Big Ideas Math Accelerated 7-8 - Chapter 1 Assessments & Key by ... - Free Printable

Here are the step-by-step solutions for the problems on the worksheet.

Evaluate the expressions

1. $(-4) - (-8)$
* Subtracting a negative number is the same as adding a positive number.
* Change $- (-8)$ to $+ 8$.
* The problem becomes: $-4 + 8$.
* Since the signs are different, subtract the numbers ($8 - 4 = 4$) and keep the sign of the larger number (positive).
* Answer: 4

2. $(-1)^3$
* This means multiplying $-1$ by itself three times: $(-1) \times (-1) \times (-1)$.
* First, $(-1) \times (-1) = 1$.
* Then, $1 \times (-1) = -1$.
* Answer: -1

3. $-9^2$
* Be careful here! There are no parentheses around the $-9$. This means you square the $9$ first, then apply the negative sign.
* $9^2 = 81$.
* Apply the negative sign: $-81$.
* Answer: -81

4. $-18 \div (-6)$
* When dividing two negative numbers, the answer is always positive.
* $18 \div 6 = 3$.
* Answer: 3

5. $3 - 10^2$
* Follow the order of operations (exponents first).
* $10^2 = 100$.
* Now subtract: $3 - 100$.
* Answer: -97

6. $7 + (-8)$
* Adding a negative number is the same as subtraction.
* The problem becomes: $7 - 8$.
* Start at 7 on the number line and move 8 steps to the left. You land on -1.
* Answer: -1

7. $(-1)(-2)(-3)(2)$
* Multiply from left to right.
* $(-1) \times (-2) = 2$ (negative times negative is positive).
* $2 \times (-3) = -6$ (positive times negative is negative).
* $-6 \times 2 = -12$ (negative times positive is negative).
* Answer: -12

8. $\frac{-16}{-8}$
* A negative divided by a negative is a positive.
* $16 \div 8 = 2$.
* Answer: 2

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Order the numbers from least to greatest

Numbers: $-8, |-1|, |3|, -6, -5, 10, -4, 2$

1. First, simplify the absolute values:
* $|-1| = 1$
* $|3| = 3$
2. The list of numbers to sort is: $-8, 1, 3, -6, -5, 10, -4, 2$.
3. Let's put them in order from smallest (most negative) to largest:
* Negatives: $-8, -6, -5, -4$
* Positives: $1, 2, 3, 10$

Answer: $-8, -6, -5, -4, 1, 2, 3, 10$
*(Note: You can write the original forms back if required: $-8, -6, -5, -4, |-1|, 2, |3|, 10$)*

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Word Problems

9. Dolphin depth
* Starting point: $-4$ feet (below surface).
* Action: Dives deeper 10 feet. "Deeper" means going further down into the negatives, so we subtract 10.
* Equation: $-4 - 10$.
* Calculation: $-14$.
* Answer: -14 ft

10. Submarine depth
* Starting point: $-10$ meters.
* Action: Rises 5 meters. "Rising" means going up towards zero, so we add 5.
* Equation: $-10 + 5$.
* Calculation: $-5$.
* Answer: -5 m

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Evaluate the expression when $x = 3$, $y = -8$, and $z = -5$

11. $3xy - 5y$
* Substitute the values: $x = 3$ and $y = -8$.
* Expression: $3(3)(-8) - 5(-8)$.
* Step 1: Multiply the first part $3 \times 3 \times -8$.
* $3 \times 3 = 9$.
* $9 \times -8 = -72$.
* Step 2: Multiply the second part $-5 \times -8$.
* Negative times negative is positive.
* $5 \times 8 = 40$.
* Step 3: Combine them.
* $-72 + 40$.
* Signs are different, so subtract: $72 - 40 = 32$. Keep the sign of the larger number (negative).
* Answer: -32

12. $-xy^2 + \frac{12}{y}$
* Substitute the values: $x = 3$ and $y = -8$.
* Expression: $-(3)(-8)^2 + \frac{12}{-8}$.
* Step 1: Handle the exponent first. $(-8)^2 = 64$.
* Note: The negative sign outside is not squared.
* So, $-xy^2$ becomes $-(3)(64)$.
* $3 \times 64 = 192$.
* Apply the negative sign: $-192$.
* Step 2: Handle the fraction $\frac{12}{-8}$.
* Positive divided by negative is negative.
* $\frac{12}{8}$ simplifies to $\frac{3}{2}$ or $1.5$.
* So, this part is $-1.5$.
* Step 3: Add them together.
* $-192 + (-1.5)$.
* $-192 - 1.5 = -193.5$.
* Answer: -193.5 (or $-\frac{387}{2}$)

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Final Answer:
1. 4
2. -1
3. -81
4. 3
5. -97
6. -1
7. -12
8. 2
9. Order: -8, -6, -5, -4, |-1|, 2, |3|, 10
10. -14 ft
11. -5 m
12. -32
13. -193.5