A jar contains 0.25 liter of apple juice and 0.30 liter of grape juice. Melissa poured 0.75 liter of pineapple juice into the jar. She then drank 0.20 liter of the mixture.
Part A: Write an expression to represent the total amount of juice left in the jar. (5 points)
Part B: Simplify the expression and identify which property is used in each step. (5 points)
Part A: To represent the total amount of juice left in the jar, we need to subtract the amount of juice Melissa poured into the jar and the amount of juice she drank from the initial amount of juice in the jar.
Let's denote the initial amount of apple juice as A, the initial amount of grape juice as G, the amount of pineapple juice Melissa poured into the jar as P, and the amount of juice Melissa drank as D.
The initial amount of apple juice in the jar is 0.25 liters, and the initial amount of grape juice is 0.30 liters. Melissa poured 0.75 liters of pineapple juice into the jar, so the total amount of pineapple juice in the jar is now 0.75 liters. Melissa then drank 0.20 liters of the mixture.
The simplified expression to represent the total amount of juice left in the jar is:
(A + G + P) - D
Part B: To simplify the expression and identify the property used in each step, we'll start with the given quantities and simplify the expression step by step. Let's go through the process:
1. Start with the expression: (A + G + P) - D
2. Substitute the given values: (0.25 + 0.30 + 0.75) - 0.20
3. Simplify the addition inside the parentheses: (1.30 + 0.75) - 0.20
4. Combine the two values: 2.05 - 0.20
5. Perform the subtraction: 1.85
The simplified expression for the total amount of juice left in the jar is 1.85 liters.
Properties used in each step:
- Commutative property of addition: This property allows us to change the order of the terms when adding. For example, we can add 0.25 and 0.30 first, and then add the result to 0.75.
- Associative property of addition: This property allows us to change the grouping of the terms when adding. For example, we can group (0.25 + 0.30) first, and then add the result to 0.75.
- Substitution property: This property allows us to replace variables with their given values.
- Commutative property of subtraction: This property allows us to change the order of the terms when subtracting. For example, we can subtract 0.20 from 2.05 instead of subtracting 2.05 from 0.20.
- Identity property of subtraction: This property states that subtracting zero from a number leaves the number unchanged. In this case, subtracting 0.20 from 2.05 does not affect the value of 2.05.
- Associative property of subtraction: This property allows us to change the grouping of the terms when subtracting. In this case, there is no need to change the grouping.
- Subtraction: This is the basic operation of subtracting two numbers. In this case, we subtract 0.20 from 2.05 to find the final amount of juice left in the jar.