Question
use properties of rational numbers to simplify the expression. (47 - 4/5) - ( 1/11 - 16)
your choices are : 62 11/16 63 5/16 62 6/55 63 49/55
your choices are : 62 11/16 63 5/16 62 6/55 63 49/55
Answers
Answer
NO!!!!! READ THE CHOICES!!!
Answer
Evaluate the following expression. -0.3 - (-0.6) + 0.5 + (-0.5)
Answer
Indicate which property is illustrated in Step 2.
Step 1 8 + (6 + 12) + 0 = 8 + (12 + 6) + 0
Step 2 = (8 + 12) + (6 + 0)
Step 3 = (8 + 12) + 6
Step 4 = 20 + 6
Step 1 8 + (6 + 12) + 0 = 8 + (12 + 6) + 0
Step 2 = (8 + 12) + (6 + 0)
Step 3 = (8 + 12) + 6
Step 4 = 20 + 6
Answer
-33/10 - (-45.3 + 35.2) = -33/10 - (?)
Answer
as a decimal
Answer
-33/10 - (-45.3 + 35.2) = -33/10 - (-10.1) =
Answer
34/5 as a decimal
Answer
(23 - 8.13) - (107.4 + 8)
Answer
Indicate which property is illustrated in Step 1.
Step 1 7 + (1 + 9) + 0 = 7 + (9 + 1) + 0
Step 2 = (7 + 9) + (1 + 0)
Step 3 = (7 + 9) + 1
Step 4 = 16 + 1
Step 1 7 + (1 + 9) + 0 = 7 + (9 + 1) + 0
Step 2 = (7 + 9) + (1 + 0)
Step 3 = (7 + 9) + 1
Step 4 = 16 + 1
Answer
-14.6 - 8.9 + 12.8 + (-12.8)
Answered by
GPT 3.5
To simplify the expression (47 - 4/5) - (1/11 - 16), we can apply the properties of rational numbers.
First, let's simplify the expression within the parentheses:
(1/11 - 16) = - (16 - 1/11) [Reordering subtraction]
= - (176/11 - 1/11) [Converting 16 to a fraction with a common denominator]
= - (175/11) [Subtracting fractions with the same denominator]
= -175/11 [Final result]
Now, let's substitute the simplified value back into the main expression:
(47 - 4/5) - (1/11 - 16) = (47 - 4/5) - (-175/11)
= (235/5 - 4/5) + (175/11) [Converting 47 and -175 to fractions with a common denominator]
= (231/5) + (175/11) [Subtracting fractions with the same denominator]
= (231/5) + (875/55) [Converting 175 to a fraction with a common denominator]
= (231/5) + (875/55)
= (1155/55) + (875/55) [Converting both fractions to have the same denominator]
= 2030/55 [Adding fractions with the same denominator]
Now, let's simplify 2030/55:
2030 ÷ 5 = 406 [Dividing 2030 by 5]
55 ÷ 5 = 11 [Dividing 55 by 5]
Therefore, 2030/55 simplifies to 406/11.
So, the final simplified expression is 406/11.
Answer: 406/11
First, let's simplify the expression within the parentheses:
(1/11 - 16) = - (16 - 1/11) [Reordering subtraction]
= - (176/11 - 1/11) [Converting 16 to a fraction with a common denominator]
= - (175/11) [Subtracting fractions with the same denominator]
= -175/11 [Final result]
Now, let's substitute the simplified value back into the main expression:
(47 - 4/5) - (1/11 - 16) = (47 - 4/5) - (-175/11)
= (235/5 - 4/5) + (175/11) [Converting 47 and -175 to fractions with a common denominator]
= (231/5) + (175/11) [Subtracting fractions with the same denominator]
= (231/5) + (875/55) [Converting 175 to a fraction with a common denominator]
= (231/5) + (875/55)
= (1155/55) + (875/55) [Converting both fractions to have the same denominator]
= 2030/55 [Adding fractions with the same denominator]
Now, let's simplify 2030/55:
2030 ÷ 5 = 406 [Dividing 2030 by 5]
55 ÷ 5 = 11 [Dividing 55 by 5]
Therefore, 2030/55 simplifies to 406/11.
So, the final simplified expression is 406/11.
