Evaluate the numerical expression. 1/2 − (−3/4)
To evaluate the expression 1/2 - (-3/4), we simplify it step by step:
First, let's simplify the subtraction of fractions:
1/2 - (-3/4) = 1/2 + 3/4
To add fractions, they need a common denominator. In this case, the common denominator is 4.
1/2 + 3/4 = 2/4 + 3/4
Now, we can add the fractions, keeping the common denominator:
2/4 + 3/4 = (2 + 3)/4 = 5/4
Therefore, the expression 1/2 - (-3/4) simplifies to 5/4.
Evaluate this expression.
75.5 − 32.55
To evaluate the expression 75.5 - 32.55, subtract 32.55 from 75.5:
75.5 - 32.55 = 42.95
Therefore, the expression 75.5 - 32.55 equals 42.95.
Evaluate this expression.
32 + (−72.1)
To evaluate the expression 32 + (-72.1), we perform the addition:
32 + (-72.1) = -40.1
Therefore, the expression 32 + (-72.1) equals -40.1.
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?
To find the temperature at 9:00 PM, we need to subtract 16.2 degrees from the temperature at noon.
Temperature at 9:00 PM = Temperature at noon - Temperature drop
Temperature at 9:00 PM = 14°F - 16.2°F
Performing the subtraction:
Temperature at 9:00 PM = -2.2°F
Therefore, the temperature at 9:00 PM was -2.2°F.
Determine the value of the expression –5.45 + 4.12 –8.66.
To determine the value of the expression –5.45 + 4.12 –8.66, we perform the addition and subtraction:
–5.45 + 4.12 – 8.66 = -1.33 - 8.66
Now, subtracting:
-1.33 - 8.66 = -9.99
Therefore, the value of the expression –5.45 + 4.12 –8.66 is -9.99.
Simplify.
7.829 − 3.21
To simplify the expression 7.829 - 3.21, we perform the subtraction:
7.829 - 3.21 = 4.619
Therefore, the simplified expression is 4.619.
Simplify.
7 /23 +− 5 1/4
To simplify the expression 7/23 - 5 1/4, we need to convert the mixed number 5 1/4 into an improper fraction.
First, let's convert 5 1/4 into an improper fraction:
5 1/4 = (4 * 5 + 1) / 4 = 21/4
Now we can rewrite the expression:
7/23 - 21/4
To subtract fractions, we need a common denominator. In this case, the common denominator is 4.
7/23 - 21/4 = (7/23) * (4/4) - 21/4 = 28/92 - 21/4
Now, we can subtract the fractions, keeping the common denominator:
28/92 - 21/4 = (28 - (21 * 23))/92 = (28 - 483)/92 = -455/92
Therefore, the simplified expression is -455/92.
Simplify.
7 2/3 +− 5 1/4
A -2
B 2 5/12
C 2 11/12
D 12 11/12
To simplify the expression 7 2/3 - 5 1/4, we need to convert the mixed numbers into improper fractions.
7 2/3 is equivalent to (3 * 7 + 2) / 3 = 23/3
5 1/4 is equivalent to (4 * 5 + 1) / 4 = 21/4
Now we can rewrite the expression:
23/3 - 21/4
To subtract fractions, we need a common denominator. In this case, the common denominator is 12.
23/3 - 21/4 = (23/3) * (4/4) - (21/4) * (3/3) = 92/12 - 63/12
Now, we can subtract the fractions, keeping the common denominator:
92/12 - 63/12 = (92 - 63) / 12 = 29/12
Therefore, the expression 7 2/3 - 5 1/4 simplifies to 2 5/12.
Answer: B) 2 5/12
Add and Subtract Rational Numbers
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 14 − 1/2 + 1/2 − 1/4+ 3/5 + 2/5
B 14 − 14 + 12 − 14+ 35 + 251 4 − 1 4 + 1 2 − 1 4 + 3 5 + 2 5
C 14 − 12 + 12 − 14+ 45 + 251 4 − 1 2 + 1 2 − 1 4 + 4 5 + 2 5
D 14 − 12 − 12 − 14+ 35 + 251 4 − 1 2 − 1 2 − 1 4 + 3 5 + 2 5
Question 2
Find the sum.
Responses
A 00
B 11
C 1121 1 2
D 12
For question 1, the expression that correctly represents the given expression using fractions is:
A) 14 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
For question 2, we need to simplify the expression:
14 − 0.5 + 12 − 0.25 + 35 + 0.4
Using the correct expression in option A:
14 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
Now, we can add and subtract the fractions and whole numbers separately:
14 - 1/2 + 1/2 - 1/4 + 3/5 + 2/5 = 13 ½ - ¼ + 6/5
To add and subtract fractions, we need a common denominator. The common denominator for 2, 4, and 5 is 20.
13 ½ - ¼ + 6/5 = 13 * 20/20 + 10/20 - 4/20 + 24/20
Simplifying the fractions, we get:
260/20 + 10/20 - 4/20 + 24/20 = 290/20
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10:
290/20 = 29/2
Therefore, the sum of the given expression is:
C) 29/2 or 14 ½
Evaluate this expression.
42.86 − 23.42
To evaluate the expression 42.86 - 23.42, we subtract 23.42 from 42.86:
42.86 - 23.42 = 19.44
Therefore, the expression 42.86 - 23.42 equals 19.44.
Evaluate 4 1/2 − 2 − 5 2/3
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to convert the mixed numbers into improper fractions.
4 1/2 is equivalent to (2 * 4 + 1) / 2 = 9/2
5 2/3 is equivalent to (3 * 5 + 2) / 3 = 17/3
Now we can rewrite the expression:
9/2 - 2 - 17/3
To subtract fractions, we need a common denominator. In this case, the common denominator is 6.
9/2 - 2 - 17/3 = (9/2) * (3/3) - (2 * 3/3) - (17/3) * (2/2)
= 27/6 - 6/6 - 34/6
Now we can subtract the fractions, keeping the common denominator:
27/6 - 6/6 - 34/6 = (27 - 6 - 34) / 6 = -13/6
Therefore, the expression 4 1/2 - 2 - 5 2/3 simplifies to -13/6.