).
    • Correct: Always reduce the fraction to its simplest form.

3.4. Dealing with Negative Numbers

  1. Ignoring Negative Signs: When dealing with negative fractions, pay close attention to the signs.
    • Mistake: Neglecting the negative sign, leading to incorrect comparisons or solutions.
    • Correct: Apply the rules of multiplying negative numbers: a negative times a positive is negative, and a negative times a negative is positive.
  2. Incorrectly Distributing Negative Signs: Ensure the negative sign is correctly applied to the entire numerator or denominator.
    • Mistake: Treating (frac{-a}{b}) differently from (frac{a}{-b}) or -(frac{a}{b}).
    • Correct: Remember that all three expressions are equivalent and treat them consistently.

3.5. Examples of Common Mistakes

  1. Incorrect Multiplication:
    • Problem: Compare (frac{3}{5}) and (frac{2}{7}).
    • Mistake: Multiplying (3 times 5) and (2 times 7) instead of (3 times 7) and (2 times 5).
    • Correct: (3 times 7 = 21) and (2 times 5 = 10), so (frac{3}{5} > frac{2}{7}).
  2. Misinterpreting Inequality:
    • Problem: Compare (frac{4}{9}) and (frac{5}{11}).
    • Mistake: Getting (4 times 11 = 44) and (5 times 9 = 45), then concluding (frac{4}{9} > frac{5}{11}).
    • Correct: Since 44 < 45, (frac{4}{9} < frac{5}{11}).
  3. Not Simplifying:
    • Problem: Solve (frac{6}{8} = frac{x}{12}).
    • Mistake: Getting (6 times 12 = 72) and (8x = 72), then stating (x = frac{72}{8}) without simplifying.
    • Correct: Simplify (frac{72}{8}) to (x = 9).
  4. Ignoring Negative Signs:
    • Problem: Compare (frac{-2}{3}) and (frac{1}{4}).
    • Mistake: Ignoring the negative sign and concluding (frac{-2}{3} > frac{1}{4}).
    • Correct: Recognizing that any negative fraction is less than any positive fraction, so (frac{-2}{3} < frac{1}{4}).

By avoiding these common mistakes, you can improve your accuracy and confidence when using cross multiplication.

4. Advanced Applications of Cross Multiplication

Cross multiplication extends beyond basic fraction comparisons and solving simple equations. It has several advanced applications in mathematics and real-world scenarios. Understanding these applications can enhance your problem-solving skills and provide a deeper appreciation for this versatile technique.

4.1. Solving Complex Equations

  1. Equations with Multiple Fractions: Cross multiplication can simplify equations involving multiple fractions by reducing them to a more manageable form.
    • Example: Solve for x in (frac{x+1}{3} = frac{2x-1}{5}).
    • Cross multiply: (5(x+1) = 3(2x-1))
    • Simplify: (5x + 5 = 6x – 3)
    • Solve: (x = 8)
  2. Proportions and Ratios: It is frequently used to solve problems involving proportions and ratios, making it easier to find unknown quantities.
    • Example: If the ratio of boys to girls in a class is 3:4 and there are 15 boys, how many girls are there?
    • Set up the proportion: (frac{3}{4} = frac{15}{x})
    • Cross multiply: (3x = 60)
    • Solve: (x = 20) girls

4.2. Comparing Multiple Fractions

  1. Pairwise Comparison: When comparing more than two fractions, cross multiplication can be used to compare them in pairs.
    • Example: Compare (frac{2}{5}), (frac{3}{7}), and (frac{4}{9}).
    • Compare (frac{2}{5}) and (frac{3}{7}): (2 times 7 = 14) and (3 times 5 = 15), so (frac{2}{5} < frac{3}{7}).
    • Compare (frac{3}{7}) and (frac{4}{9}): (3 times 9 = 27) and (4 times 7 = 28), so (frac{3}{7} < frac{4}{9}).
    • Conclusion: (frac{2}{5} < frac{3}{7} < frac{4}{9})
  2. Ordering Fractions: By comparing fractions in pairs, you can order them from least to greatest or greatest to least.

