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Unitary Method
Unitary Method for Ratio and Proportion The Unitary Method is a systematic approach to finding missing values in a ratio or proportion. It involves anal...
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Unitary Method for Ratio and Proportion The Unitary Method is a systematic approach to finding missing values in a ratio or proportion. It involves anal...
Unitary Method for Ratio and Proportion
The Unitary Method is a systematic approach to finding missing values in a ratio or proportion. It involves analyzing the relationships between ratios or proportions and using this knowledge to develop a consistent and efficient method for solving problems.
Key Principles:
Equivalent ratios: Ratios or proportions that are equal are equivalent and represent the same value. For example, 2/3 and 4/6 are equivalent ratios.
Equivalent proportions: Proportions that are equal also represent the same value. For example, 1/2 and 2/4 are equivalent proportions.
Corresponding parts: Corresponding parts of similar figures are proportional. For example, if two figures have the same shape, their corresponding parts will have the same ratios or proportions.
Steps of the Unitary Method:
Identify the given ratios or proportions.
Express the ratios or proportions as fractions with the same denominator.
Find the least common multiple (LCM) of the denominators.
Convert the fractions to equivalent fractions with the LCM denominator.
Equate the fractions and solve for the unknown variable.
Simplify the resulting fraction if necessary.
Examples:
Example 1:
If you have 2/3 of a pizza and 4/5 of another pizza, what is the total amount of pizzas?
Using the unitary method, we can:
Express the ratios as fractions: 2/3 = 4/6.
Find the LCM of 3 and 6: 6.
Convert the fractions to equivalent fractions with 6 as the denominator: 2/3 = 8/24 and 4/5 = 24/20.
Equate the fractions: 8/24 = 24/20.
Simplify the fraction: 8/24 = 1/3.
Therefore, the total amount of pizzas is 3 pizzas.
Example 2:
If you have 1/2 of a recipe and 1/4 of another recipe, what is the total amount of recipes?
Using the unitary method, we can:
Express the ratios as fractions: 1/2 = 4/8 and 1/4 = 2/8.
Find the LCM of 8: 8.
Convert the fractions to equivalent fractions with 8 as the denominator: 1/2 = 4/8 and 1/4 = 2/8.
Equate the fractions: 4/8 = 2/8.
Simplify the fraction: 4/8 = 1/2.
Therefore, the total amount of recipes is 2 recipes