I. -28/4
-7 ***
7
- 1/7
1/7
II. Which equation represents “fifteen more than r is sixty-one”?
r + 61 = 15
r + 15 = 61 ***
r – 15 = 61
r – 61 = 15
III. What is the value of 4^2 – 2(3 x 5 + 1)?
8
1
-16 ***
-21
IV. What symbol is needed between -2 and |-3| to make a true statement?
< ***
>
=
V. What is the value of (3^2 + 1) – 14 / 2?
2
3 ***
-3
-2
VI. Which set of integers are in the right order from least to greatest?
|-10|, -3, 2, 7
7, |-10|, -3, 2
2, -3, 7, |-10|
-3, 2, 7, |-10| ***
VII. What is the additive inverse of -42?
-42
42 ***
-(-(-42))
-|-42|
VIII. What is the solution to 107 – (-25)?
132 ***
82
-82
-132
I agree you.
I. To find the value of -28/4, we need to divide -28 by 4. Division is the process of splitting a number into equal parts. When dividing a negative number by a positive number, the quotient will be negative.
Calculation: -28 ÷ 4 = -7
So, -28/4 is equal to -7.
II. The equation "fifteen more than r is sixty-one" can be represented as "r + 15 = 61". To solve this equation, we need to isolate the variable 'r' which means we want to move '15' to the other side of the equation.
Steps:
1. Start with the equation: r + 15 = 61
2. Subtract 15 from both sides of the equation to isolate 'r':
(r + 15) - 15 = 61 - 15
r = 61 - 15
3. Calculate the right side of the equation:
r = 46
So, the equation that represents "fifteen more than r is sixty-one" is r + 15 = 61, and the solution to the equation is r = 46.
III. To find the value of 4^2 - 2(3 x 5 + 1), we need to follow the order of operations (also known as PEMDAS/BODMAS). The operations inside parentheses should be done first, then multiplication and division, and finally addition and subtraction.
Steps:
1. Simplify the expression inside parentheses: 3 x 5 + 1 = 15 + 1 = 16
2. Substitute the simplified expression back into the original equation: 4^2 - 2(16)
3. Calculate the exponent first: 4^2 = 4 x 4 = 16
4. Simplify the multiplication: 2 x 16 = 32
5. Finally, subtract 32 from 16: 16 - 32 = -16
So, the value of 4^2 - 2(3 x 5 + 1) is -16.
IV. To make a true statement between -2 and |-3|, we need to compare their values. The absolute value of a number represents the distance of that number from zero on the number line. It is always positive.
The absolute value of -3 is written as |-3|, and it is equal to 3.
Since -2 is less than 3, we use the '<' symbol.
Therefore, the symbol needed between -2 and |-3| to make a true statement is '<'.
V. To find the value of (3^2 + 1) - 14 / 2, we need to follow the order of operations (PEMDAS/BODMAS) where parentheses come first, followed by exponents, multiplication and division, and finally addition and subtraction.
Steps:
1. Calculate the exponent: 3^2 = 3 x 3 = 9
2. Multiply 14 by 2: 14 x 2 = 28
3. Divide 28 by 2: 28 ÷ 2 = 14
4. Add 1 to 9: 9 + 1 = 10
5. Subtract 14 from 10: 10 - 14 = -4
So, the value of (3^2 + 1) - 14 / 2 is -4.
VI. To determine the set of integers that are in the right order from least to greatest among |-10|, -3, 2, and 7, we need to compare their numerical values.
|-10| represents the absolute value of -10, which is 10. So, we have 10, -3, 2, and 7.
From least to greatest order, the integers are:
-10 < -3 < 2 < 7
Therefore, the correct order is -3, 2, 7, |-10|.
VII. The additive inverse of a number is the value that, when added to the original number, gives a sum of zero. To find the additive inverse of -42, we need to find the number that, when added to -42, equals zero.
Calculation: -42 + 42 = 0
So, the additive inverse of -42 is 42.
VIII. To solve the equation 107 - (-25), we need to apply the rules of subtracting a negative number. Subtracting a negative is the same as adding a positive.
Steps:
1. Rewrite the equation as addition: 107 + 25.
2. Add 107 and 25: 107 + 25 = 132.
So, the solution to 107 - (-25) is 132.