4.3. Real-World Applications

  1. Cooking and Baking: Adjusting recipes involves scaling ingredients using proportions, where cross multiplication is useful.
    • Example: A recipe calls for (frac{2}{3}) cup of flour and you want to make half the recipe. How much flour do you need?
    • Set up the proportion: (frac{1}{2} = frac{x}{frac{2}{3}})
    • Cross multiply: (2x = frac{2}{3})
    • Solve: (x = frac{1}{3}) cup of flour
  2. Finance: Calculating percentage increases or decreases often involves comparing fractions or ratios.
    • Example: If a stock price increases from $50 to $55, what is the percentage increase?
    • Calculate the fraction increase: (frac{5}{50})
    • Convert to percentage: (frac{5}{50} = frac{x}{100})
    • Cross multiply: (50x = 500)
    • Solve: (x = 10)%, so the increase is 10%.
  3. Scale Models and Maps: Determining actual distances from scale models or maps utilizes proportions and cross multiplication.
    • Example: On a map, 1 inch represents 20 miles. If two cities are (3frac{1}{2}) inches apart on the map, what is the actual distance?
    • Set up the proportion: (frac{1}{20} = frac{3.5}{x})
    • Cross multiply: (x = 20 times 3.5)
    • Solve: (x = 70) miles

4.4. Using Cross Multiplication in Geometry

  1. Similar Triangles: Determining the lengths of sides in similar triangles involves setting up proportions that can be solved using cross multiplication.
    • Example: Two triangles are similar. The sides of the first triangle are 3, 4, and 5. The shortest side of the second triangle is 6. Find the length of the corresponding longest side.
    • Set up the proportion: (frac{3}{6} = frac{5}{x})
    • Cross multiply: (3x = 30)
    • Solve: (x = 10)
  2. Finding Unknown Lengths: Cross multiplication can be used to find unknown lengths in geometric figures by setting up appropriate proportions.

4.5. Examples of Advanced Applications

  1. Complex Equation:
    • Problem: Solve (frac{2x+1}{4} = frac{3x-2}{5}).
    • Cross multiply: (5(2x+1) = 4(3x-2))
    • Simplify: (10x + 5 = 12x – 8)
    • Solve: (2x = 13), so (x = frac{13}{2})
  2. Multiple Fractions:
    • Problem: Order (frac{5}{12}), (frac{7}{15}), and (frac{3}{8}) from least to greatest.
    • Compare (frac{5}{12}) and (frac{7}{15}): (5 times 15 = 75) and (7 times 12 = 84), so (frac{5}{12} < frac{7}{15}).
    • Compare (frac{7}{15}) and (frac{3}{8}): (7 times 8 = 56) and (3 times 15 = 45), so (frac{3}{8} < frac{7}{15}).
    • Compare (frac{5}{12}) and (frac{3}{8}): (5 times 8 = 40) and (3 times 12 = 36), so (frac{3}{8} < frac{5}{12}).
    • Order: (frac{3}{8} < frac{5}{12} < frac{7}{15})
  3. Real-World Problem:
    • Problem: If 3 apples cost $2.50, how much will 7 apples cost?
    • Set up the proportion: (frac{3}{2.50} = frac{7}{x})
    • Cross multiply: (3x = 17.50)
    • Solve: (x = $5.83) (rounded to the nearest cent)

By mastering these advanced applications, you can leverage cross multiplication to solve a wide range of mathematical and practical problems.

5. Advantages and Limitations

Cross multiplication is a powerful tool, but it’s essential to understand its strengths and weaknesses to use it effectively. Knowing when to use it and when to opt for other methods can improve your problem-solving approach.

