7 2/3+(−5 1/4)
To add 7 2/3 and -5 1/4, we first need to convert both mixed numbers into improper fractions.
To convert 7 2/3 into an improper fraction:
7 * 3 = 21
21 + 2 = 23
Therefore, 7 2/3 can be written as the improper fraction 23/3.
To convert -5 1/4 into an improper fraction:
-5 * 4 = -20
-20 + 1 = -19
Therefore, -5 1/4 can be written as the improper fraction -19/4.
Now we can add the fractions:
23/3 + -19/4
Since the denominators are different, we need to find a common denominator.
The least common multiple of 3 and 4 is 12.
Multiply the numerator and denominator of the first fraction (23/3) by 4 to get the denominator to 12:
(23/3) * (4/4) = 92/12
Multiply the numerator and denominator of the second fraction (-19/4) by 3 to get the denominator to 12:
(-19/4) * (3/3) = -57/12
Now we can add the fractions:
92/12 + -57/12 = (92 - 57) / 12 = 35/12
Therefore, the sum of 7 2/3 and -5 1/4 is 35/12.
35/12. simplalifyed
To simplify 35/12, we can find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that value.
The GCD of 35 and 12 is 1, so we can divide both numerator and denominator by 1:
35/12 ÷ 1/1 = 35/12
Therefore, the simplified form of 35/12 is 35/12.
723+−514
Responses
A -2
B 2 5/12
C 2 11/12
D 12 11/12
To add 723 and -514, simply perform the arithmetic operation:
723 + (-514) = 209
Therefore, the sum of 723 and -514 is 209.
None of the given options (A, B, C, or D) matches the result obtained.
7.829 − 3.21
Responses
A 3.1273.127
B 4.2094.209
C 4.6194.619
D 11.039
To subtract 3.21 from 7.829, you should subtract the decimal numbers as follows:
7.829 - 3.21 = 4.619
Therefore, the correct answer is option C: 4.619.
Consider this expression:
14 − 0.5 + 12 − 0.25 + 35 + 0.4
Question 1
You are asked to find the sum by using fractions. Which expression could you use?
Responses
A 1/4 − 1/2 + 1/2 − 1/4+ 3/5 + 2/5
B 1/4 − 1/4 + 1/2 − 1/4+ 3/5 + 2/5
C 1/4 − 1/2 + 1/2 − 1/4+ 4/5 + 2/5
D 1/4 − 1/2 − 1/2 − 1/4+ 3/5 + 2/5
To find the sum of 14 − 0.5 + 12 − 0.25 + 35 + 0.4 using fractions, we need to convert the decimal numbers into fractions.
0.5 can be written as 1/2.
0.25 can be written as 1/4.
0.4 can be written as 2/5.
So the original expression becomes:
14 − 1/2 + 12 − 1/4 + 35 + 2/5
To add these fractions and whole numbers, we need to find a common denominator.
The common denominator for 2, 4, and 5 is 20.
Converting each fraction to have a denominator of 20:
14 = 280/20
-1/2 = -10/20
12 = 240/20
-1/4 = -5/20
35 = 700/20
2/5 = 8/20
The revised expression becomes:
280/20 - 10/20 + 240/20 - 5/20 + 700/20 + 8/20
Now we can simplify and compute the sum:
(280 - 10 + 240 - 5 + 700 + 8) / 20 = 1213/20
Therefore, the expression that represents the sum using fractions is:
A) 1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
Consider this expression:
1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4
Find the sum.
Responses
A 0
B 1
C 1 1/2
D 1/2
To find the sum of 1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4, we need to combine the fractions and decimals.
Let's convert the decimals to fractions:
0.5 can be written as 1/2.
0.25 can be written as 1/4.
0.4 can be written as 2/5.
The expression now becomes:
1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
To add these fractions, we need to find a common denominator. The common denominator for 4, 2, and 5 is 20.
(1/4) * (5/5) = 5/20
(1/2) * (10/10) = 10/20
(1/2) * (10/10) = 10/20
(1/4) * (5/5) = 5/20
Now, the expression is:
5/20 − 10/20 + 10/20 − 5/20 + 3/5 + 2/5
Combining the like terms, we get:
(5 − 10 + 10 − 5)/20 + 3/5 + 2/5
= 0/20 + 3/5 + 2/5
= 0 + 3/5 + 2/5
= (3 + 2) / 5
= 5/5
= 1
Therefore, the simplified sum of the expression is 1.
The correct answer is B) 1.
Consider this expression:
1/4 − 0.5 + 1/2 − 0.2/5 + 3/5 + 0.4
Question 1
You are asked to find the sum by using fractions. Which expression could you use?
Responses
A 1/4 − 1/2 + 1/2 − 1/4+ 3/5 + 2/5
B 1/4 − 1/4 + 1/2 − 1/4+ 3/5 + 2/5
C 1/4 − 1/2 + 1/2 − 1/4+ 4/5 + 2/5
D 1/4 − 1/2 − 1/2 − 1/4+ 3/5 + 2/5
To find the sum of 1/4 − 0.5 + 1/2 − 0.2/5 + 3/5 + 0.4 using fractions, we need to convert the decimal numbers into fractions.
0.5 can be written as 1/2.
0.2/5 can be simplified to 0.04, but we'll keep it as a fraction.
So the original expression becomes:
1/4 − 1/2 + 1/2 − 0.04 + 3/5 + 0.4
To add these fractions and the remaining decimal fraction, we need to find a common denominator.
The common denominator for 4, 2, and 5 is 20.
Converting each fraction to have a denominator of 20:
1/4 = 5/20
-1/2 = -10/20
1/2 = 10/20
-0.04 = -0.04 * 20 / 20 = -0.8/20
3/5 = 12/20
0.4 = 0.4 * 20 / 20 = 8/20
The revised expression becomes:
5/20 − 10/20 + 10/20 − 0.8/20 + 12/20 + 8/20
Now we can simplify and compute the sum:
(5 - 10 + 10 - 0.8 + 12 + 8) / 20 = 24.2/20 = 1.21
Therefore, none of the given options (A, B, C, or D) matches the result obtained.
The temperature in Antarctica at noon is 14°F. By 9:00PM, the temperature had dropped by 16.2 degrees. What was the temperature at 9:00PM?
Responses
A –2.2°F–2.2°F
B 2.2°F2.2°F
C –30.2°F–30.2°F
D 30.2°F30.2°F
To find the temperature at 9:00 PM, we need to subtract the temperature drop of 16.2 degrees from the original temperature of 14 degrees.
14°F - 16.2°F = -2.2°F
Therefore, the temperature at 9:00 PM was -2.2°F.
The correct answer is A) –2.2°F.
Evaluate this expression.
75.5 − 32.55
Responses
A 33.6533.65
B 41.6541.65
C 42.9542.95
D 108.05
To evaluate the expression 75.5 - 32.55, simply subtract the decimal numbers:
75.5 - 32.55 = 42.95
Therefore, the value of the expression is 42.95.
The correct answer is C) 42.95.