Sally saved $26 in January, $19 in February, $47 in March, and $20 in April. How much money has she saved so far this year?(1 point)
To find the total amount of money Sally has saved, you need to add up the savings from each month.
$26 + $19 + $47 + $20 = $<<26+19+47+20=112>>112
Therefore, Sally has saved $112 so far this year.
Use the image to answer the question.
A number line with arrows at both the ends ranges from negative 110 to negative 70 in increments of 1, but labeled in increments of 10. A closed circle is placed on negative 75, which is also labeled, and negative 105. A curved arrow is drawn leftward from negative 75 to negative 105.
Which word problem matches the model?
(1 point)
Responses
Miguel has a negative balance in his bank account of $75. He deposited $30 into his account. What is his current balance?
Miguel has a negative balance in his bank account of $75. He deposited $30 into his account. What is his current balance?
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
Miguel made $75 mowing lawns and another $30 pulling weeds during the month of May. How much money did he earn?
Miguel made $75 mowing lawns and another $30 pulling weeds during the month of May. How much money did he earn?
Miguel has saved $75. He spent $30 at the store. How much money does he have now?
The word problem that matches the model is:
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
Yes
Great! The word problem that matches the model is:
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
What is the current balance?
To determine Miguel's current balance, we need to subtract the amount he spent and the overdraft fee from his initial negative balance of $75.
$75 (initial balance) - $25 (spent at the store) - $5 (overdraft fee) = $<<75-25-5=45>>45
Therefore, Miguel's current balance is -$45.
Rudy received a bonus of $2,000. He then paid his rent of $775, spent $250 on utilities, and paid his cell phone bill of $82. How much money does Rudy have left from his bonus after paying his bills?(1 point)
To determine how much money Rudy has left from his bonus after paying his bills, we need to subtract the total amount he spent from his initial bonus.
$2,000 (initial bonus) - $775 (rent) - $250 (utilities) - $82 (cell phone bill) = $<<2000-775-250-82=893>>893
Therefore, Rudy has $893 left from his bonus after paying his bills.
Miki is trying to help her younger brother understand why 12−(−5) is equal to 17. She draws a number line to help. Explain how a number line could help to show that 12−(−5) is equal to 17. (1 point)
A number line can help to show why 12 - (-5) is equal to 17 by visually demonstrating the concept of subtracting a negative number.
- On the number line, Miki would start at the number 12.
- To subtract -5, she would move 5 units to the left on the number line, as subtracting a negative is equivalent to adding a positive.
- This would bring her to the number 17, which represents the result of the subtraction.
Thus, the number line would show that starting at 12 and subtracting -5 results in the number 17, helping to explain why 12 - (-5) equals 17.
How can you represent −5⋅−4 with a model?(1 point)
To represent -5 * -4 with a model, you can use a rectangular grid or an array.
- Draw a grid with 5 rows and 4 columns.
- Label the rows with numbers from -1 to -5 and label the columns with numbers from -1 to -4.
- Each square within the grid represents a multiplication problem.
- Shade in the squares that correspond to the multiplication of -5 and -4, which would be the squares in the fifth row and fourth column.
- Count the number of shaded squares to find the product of -5 * -4.
By using this model, you can demonstrate that -5 * -4 equals a positive number.
Thank you
You're welcome! If you have any more questions, feel free to ask.
Multiply −9⋅(−18).(1 point)
To multiply -9 * (-18), you can follow these steps:
1. Multiply the absolute values of the two numbers: 9 * 18 = 162.
2. Determine the sign of the product:
- When multiplying two negative numbers, the product is always positive.
- Therefore, the product of -9 * (-18) is positive.
Hence, -9 * (-18) = 162.
Connect the model −(7+7+7+7+7+7) to the algorithm for solving the multiplication problem it models.(1 point)
The model "-(7+7+7+7+7+7)" represents the multiplication problem of -6 * 7 using the algorithm for solving multiplication.
The algorithm for solving multiplication involves multiplying the absolute values of the numbers and then determining the sign of the product based on the signs of the original numbers.
In this case, we have -6 * 7, which means we multiply the absolute values of the numbers:
6 * 7 = 42.
The sign of the product is determined by the rule that "the product of a negative number and a positive number is always negative".
Since -6 is negative and 7 is positive, the product of -6 * 7 is negative.
Therefore, the model "-(7+7+7+7+7+7)" can be connected to the algorithm for solving the multiplication problem by following the steps mentioned above:
-(7+7+7+7+7+7) = -42.
What model can you use to represent −30÷−6?(1 point)
One model that can be used to represent -30 ÷ -6 is a group or set model, where you divide a group or set of objects into smaller, equal-sized groups or sets.
To represent -30 ÷ -6 using this model:
1. Start with a group of 30 objects (represented as circles or any other shape).
2. Divide the group into smaller, equal-sized groups of 6 objects each.
3. Count the number of smaller groups that are formed.
Since we are dividing a negative number by a negative number, the result will be positive.
So, in this case, you would have 5 smaller groups of 6 objects each.
Therefore, the model for -30 ÷ -6 would be dividing a group of 30 objects into 5 equal-sized groups of 6 objects each.
What is the result of dividing −245÷35?
The result of dividing -245 ÷ 35 is -7.
To calculate this division, we divide the absolute values of the numbers and assign the sign based on the rules of dividing with negative numbers.
245 ÷ 35 = 7.
Since we are dividing a negative number (-245) by a positive number (35), the result will be negative.
Therefore, -245 ÷ 35 = -7.
What is the result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18)=0?(1 point
To find the result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18)=0, we need to simplify the expression and evaluate if it indeed equals 0.
-108 - (-18) - (-18) - (-18) - (-18) - (-18) - (-18) = 0
Using the rule that subtracting a negative is equivalent to adding a positive:
-108 + 18 + 18 + 18 + 18 + 18 + 18 = 0
Combining like terms:
-108 + 18 + 18 + 18 + 18 + 18 + 18 = -0
Simplifying further:
0 = 0
Therefore, the expression −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18) does indeed equal 0.
Elaine used the subtraction algorithm to subtract −17−(−3). She got the answer −14, but she does not feel confident that she is correct. Connect the expression −17−(−3) to a two-color counter model. Explain how the two-color counter model can be used to confirm whether Elaine’s answer is correct.(2 points)
To connect the expression −17−(−3) to a two-color counter model, we can use red counters to represent negative numbers and blue counters to represent positive numbers.
- Start with a set of 17 red counters (representing -17).
- Next, remove (subtract) 3 red counters (representing -3).
If Elaine's answer of -14 is correct, then the result of removing (subtracting) 3 red counters from 17 red counters should leave us with 14 red counters.
- Count the number of red counters remaining after removing 3 red counters.
If there are indeed 14 red counters remaining, Elaine's answer of -14 is correct, confirming her subtraction using the algorithm.
In summary, the two-color counter model can be used to confirm Elaine's answer (-14) for the expression -17 - (-3) by physically representing the numbers with counters and performing the subtraction operation.