5.1. Advantages of Using Cross Multiplication

  1. Efficiency: Cross multiplication is often faster than finding a common denominator, especially when dealing with fractions that have no obvious common factors.
  2. Simplicity: The technique is straightforward and easy to understand, requiring only basic multiplication skills.
  3. Versatility: It can be used to compare fractions, solve equations, and handle proportions.
  4. Reduced Complexity: It eliminates the need to find the least common denominator, which can be time-consuming and prone to errors.
  5. Wide Applicability: Cross multiplication is useful in various mathematical contexts, including algebra, geometry, and real-world problems.

5.2. Limitations of Cross Multiplication

  1. Limited to Two Fractions: Cross multiplication is most effective when comparing or solving equations involving only two fractions at a time. For multiple fractions, it must be applied pairwise.
  2. Potential for Large Numbers: When dealing with large numerators and denominators, cross multiplication can result in large products, increasing the chance of arithmetic errors.
  3. Not Suitable for Addition or Subtraction: Cross multiplication cannot be directly used for adding or subtracting fractions. You must find a common denominator for those operations.
  4. Doesn’t Simplify Fractions: It only compares or solves; it does not reduce fractions to their simplest form.
  5. Risk of Misinterpretation: Incorrect application or misinterpretation of results can lead to wrong conclusions.

5.3. When to Use Other Methods

  1. Adding or Subtracting Fractions: Always use the common denominator method for adding or subtracting fractions.
  2. Simplifying Fractions: To simplify a single fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD.
  3. Complex Equations with Multiple Terms: For equations with multiple terms and fractions, consider algebraic manipulation or other equation-solving techniques.
  4. Fractions with Obvious Common Denominators: When fractions have an obvious common denominator, using that denominator can be simpler than cross multiplication.

5.4. Comparison with Other Methods

Method Advantages Limitations When to Use
Cross Multiplication Efficient for comparing two fractions, simple, versatile Limited to two fractions, potential for large numbers, not for addition/subtraction Comparing two fractions, solving proportions
Common Denominator Suitable for adding/subtracting fractions, provides a clear common base Can be time-consuming, requires finding the least common denominator Adding/subtracting fractions, complex equations with multiple fractions
Simplification (GCD) Reduces fractions to their simplest form, easy to understand Only simplifies a single fraction, doesn’t compare or solve equations Simplifying a single fraction
Algebraic Manipulation Versatile for solving complex equations, can handle multiple terms Requires strong algebraic skills, can be more time-consuming Complex equations with multiple terms and fractions

5.5. Examples Illustrating Advantages and Limitations

  1. Advantage: Efficiency
    • Problem: Compare (frac{17}{23}) and (frac{29}{37}).
    • Cross multiplication: (17 times 37 = 629) and (29 times 23 = 667), so (frac{17}{23} < frac{29}{37}).
    • Finding a common denominator would involve larger numbers and more complex calculations.
  2. Limitation: Not for Addition
    • Problem: Add (frac{1}{3}) and (frac{1}{4}).
    • Cross multiplication cannot be directly used.
    • Correct approach: Find a common denominator (12), so (frac{4}{12} + frac{3}{12} = frac{7}{12}).
  3. Advantage: Versatility
    • Problem: Solve (frac{x}{8} = frac{3}{5}).
    • Cross multiplication: (5x = 24), so (x = frac{24}{5}).
    • It efficiently solves for the unknown variable.
  4. Limitation: Large Numbers
    • Problem: Compare (frac{123}{456}) and (frac{456}{789}).
    • Cross multiplication: (123 times 789 = 97047) and (456 times 456 = 207936), so (frac{123}{456} < frac{456}{789}).
    • The large numbers make the multiplication more prone to errors; simplifying fractions first might be beneficial.

By understanding these advantages and limitations, you can strategically use cross multiplication to efficiently solve problems while avoiding potential pitfalls.

6. Practice Problems and Solutions

To solidify your understanding of cross multiplication, working through practice problems is essential. These problems cover various scenarios, from simple fraction comparisons to more complex equation-solving. Detailed solutions are provided to help you check your work and understand the process thoroughly.

