Which expressions represent the amount of olive oil needed for 4 tablespoons of lemon juice? Write an expression to show the amount of olive oil in the recipe, letting j equal the... Which expressions represent the amount of olive oil needed for 4 tablespoons of lemon juice? Write an expression to show the amount of olive oil in the recipe, letting j equal the number of tablespoons of lemon juice.
Understand the Problem
The question is asking for two parts: first, to identify which mathematical expressions correctly represent the quantity of olive oil needed for a specific amount of lemon juice; second, to write an expression using a variable to denote the olive oil needed, based on the amount of lemon juice specified (represented by j).
Answer
The expressions are $4 \times 2$ and $4 + 4$, and the algebraic expression for olive oil is $2j$.
Answer for screen readers
- The correct expressions that represent the amount of olive oil needed for 4 tablespoons of lemon juice are: $4 \times 2$ and $4 + 4$.
- The algebraic expression for olive oil in terms of lemon juice is: $2j$.
Steps to Solve
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Identify the relationship between olive oil and lemon juice
The problem states that the recipe requires twice as much olive oil as lemon juice. If lemon juice is measured in tablespoons, we need to find the equivalent amount of olive oil.
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Calculate olive oil for a specific amount of lemon juice
For 4 tablespoons of lemon juice, we need to calculate the equivalent amount of olive oil. This can be expressed as: $$ \text{Olive Oil} = 2 \times \text{Lemon Juice} $$ Thus for 4 tablespoons of lemon juice: $$ \text{Olive Oil} = 2 \times 4 = 8 $$
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Identify correct expressions
We need to determine which expressions correctly represent this calculation. The options provided are:
- $4 \times 2$
- $4 + 4$
Both expressions must be evaluated:
- $4 \times 2 = 8$ (correct, represents the olive oil needed)
- $4 + 4 = 8$ (also correct, represents the same total)
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Write the algebraic expression for general cases
To represent the amount of olive oil needed based on the tablespoons of lemon juice (denoted by $j$), we can write the expression: $$ \text{Olive Oil} = 2j $$
- The correct expressions that represent the amount of olive oil needed for 4 tablespoons of lemon juice are: $4 \times 2$ and $4 + 4$.
- The algebraic expression for olive oil in terms of lemon juice is: $2j$.
More Information
In this recipe, the relationship between olive oil and lemon juice is directly proportional, meaning that if the amount of lemon juice increases, the amount of olive oil needed also increases accordingly. This concept can be applied in various recipes and scenarios.
Tips
- A common mistake may include misunderstanding the relationship; remembering that "twice as much" means multiplication by 2 rather than addition.
- Another mistake could be incorrectly calculating or misinterpreting the expressions that represent doubling the amount.
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