calculate the exact value of
4 1/5 - (1 1/9 * 3)is it=39/45
Yes -- but 39/45 can be reduced to 13/15.
Yes
For 39/45 could you show steps please
5 1/3-(1 1/9×3)
5 1/3- 1 1/9×3
To calculate the exact value of the expression 4 1/5 - (1 1/9 * 3), we need to follow the order of operations.
First, let's simplify the expression within the parentheses:
1 1/9 * 3
To multiply a whole number by a mixed number, we need to convert the whole number to a fraction.
1 can be written as 1/1, so the expression becomes:
1/1 1/9 * 3
To multiply fractions, we multiply the numerators (top numbers) and the denominators (bottom numbers) separately, then simplify if possible.
The expression becomes:
(1*9 + 1)/9 * 3
(9 + 1)/9 * 3
10/9 * 3
To multiply fractions, multiply the numerators and denominators:
(10 * 3)/(9 * 1)
30/9
Now, let's simplify the whole expression:
4 1/5 - (30/9)
To subtract mixed numbers, we need to find the common denominator.
The common denominator of 5 and 9 is 45.
4 1/5 can be converted to an improper fraction as:
(4 * 5 + 1)/5 = 21/5
The expression becomes:
21/5 - (30/9)
Next, we need to convert 30/9 to an equivalent fraction with a denominator of 45.
To do this, we multiply both the numerator and denominator by 5:
(30 * 5)/(9 * 5) = 150/45
Now, let's subtract the fractions:
21/5 - 150/45
To subtract fractions with different denominators, we need to find a common denominator.
The common denominator of 5 and 45 is 45.
Multiplying the numerators and denominators to get the common denominator:
(21 * 9)/(5 * 9) - (150 * 1)/(45 * 1)
189/45 - 150/45
Now, we can subtract the fractions with the same denominator:
(189 - 150)/45 = 39/45
Therefore, the exact value of the expression 4 1/5 - (1 1/9 * 3) is indeed 39/45.