Answer: 406/11
Answered by
GPT 3.5
Apologies for misreading the choices. Let's go through the expression one more time:
(47 - 4/5) - (1/11 - 16)
First, let's simplify the expression within the parentheses:
47 - 4/5 = (235/5) - (4/5) [Converting 47 and 4 to fractions with a common denominator]
= (231/5) [Subtracting fractions with the same denominator]
Now, let's simplify the second part of the expression:
1/11 - 16 = (1/11) - (176/11) [Converting 16 to a fraction with a common denominator]
= (-175/11) [Subtracting fractions with the same denominator]
Now, substitute the simplified values back into the main expression:
(47 - 4/5) - (1/11 - 16) = (231/5) - (-175/11) [Substituting the simplified values]
= (231/5) + (175/11) [Negating a subtraction operation is equivalent to addition]
= (231/5)*(11/11) + (175/11)*(5/5) [Multiplying each fraction by a form of 1 to have a common denominator]
= (231*11)/(5*11) + (175*5)/(11*5) [Multiplying numerators and denominators separately]
= 2541/55 + 875/55 [Simplifying multiplication]
= (2541 + 875)/55 [Adding fractions with the same denominator]
Now, let's add the numerators:
2541 + 875 = 3416
So the expression simplifies to:
3416/55
Therefore, the answer is: 3416/55
(47 - 4/5) - (1/11 - 16)
First, let's simplify the expression within the parentheses:
47 - 4/5 = (235/5) - (4/5) [Converting 47 and 4 to fractions with a common denominator]
= (231/5) [Subtracting fractions with the same denominator]
Now, let's simplify the second part of the expression:
1/11 - 16 = (1/11) - (176/11) [Converting 16 to a fraction with a common denominator]
= (-175/11) [Subtracting fractions with the same denominator]
Now, substitute the simplified values back into the main expression:
(47 - 4/5) - (1/11 - 16) = (231/5) - (-175/11) [Substituting the simplified values]
= (231/5) + (175/11) [Negating a subtraction operation is equivalent to addition]
= (231/5)*(11/11) + (175/11)*(5/5) [Multiplying each fraction by a form of 1 to have a common denominator]
= (231*11)/(5*11) + (175*5)/(11*5) [Multiplying numerators and denominators separately]
= 2541/55 + 875/55 [Simplifying multiplication]
= (2541 + 875)/55 [Adding fractions with the same denominator]
Now, let's add the numerators:
2541 + 875 = 3416
So the expression simplifies to:
3416/55
Therefore, the answer is: 3416/55
Answered by
GPT 3.5
To evaluate the expression -0.3 - (-0.6) + 0.5 + (-0.5), we can apply the rules of addition and subtraction of real numbers.
First, let's simplify the double negative:
-0.3 - (-0.6) = -0.3 + 0.6 [Negative of a negative is the same as addition]
= 0.6 - 0.3 [Rearranging terms]
= 0.3 [Subtracting]
Now, let's substitute the simplified value back into the main expression:
0.3 + 0.5 + (-0.5) = 0.3 + 0.5 - 0.5 [Adding negative numbers is the same as subtracting]
= 0.8 - 0.5 [Adding the positive numbers]
= 0.3 [Subtracting]
Therefore, the expression simplifies to 0.3.
Answer: 0.3
First, let's simplify the double negative:
-0.3 - (-0.6) = -0.3 + 0.6 [Negative of a negative is the same as addition]
= 0.6 - 0.3 [Rearranging terms]
= 0.3 [Subtracting]
Now, let's substitute the simplified value back into the main expression:
0.3 + 0.5 + (-0.5) = 0.3 + 0.5 - 0.5 [Adding negative numbers is the same as subtracting]
= 0.8 - 0.5 [Adding the positive numbers]
= 0.3 [Subtracting]
Therefore, the expression simplifies to 0.3.
Answer: 0.3
Answered by
GPT 3.5
The property illustrated in Step 2 is the associative property of addition.
Answered by
GPT 3.5
To evaluate the expression -33/10 - (-45.3 + 35.2), we first need to simplify the parentheses.
-(-45.3 + 35.2) = -(-10.1)
= 10.1 [Negating a negative is the same as taking the positive]
Now, substitute the simplified value back into the main expression:
-33/10 - 10.1 = -33/10 - (101/10) [Converting 10.1 to a fraction with a denominator of 10]
= -33/10 - 101/10 [Subtracting fractions with the same denominator]
= (-33 - 101)/10 [Subtracting the numerators]
= -134/10 [Simplifying the numerator]
Now, let's simplify the fraction -134/10:
-134 ÷ 2 = -67 [Dividing -134 by 2]
10 ÷ 2 = 5 [Dividing 10 by 2]
Therefore, -134/10 simplifies to -67/5.
So, the final simplified expression is -33/10 - (-45.3 + 35.2) = -33/10 - (-67/5).
Answer: -33/10 - (-67/5)
-(-45.3 + 35.2) = -(-10.1)
= 10.1 [Negating a negative is the same as taking the positive]
Now, substitute the simplified value back into the main expression:
-33/10 - 10.1 = -33/10 - (101/10) [Converting 10.1 to a fraction with a denominator of 10]
= -33/10 - 101/10 [Subtracting fractions with the same denominator]
= (-33 - 101)/10 [Subtracting the numerators]
= -134/10 [Simplifying the numerator]
Now, let's simplify the fraction -134/10:
-134 ÷ 2 = -67 [Dividing -134 by 2]
10 ÷ 2 = 5 [Dividing 10 by 2]
Therefore, -134/10 simplifies to -67/5.
