5/8 + 1 7/9 +3. Simplify the expression
A) 4 29/72
B) 4 12/17
C) 5 7/18
D) 5 29/72
5/8 + 1 7/9 + 3
45/72 + 1 56/72 + 3
4 101/72
5 29/72
by inspection , the sum is over 5 , and the denominator is 72
To simplify the expression 5/8 + 1 7/9 + 3, we need to convert the mixed number 1 7/9 into an improper fraction and find a common denominator among all the fractions.
Let's start by converting 1 7/9 into an improper fraction:
1 7/9 = (9 * 1 + 7)/9 = 16/9
Now, we need to find a common denominator among 8, 9, and 1:
The least common multiple of 8 and 9 is 72, so we can use that as the common denominator.
Now, let's rewrite each fraction with the common denominator:
5/8 = (5 * 9)/(8 * 9) = 45/72
16/9 = (16 * 8)/(9 * 8) = 128/72
3 can be expressed as 3/1 since any whole number can be written as a fraction with a numerator and a denominator of 1. Therefore, 3/1.
Now, we can add the fractions:
45/72 + 128/72 + 3/1 = (45 + 128 + 216)/72 = 389/72
Next, we can simplify the fraction 389/72:
The simplified mixed number is 5 with a remainder of 29, so the answer is 5 29/72.
Therefore, the simplified expression 5/8 + 1 7/9 + 3 is equal to 5 29/72.
The answer is D) 5 29/72.
To simplify the expression 5/8 + 1 7/9 + 3, we need to convert all the mixed numbers into improper fractions and then find a common denominator to add them together.
Step 1: Convert the mixed numbers into improper fractions:
1 can be written as 9/9 because it's a whole number.
1 7/9 can be simplified to (9 * 1 + 7)/9 = 16/9.
Step 2: Find a common denominator:
The denominators are 8 and 9, which are not divisible evenly. To find a common denominator, we multiply the two denominators together: 8 * 9 = 72.
Step 3: Convert all the fractions to have a denominator of 72:
5/8 can be simplified to (5 * 9)/ (8 * 9) = 45/72
9/9 remains the same.
16/9 can be simplified to (16 * 8)/(9 * 8) = 128/72.
Now, we have the expression: 45/72 + 9/9 + 128/72.
Step 4: Add the fractions together:
To add fractions with the same denominator, we add their numerators and keep the denominator the same.
(45 + 9 + 128)/72 = 182/72.
Step 5: Simplify the fraction:
182/72 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. 182 divided by 2 is 91, and 72 divided by 2 is 36.
So, 182/72 simplifies to 91/36.
Step 6: Convert the improper fraction into a mixed number:
91/36 can be simplified to 2 19/36.
Therefore, the simplified expression 5/8 + 1 7/9 + 3 is equal to 2 19/36, which corresponds to option B) 4 12/17.