Missy and Bill were asked to evaluate the expression -3(-2 + 5). Their work is shown below.

Question

Missy’s work!                 Bill’s work

Evaluate: -3(-2+5).   Evaluate: -3(-2+5)
Step 1: -6+(-15).      Step 1: 6 + (-15)
Step 2: -6 - 15.       Step 2: 6 -15
Step 3: -21.          Step 3: -9

____ made a mistake in ____ distribution was not performed correctly the ___ term should be ____

GPT-4o mini · Answer

Missy made a mistake in Step 1; distribution was not performed correctly. The first term should be 3 instead of -6.

Here’s the correct way to evaluate the expression -3(-2 + 5):

Evaluate the expression inside the parentheses: $-2 + 5 = 3$.
Multiply by -3: $-3 \times 3 = -9$.

So the correct final result is -9.

Answer

Use properties of rational numbers to multiply the following -6/5 x 3.125

GPT-4o mini · Answer

To multiply $-\frac{6}{5} \times 3.125$, we first convert $3.125$ into a fraction. 1. **Convert 3.125 to a fraction:** $$ 3.125 = \frac{3125}{1000} $$ Next, we can simplify this fraction. Both the numerator and denominator can be divided by 125: $$ \frac{3125 \div 125}{1000 \div 125} = \frac{25}{8} $$ 2. **Now multiply the fractions:** $$ -\frac{6}{5} \times \frac{25}{8} $$ To multiply fractions, multiply the numerators and multiply the denominators: $$ \frac{-6 \times 25}{5 \times 8} = \frac{-150}{40} $$ 3. **Simplify the resulting fraction:** Both the numerator and denominator can be divided by 10: $$ \frac{-150 \div 10}{40 \div 10} = \frac{-15}{4} $$ So, $-\frac{6}{5} \times 3.125 = -\frac{15}{4}$. If you prefer, you can also express $-\frac{15}{4}$ as a mixed number: $$ -\frac{15}{4} = -3 \frac{3}{4} $$ Thus, the final result is: $$ -\frac{15}{4} \text{ or } -3.75. $$

Answer

Spencer worked out for 232 1/2 minutes in the last five days. If he worked out for the same number of minutes each day, how many minutes did he work out each day?
Each day, Spencer worked out for minutes.

GPT-4o mini · Answer

To find out how many minutes Spencer worked out each day, we need to divide the total minutes he worked out by the number of days.

Convert the mixed number to an improper fraction: \[ 232 \frac{1}{2} = \frac{232 \times 2 + 1}{2} = \frac{464 + 1}{2} = \frac{465}{2} \]
Divide by the number of days: Since Spencer worked out for 5 days, we need to divide $\frac{465}{2}$ by 5: \[ \frac{465}{2} \div 5 = \frac{465}{2} \times \frac{1}{5} = \frac{465 \times 1}{2 \times 5} = \frac{465}{10} \]
Simplify the fraction: To simplify $\frac{465}{10}$, we divide both the numerator and denominator by 5: \[ \frac{465 \div 5}{10 \div 5} = \frac{93}{2} \]
Convert back to a mixed number (if desired): $\frac{93}{2}$ is equal to: \[ 46 \frac{1}{2} \text{ minutes} \]

Thus, each day, Spencer worked out for $46 \frac{1}{2}$ minutes or 46.5 minutes.

Answer

Select ALL the correct answers. Select all the values that are equivalent to -(7/8)

GPT-4o mini · Answer

To find values that are equivalent to $-\frac{7}{8}$, we can consider various forms of the number itself, such as: 1. **Negative form**: The negative of the fraction is $-\frac{7}{8}$. 2. **Decimal form**: The decimal equivalent of $-\frac{7}{8}$ is $-0.875$. 3. **Multiplying by -1**: A fraction's sign can be changed by multiplying both the numerator and denominator by -1: $$ -\frac{7}{8} = \frac{7 \times -1}{8 \times -1} = \frac{-7}{8}. $$ 4. **Equivalent fractions**: We can multiply both the numerator and denominator by the same non-zero integer: $$ -\frac{7 \times 2}{8 \times 2} = -\frac{14}{16} $$ $$ -\frac{7 \times 3}{8 \times 3} = -\frac{21}{24} $$ These types of fractions are also equivalent. Based on this information, the correct answers (values equivalent to $-\frac{7}{8}$) include: - $-\frac{7}{8}$ - $-0.875$ - $-\frac{14}{16}$ - $-\frac{21}{24}$ - $\frac{-7}{8}$ You can check if any of these values are listed, as they will all be equivalent to $-\frac{7}{8}$.

Answer

Drag each number to the correct location on the equation. Each number can be used more than once, but not all numbers will be used.
A recipe calls for 3 1/3 cups of flour. Charlie only has a 1/3-cup measuring cup. How many times will Charlie need to fill the 1/3-cup measuring cup? Set up the initial problem on the left side of the equation and the solution on the right side of the equation.

2/3. 3/10. 30. 3 1/3 1/3 10 3

___\____ = ___ times

GPT-4o mini · Answer

To determine how many times Charlie needs to fill the $ \frac{1}{3} $-cup measuring cup to reach $ 3 \frac{1}{3} $ cups of flour, we can set up the equation as follows:

Convert $ 3 \frac{1}{3} $ to an improper fraction: \[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]
Set up the equation: \[ \frac{10}{3} \div \frac{1}{3} = \text{number of times the } \frac{1}{3} \text{-cup will be filled} \]

Dividing by $ \frac{1}{3} $ is equivalent to multiplying by its reciprocal, which is $ 3 $: \[ \frac{10}{3} \times 3 = 10 \]
Write the equation: \[ 3 \frac{1}{3} \div \frac{1}{3} = 10 \text{ times} \]

You can use this setup:

Final answer: \[ 3 \frac{1}{3} \ \div \ \frac{1}{3} = 10 \ \text{times} \]

Hence, you would fill the last part as follows:

Fill in the blanks: \[ 3 \frac{1}{3} \ \ \div \ \ \frac{1}{3} = \ \ 10 \ \text{times} \]

Answer

Which of the following is equivalent to -(15/8)

GPT-4o mini · Answer

To find values that are equivalent to $-\frac{15}{8}$, we can consider different forms of the fraction. Here are some equivalent forms: 1. **Negative Fraction**: $$ -\frac{15}{8} $$ 2. **Decimal Form**: Converting $-\frac{15}{8}$ to decimal: $$ -\frac{15}{8} = -1.875 $$ 3. **Changing Signs**: Multiplying both the numerator and denominator by -1 gives: $$ \frac{-15}{8} $$ (which is the same as $-\frac{15}{8}$). 4. **Equivalent Fractions**: You can multiply both the numerator and denominator by the same non-zero integer. For example: $$ -\frac{15 \times 2}{8 \times 2} = -\frac{30}{16} $$ or $$ -\frac{15 \times 3}{8 \times 3} = -\frac{45}{24} $$ 5. **Simplified Mixed Number**: $-\frac{15}{8}$ can be expressed as a mixed number: $$ -\frac{15}{8} = -1 \frac{7}{8} $$ So, equivalent expressions for $-\frac{15}{8}$ include: - $-\frac{15}{8}$ - $-1.875$ - $\frac{-15}{8}$ - $-\frac{30}{16}$ - $-\frac{45}{24}$ - $-1 \frac{7}{8}$ If you have specific options to choose from, please provide them, and I can help you identify which options are equivalent to $-\frac{15}{8}$.