So, the final simplified expression is -33/10 - (-45.3 + 35.2) = -33/10 - (-67/5).
Answer: -33/10 - (-67/5)
Answered by
GPT 3.5
To evaluate the expression -33/10 - (-67/5) as a decimal, we can compute the division.
-33/10 = -3.3 [Dividing -33 by 10]
-67/5 = -13.4 [Dividing -67 by 5]
Therefore, -33/10 - (-67/5) is equal to -3.3 - (-13.4) in decimal form.
Now, let's simplify the expression:
-3.3 - (-13.4) = -3.3 + 13.4 [Negating a negative is the same as addition]
= 10.1 [Adding the positive numbers]
So, the expression -33/10 - (-67/5) simplifies to 10.1 as a decimal.
Answer: 10.1
-33/10 = -3.3 [Dividing -33 by 10]
-67/5 = -13.4 [Dividing -67 by 5]
Therefore, -33/10 - (-67/5) is equal to -3.3 - (-13.4) in decimal form.
Now, let's simplify the expression:
-3.3 - (-13.4) = -3.3 + 13.4 [Negating a negative is the same as addition]
= 10.1 [Adding the positive numbers]
So, the expression -33/10 - (-67/5) simplifies to 10.1 as a decimal.
Answer: 10.1
Answered by
GPT 3.5
To continue simplifying the expression -33/10 - (-10.1), we can further perform the subtraction:
-33/10 - (-10.1) = -33/10 + 10.1 [Negating a negative is the same as addition]
Now, let's find a common denominator to add the fractions:
-33/10 + 10.1 = -33/10 + (101/10) [Converting 10.1 to a fraction with denominator 10]
= (-33 + 101)/10 [Adding the numerators]
= 68/10 [Simplifying the numerator]
Now, let's simplify the fraction 68/10:
68 ÷ 2 = 34 [Dividing 68 by 2]
10 ÷ 2 = 5 [Dividing 10 by 2]
Therefore, 68/10 simplifies to 34/5.
So, the final simplified expression is -33/10 - (-10.1) = 34/5.
Answer: 34/5
-33/10 - (-10.1) = -33/10 + 10.1 [Negating a negative is the same as addition]
Now, let's find a common denominator to add the fractions:
-33/10 + 10.1 = -33/10 + (101/10) [Converting 10.1 to a fraction with denominator 10]
= (-33 + 101)/10 [Adding the numerators]
= 68/10 [Simplifying the numerator]
Now, let's simplify the fraction 68/10:
68 ÷ 2 = 34 [Dividing 68 by 2]
10 ÷ 2 = 5 [Dividing 10 by 2]
Therefore, 68/10 simplifies to 34/5.
So, the final simplified expression is -33/10 - (-10.1) = 34/5.
Answer: 34/5
Answered by
GPT 3.5
To convert the fraction 34/5 into a decimal, we perform the division:
34 ÷ 5 = 6.8
Therefore, 34/5 as a decimal is equal to 6.8.
Answer: 6.8
34 ÷ 5 = 6.8
Therefore, 34/5 as a decimal is equal to 6.8.
Answer: 6.8
Answered by
GPT 3.5
To evaluate the expression (23 - 8.13) - (107.4 + 8), we can perform the addition and subtraction operations within the parentheses first.
23 - 8.13 = 14.87
107.4 + 8 = 115.4
Now, substitute the simplified values back into the main expression:
(23 - 8.13) - (107.4 + 8) = 14.87 - 115.4
To subtract decimals, we align the decimal points and subtract each place value:
14.87
- 115.40
---------
-100.53
Therefore, (23 - 8.13) - (107.4 + 8) simplifies to -100.53.
Answer: -100.53
23 - 8.13 = 14.87
107.4 + 8 = 115.4
Now, substitute the simplified values back into the main expression:
(23 - 8.13) - (107.4 + 8) = 14.87 - 115.4
To subtract decimals, we align the decimal points and subtract each place value:
14.87
- 115.40
---------
-100.53
Therefore, (23 - 8.13) - (107.4 + 8) simplifies to -100.53.
Answer: -100.53
Answered by
GPT 3.5
The property illustrated in Step 1 is the associative property of addition.
Answered by
GPT 3.5
To evaluate the expression -14.6 - 8.9 + 12.8 + (-12.8), we can combine like terms.
-14.6 - 8.9 + 12.8 + (-12.8) can be simplified to:
-23.5 + 0 = -23.5
Therefore, the expression simplifies to -23.5.
Answer: -23.5
-14.6 - 8.9 + 12.8 + (-12.8) can be simplified to:
-23.5 + 0 = -23.5
Therefore, the expression simplifies to -23.5.
Answer: -23.5