6.1. Basic Fraction Comparisons

  1. Problem: Compare (frac{3}{7}) and (frac{4}{9}).
    • Solution:
      • Cross multiply: (3 times 9 = 27) and (4 times 7 = 28)
      • Since 27 < 28, (frac{3}{7} < frac{4}{9})
  2. Problem: Compare (frac{5}{11}) and (frac{2}{5}).
    • Solution:
      • Cross multiply: (5 times 5 = 25) and (2 times 11 = 22)
      • Since 25 > 22, (frac{5}{11} > frac{2}{5})
  3. Problem: Determine if (frac{6}{10}) and (frac{9}{15}) are equal.
    • Solution:
      • Cross multiply: (6 times 15 = 90) and (9 times 10 = 90)
      • Since 90 = 90, (frac{6}{10} = frac{9}{15})

6.2. Solving for Unknown Variables

  1. Problem: Solve (frac{x}{6} = frac{5}{8}).
    • Solution:
      • Cross multiply: (8x = 30)
      • Solve: (x = frac{30}{8} = frac{15}{4})
  2. Problem: Solve (frac{7}{x} = frac{14}{16}).
    • Solution:
      • Cross multiply: (14x = 112)
      • Solve: (x = frac{112}{14} = 8)
  3. Problem: Solve (frac{4}{9} = frac{x}{27}).
    • Solution:
      • Cross multiply: (9x = 108)
      • Solve: (x = frac{108}{9} = 12)

6.3. Complex Equations

  1. Problem: Solve (frac{x+2}{5} = frac{3x-1}{8}).
    • Solution:
      • Cross multiply: (8(x+2) = 5(3x-1))
      • Simplify: (8x + 16 = 15x – 5)
      • Solve: (7x = 21), so (x = 3)
  2. Problem: Solve (frac{2x+3}{7} = frac{x-1}{3}).
    • Solution:
      • Cross multiply: (3(2x+3) = 7(x-1))
      • Simplify: (6x + 9 = 7x – 7)
      • Solve: (x = 16)
  3. Problem: Solve (frac{5}{2x+1} = frac{3}{x-2}).
    • Solution:
      • Cross multiply: (5(x-2) = 3(2x+1))
      • Simplify: (5x – 10 = 6x + 3)
      • Solve: (x = -13)

6.4. Real-World Problems

  1. Problem: If 4 oranges cost $3.00, how much will 10 oranges cost?
    • Solution:
      • Set up the proportion: (frac{4}{3.00} = frac{10}{x})
      • Cross multiply: (4x = 30)
      • Solve: (x = $7.50)
  2. Problem: A map scale is 1 inch = 25 miles. If two cities are 4.5 inches apart on the map, what is the actual distance?
    • Solution:
      • Set up the proportion: (frac{1}{25} = frac{4.5}{x})
      • Cross multiply: (x = 25 times 4.5)
      • Solve: (x = 112.5) miles
  3. Problem: In a school, the ratio of teachers to students is 1:15. If there are 600 students, how many teachers are there?
    • Solution:
      • Set up the proportion: (frac{1}{15} = frac{x}{600})
      • Cross multiply: (15x = 600)
      • Solve: (x = 40) teachers

6.5. Mixed Practice

  1. Problem: Compare (frac{-2}{5}) and (frac{-3}{8}).
    • Solution:
      • Cross multiply: (-2 times 8 = -16) and (-3 times 5 = -15)
      • Since -16 < -15, (frac{-2}{5} < frac{-3}{8})
  2. Problem: Solve (frac{3x}{4} = frac{9}{10}).
    • Solution:
      • Cross multiply: (30x = 36)
      • Solve: (x = frac{36}{30} = frac{6}{5})
  3. Problem: If a recipe calls for (frac{2}{3}) cup of sugar and you want to make (frac{3}{4}) of the recipe, how much sugar do you need?
    • Solution:
      • Set up the proportion: (frac{2/3}{1}

Comments

No comments yet. Why don’t you start the discussion?

Leave a Reply

Your email address will not be published. Required fields are marked *