consider the given expression 4/5 x 2/3

Question

A: Brianna performs a chemistry experiment that involves boiling 4/5 of a liter of water when 2/3 of a liter evaporates how much of the water has evaporated

B: Melvin has 4/5 of a gallon of a paint in a can he uses 2/3 of a gallon to paint a wall how much of a gallon of paint is left in the can?

C: Alyssa has 4/5 of a pound of potatoes she bye 2/3 of a pound more how many pounds of potatoes does she have now?

D: Ms. Kubrick has 4/5 of a pound of grapes in a bowl her family ate 2/3 of the grapes how much of a pound of grapes did they eat?

Answer 1

Let's analyze each scenario while performing the calculations for the fractions provided.

A: Brianna's Chemistry Experiment

Brianna starts with \( \frac{4}{5} \) of a liter of water and \( \frac{2}{3} \) of a liter evaporates.

To find the amount of water that evaporated, we simply take \( \frac{2}{3} \) of \( \frac{4}{5} \): \[ \text{Amount evaporated} = \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \] So, \( \frac{8}{15} \) liters of water has evaporated.

B: Melvin's Paint

Melvin has \( \frac{4}{5} \) of a gallon of paint and uses \( \frac{2}{3} \) of a gallon. To find out how much paint is left in the can, we first determine how much paint Melvin uses: \[ \text{Amount used} = \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \] Now, convert \( \frac{4}{5} \) to a fraction with a denominator of 15 to subtract: \[ \frac{4}{5} = \frac{12}{15} \] Now, subtract the amount used from the total: \[ \text{Amount left} = \frac{12}{15} - \frac{8}{15} = \frac{4}{15} \] So, Melvin has \( \frac{4}{15} \) gallons of paint left.

C: Alyssa's Potatoes

Alyssa has \( \frac{4}{5} \) of a pound of potatoes and buys \( \frac{2}{3} \) of a pound more. We add these two amounts together: \[ \text{Total potatoes} = \frac{4}{5} + \frac{2}{3} \] To add these fractions, find a common denominator, which is 15: \[ \frac{4}{5} = \frac{12}{15}, \quad \frac{2}{3} = \frac{10}{15} \] Now, add: \[ \text{Total potatoes} = \frac{12}{15} + \frac{10}{15} = \frac{22}{15} \] So Alyssa now has \( \frac{22}{15} \) pounds of potatoes.

D: Ms. Kubrick's Grapes

Ms. Kubrick has \( \frac{4}{5} \) of a pound of grapes, and her family eats \( \frac{2}{3} \) of that amount. We find out how much they ate: \[ \text{Amount eaten} = \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \] Thus, the family ate \( \frac{8}{15} \) of a pound of grapes.

Summary of Results:

A: \( \frac{8}{15} \) liters of water evaporated.
B: \( \frac{4}{15} \) gallons of paint left.
C: \( \frac{22}{15} \) pounds of potatoes.
D: \( \frac{8}{15} \) pounds of grapes eaten.

Answer 2

you have to pick one of them sorry

Answer 3

No problem! Let's focus on one of the scenarios. How about we go with B: Melvin's Paint?

B: Melvin's Paint

Melvin has \( \frac{4}{5} \) of a gallon of paint in a can. He uses \( \frac{2}{3} \) of a gallon to paint a wall.

To find out how much paint is left in the can, we first need to calculate how much paint Melvin uses:

1. Calculate the amount of paint used: \[ \text{Amount used} = \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \]

2. Convert \( \frac{4}{5} \) to a fraction with a denominator of 15 in order to subtract: \[ \frac{4}{5} = \frac{12}{15} \]

3. Now, subtract the amount used from the total amount of paint: \[ \text{Amount left} = \frac{12}{15} - \frac{8}{15} = \frac{4}{15} \]

So, Melvin has \( \frac{4}{15} \) gallons of paint left in the can.

Answer 4

use properties of rational numbers to multiply the following -40 x (-75)

Answer 5

When multiplying two rational numbers, particularly negative numbers, we can use the properties of multiplication to simplify the process. Specifically, we have the following rules:

1. Product of Two Negative Numbers: The product of two negative numbers is positive.

Given the expression \(-40 \times (-75)\), we can apply this rule:

\[ -40 \times (-75) = 40 \times 75 \]

Now, let's calculate \(40 \times 75\):

\[ 40 \times 75 = 3000 \]

Therefore, the result of \(-40 \times (-75)\) is:

\[ \boxed{3000} \]