6.Explain why this expression results in a negative number: -¾ ( -3 + 6)
This expression results in a negative number because of the negative sign attached to the fraction -¾.
When we perform the operations inside the parenthesis, we have -3 + 6 = 3.
Then, we multiply 3 by -¾, which means taking 3 groups of -¾.
Since the fraction -¾ is negative, multiplying it by a positive number (3) will result in a negative number.
Therefore, the final result of -¾ (-3 + 6) is a negative number.
7.Makiyla was making cupcakes. She added 1¾ cup of powdered sugar to the recipe. She gave the cupcakes to 5 friends. How much powered sugar was in each friend’s delivery?
To find out how much powdered sugar was in each friend's delivery, we need to divide the total amount of powdered sugar by the number of friends.
Makiyla added 1¾ cup of powdered sugar to the recipe, which is equivalent to 7/4 cups.
To divide this among 5 friends, we simply divide the total amount of powdered sugar by 5:
(7/4 cups) ÷ 5 = 7/4 ÷ 5 = 7/4 × 1/5 = 7/20 cups
Therefore, each friend's delivery would have 7/20 cups of powdered sugar.
8.Mrs. Fowler’s family was going on a vacation to Disney Worlds. They saved $4500 for the trip. ⅖ of this amount will go to tickets. ¼ of the remaining money will towards souvenirs and snacks at the park. How much $ will be spent on souvenirs and snacks at the park?
To find out how much money will be spent on souvenirs and snacks at the park, we need to calculate the remaining money after the ticket expenses.
The family saved $4500 for the trip.
⅖ of this amount will go to tickets, so the ticket expenses would be (⅖) * $4500.
To calculate this, we multiply ⅖ by $4500:
(⅖) * $4500 = (2/5) * $4500 = $1800.
Now, we need to find ¼ of the remaining money after the ticket expenses that will be spent on souvenirs and snacks.
To calculate this, we subtract the ticket expenses from the total saved money:
$4500 - $1800 = $2700.
Now, we calculate ¼ of $2700:
(1/4) * $2700 = $675.
Therefore, $675 will be spent on souvenirs and snacks at the park.
9.Rational numbers m and n are plotted on the number line below. Based on the number line, which statement is true?
The value of n-m is positive.
The value of n+m is positive.
The value of n+m is negative.
The value of -(n-m) is negative.
Without the specific values of m and n on the number line, it is difficult to determine the exact answer. However, we can make an inference based on the given options.
If m is located to the left of n on the number line, then n-m would be positive. This is because subtracting a smaller number (m) from a larger number (n) results in a positive difference.
Based on this inference, the statement "The value of n-m is positive" is most likely to be true.
10. What is the result of the following calculation?
23 . 15 + 47 divided 34 =
To calculate this, we need to follow the order of operations (PEMDAS/BODMAS).
First, we perform the multiplication: 23.15 (the decimal point represents the multiplication sign) = 354.25.
Then, we perform the division: 47 ÷ 34 ≈ 1.382.
Finally, we add the results of the multiplication and division: 354.25 + 1.382 ≈ 355.632.
Therefore, the result of the calculation 23.15 + 47 ÷ 34 is approximately 355.632.
11. Simplify the expression: 5x - 4 + (-7x) + x - 6
To simplify the expression 5x - 4 + (-7x) + x - 6, we can combine like terms.
First, we combine the terms with the variable x: 5x + (-7x) + x.
This simplifies to -x.
Next, we combine the constant terms: -4 + (-6).
This simplifies to -10.
Putting these results together, the simplified expression becomes: -x - 10.