lesson 2 assignment
13. $m^3 - 18$ for $m = 2$
14. $\frac{d}{5} + 42$ for $d = -70$
prepare
evaluate each expression.
1. $5 \div \frac{3}{4}$
2. $0.24 \div 0.6$
3. $\frac{(14 + 8)}{2}$
4. $\frac{14}{2} + \frac{18}{2}$
5. what do you notice about the answers to questions 3 and 4?

Question

Accepted Answer

### Problem 13: $ m^3 - 18 $ for $ m = 2 $
# Explanation:
## Step 1: Substitute $ m = 2 $ into the expression
We substitute $ m = 2 $ into $ m^3 - 18 $, so we get $ 2^3 - 18 $.
## Step 2: Calculate $ 2^3 $
We know that $ 2^3 = 2 \times 2 \times 2 = 8 $.
## Step 3: Subtract 18 from the result
Now we calculate $ 8 - 18 = -10 $.
# Answer:
$ -10 $

### Problem 14: $ \frac{d}{5}+42 $ for $ d = -70 $
# Explanation:
## Step 1: Substitute $ d = -70 $ into the expression
We substitute $ d = -70 $ into $ \frac{d}{5}+42 $, so we get $ \frac{-70}{5}+42 $.
## Step 2: Calculate $ \frac{-70}{5} $
We know that $ \frac{-70}{5} = -14 $.
## Step 3: Add 42 to the result
Now we calculate $ -14 + 42 = 28 $.
# Answer:
$ 28 $

### Prepare 1: $ 5\div\frac{3}{4} $
# Explanation:
## Step 1: Recall the rule for dividing by a fraction
Dividing by a fraction is the same as multiplying by its reciprocal. So $ 5\div\frac{3}{4}=5\times\frac{4}{3} $.
## Step 2: Multiply the numbers
We calculate $ 5\times\frac{4}{3}=\frac{20}{3} \approx 6.67 $ (if we want a decimal approximation) or we can leave it as an improper fraction $ \frac{20}{3} $.
# Answer:
$ \frac{20}{3} $ (or $ 6\frac{2}{3} $ or approximately $ 6.67 $)

### Prepare 2: $ 0.24\div0.6 $
# Explanation:
## Step 1: Perform the division
We can think of this as $ \frac{0.24}{0.6} $. If we multiply both the numerator and the denominator by 100 to eliminate the decimals, we get $ \frac{24}{60} $.
## Step 2: Simplify the fraction
We simplify $ \frac{24}{60} $ by dividing both the numerator and the denominator by their greatest common divisor, which is 12. So $ \frac{24\div12}{60\div12}=\frac{2}{5} = 0.4 $.
# Answer:
$ 0.4 $

### Prepare 3: $ \frac{(14 + 8)}{2} $
# Explanation:
## Step 1: Calculate the numerator
First, we calculate the sum in the numerator: $ 14 + 8 = 22 $.
## Step 2: Divide by 2
Then we divide 22 by 2: $ \frac{22}{2}=11 $.
# Answer:
$ 11 $

### Prepare 4: $ \frac{14}{2}+\frac{18}{2} $
# Explanation:
## Step 1: Calculate each fraction
We calculate $ \frac{14}{2}=7 $ and $ \frac{18}{2}=9 $.
## Step 2: Add the results
Then we add 7 and 9: $ 7 + 9 = 11 $.
# Answer:
$ 11 $

### Prepare 5: What do you notice about the answers to Questions 3 and 4?
# Brief Explanations:
The answers to Questions 3 and 4 are both 11. This shows the distributive property of division over addition, which states that $ \frac{a + b}{c}=\frac{a}{c}+\frac{b}{c} $ (where $ c
eq0 $). In this case, $ a = 14 $, $ b = 8 $, and $ c = 2 $, so $ \frac{14 + 8}{2}=\frac{14}{2}+\frac{8}{2} $ (note that in Question 4 it is $ \frac{14}{2}+\frac{18}{2} $, there might be a typo and it should be $ \frac{14}{2}+\frac{8}{2} $ to match the numerator of Question 3, but assuming the given Question 4 is correct as $ \frac{14}{2}+\frac{18}{2} $, if we consider the numbers, maybe it's a different example, but the key is that when we have a sum in the numerator divided by a number, it's the same as dividing each term in the numerator by that number and then adding them, which is the distributive property of division over addition).
# Answer:
The answers to Questions 3 and 4 are equal (both are 11), demonstrating the distributive property of division over addition ($ \frac{a + b}{c}=\frac{a}{c}+\frac{b}{c} $ for $ c
eq0 $).

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QUESTION IMAGE

Question

Explanation:

Problem 13: \( m^3 - 18 \) for \( m = 2 \)

Step 1: Substitute \( m = 2 \) into the expression

Step 2: Calculate \( 2^3 \)

Step 3: Subtract 18 from the result

Step 1: Substitute \( d = -70 \) into the expression

Step 2: Calculate \( \frac{-70}{5} \)

Step 3: Add 42 to the result

Step 1: Recall the rule for dividing by a fraction

Step 2: Multiply the numbers

Answer:

Problem 14: \( \frac{d}{5}+42 \) for \( d = -70 \)