What is the value of the expression −6 4/9 −1 1/3
A 7 7/9
B -7 7/9
C 5 1/9
D -5 1/9
To find the value of the expression, we can subtract the mixed numbers separately. First, we subtract the whole numbers: -6 - 1 = -7. Next, we subtract the fractions: 4/9 - 1/3.
To subtract the fractions, we need a common denominator. The common denominator of 9 and 3 is 9, so we can rewrite the fractions with 9 as the denominator:
4/9 = (4/9) x (3/3) = 12/27
1/3 = (1/3) x (9/9) = 9/27
Now we can subtract the fractions:
12/27 - 9/27 = 3/27 = 1/9
Combining the whole numbers and the fraction together, we get:
-7 1/9
Therefore, the value of the expression is option B, -7 1/9.
7.4 − (−3.7)
To subtract a negative number, you can think of it as adding the opposite.
So, 7.4 - (-3.7) can be rewritten as 7.4 + 3.7.
Adding 7.4 and 3.7, we get:
7.4 + 3.7 = 11.1
Therefore, the value of the expression 7.4 - (-3.7) is 11.1.
What is 4−1 1/4+1/2
To simplify the expression, we need to first convert the mixed number 1 1/4 to an improper fraction.
1 1/4 = (4 * 1 + 1) / 4 = 5/4
Now we can rewrite the expression:
4 - 5/4 + 1/2
To add or subtract fractions, we need to have a common denominator. The common denominator of 4 and 2 is 4, so we can rewrite the fractions with 4 as the denominator:
4 = 16/4
5/4 (already in terms of 4)
1/2 = (1/2) x (2/2) = 2/4
Rewriting the expression with a common denominator, we get:
16/4 - 5/4 + 2/4
Now we can subtract the fractions:
16/4 - 5/4 + 2/4 = (16 - 5 + 2)/4 = 13/4
The simplified expression is 13/4.
However, we can still simplify the fraction further. Notice that 13 is a prime number, and 13/4 cannot be simplified any further.
Therefore, the value of the expression 4 - 1 1/4 + 1/2 is 13/4.
To simplify the expression −6 4/9 −1 1/3, we need to find a common denominator for the fractions.
The common denominator for 9 and 3 is 9.
So, we can convert 4/9 to a fraction with a denominator of 9 by multiplying the numerator and denominator by 9:
4/9 * 9/9 = 36/81
Similarly, we can convert 1/3 to a fraction with a denominator of 9 by multiplying the numerator and denominator by 3:
1/3 * 3/3 = 3/9
Now we can rewrite the expression as:
-6 36/81 - 1 3/9
Next, we need to find a common whole number for the mixed numbers. We can write -6 as -6 0/1 and -1 as -1 0/1.
So the expression becomes:
-6 36/81 - 1 3/9 = -6 36/81 - 1 3/9
Now, we can add the whole numbers and fractions separately.
First, let's add the whole numbers: -6 - 1 = -7
Now let's add the fractions:
36/81 + 3/9 = (36 * 3)/(81 * 3) + (3 * 9)/(9 * 9) = 108/243 + 27/81 = 135/243 = 5/9
Therefore, the simplified value of the expression −6 4/9 −1 1/3 is -7 5/9.
So, the correct answer is B) -7 5/9.
To find the value of the expression −6 4/9 −1 1/3, we need to perform subtraction with mixed numbers.
First, let's convert the mixed numbers to improper fractions:
-6 4/9 can be written as -(6 * 9 + 4) / 9 = -58/9
-1 1/3 can be written as -(1 * 3 + 1) / 3 = -4/3
Now, subtract the two fractions:
-58/9 - (-4/3)
To subtract fractions, we need a common denominator. In this case, the common denominator of 9 and 3 is 9.
Rewriting the fractions with a common denominator:
(-58/9) - (-4/3) = (-58/9) - (-12/9)
Subtract the numerators and keep the denominator the same:
(-58 + 12)/9 = -46/9
Finally, convert the improper fraction back to a mixed number:
-46/9 = -(46/9) = -(5 1/9)
Therefore, the value of the expression −6 4/9 −1 1/3 is D) -5 1/9.