What is 12 8/15 − 7 + 7 1/5 + 15? Simplify your answer.
To simplify the expression 12 8/15 − 7 + 7 1/5 + 15, we first need to add the whole numbers together and then add the fractions together separately.
12 + 7 = 19
Next, let's add the fractions:
8/15 + 1/5 = (8 + 1)/15 = 9/15
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3.
9/15 = (9 ÷ 3)/(15 ÷ 3) = 3/5
Now, we can rewrite the expression:
19 + 3/5 + 15
To add fractions, we need to find a common denominator. The common denominator of 5 and 1 is 5.
19 + 3/5 + 15 = 19 + 3/5 + 75/5
Now that the fractions have the same denominator, we can add them:
19 + 3/5 + 75/5 = 19 + (3 + 75)/5 = 19 + 78/5
To add fractions, we need to once again find a common denominator, which this time will be 5.
19 + 78/5 = (19 × 5)/5 + 78/5 = 95/5 + 78/5 = 173/5
Therefore, 12 8/15 − 7 + 7 1/5 + 15 simplifies to 173/5.
How should you group the following expression to make it easiest to add? 18 − 9 4/9 + 7/9 − 8(1 point)
To make it easiest to add the given expression 18 − 9 4/9 + 7/9 − 8, it is best to group the terms with like terms together. In this case, we have whole numbers, mixed numbers, and fractions.
Let's first group the whole numbers together:
18 - 8
Now let's focus on the mixed numbers:
-9 4/9 + 7/9
Finally, we have the fraction without a whole number:
-9 4/9 + 7/9
Thus, the expression can be grouped as:
18 - 8 - 9 4/9 + 7/9.
To simplify the expression 12 8/15 − 7 + 7 1/5 + 15, we can follow these steps:
Step 1: Convert mixed numbers to improper fractions:
12 8/15 = (12 * 15 + 8) / 15 = 188/15
7 1/5 = (7 * 5 + 1) / 5 = 36/5
Step 2: Add the fractions together:
188/15 - 7 + 36/5 + 15
Step 3: Find a common denominator:
The common denominator for 15 and 5 is 15.
Step 4: Convert the fractions with different denominators to have the same denominator:
(188/15) x (5/5) = 940/75
(36/5) x (15/15) = 540/75
Step 5: Add the fractions together:
940/75 - 7 + 540/75 + 15
Step 6: Simplify the fraction and combine the terms:
(940 + 540) / 75 - 7 + 15
1480 / 75 - 7 + 15
(1480 - 525 + 1125) / 75
2080 / 75
104 / 15
Therefore, the simplified answer is 104/15.