what is 12 8/15 − 7 + 7/15 + 15 in simplest form
To simplify the expression 12 8/15 - 7 + 7/15 + 15, we need to convert the mixed number 12 8/15 into an improper fraction.
12 8/15 is equal to (12 * 15 + 8) / 15 = 188/15.
Now we can substitute the values into the expression:
188/15 - 7 + 7/15 + 15
To combine fractions, we need to find a common denominator, which is 15 in this case.
Rewriting the expression with a common denominator:
(188 - 7 * 15 + 7 + 15 * 15) / 15
Simplifying the numerator:
(188 - 105 + 7 + 225) / 15
Combining like terms:
(315 + 7 + 225) / 15
(547/15) / 15
To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number:
(547/15) * (1/15)
Multiplying the numerators and denominators:
547/ (15*15)
Simplifying the denominator:
547/225
Therefore, 12 8/15 − 7 + 7/15 + 15 can be simplified to 547/225.
How should you group the following expression to make it easiest to add? 18 − 949 + 79 − 8(1 point)
Responses
(18 − 8) + (−949 + 79)
Left Parenthesis 18 minus 8 Right Parenthesis plus Left Parenthesis negative 9 Start Fraction 4 over 9 End Fraction plus Start Fraction 7 over 9 End Fraction Right Parenthesis
(18 − 9 − 8) + (−49 + 79)
Left Parenthesis 18 minus 9 minus 8 Right Parenthesis plus Left Parenthesis negative Start Fraction 4 over 9 End Fraction plus Start Fraction 7 over 9 Right Parenthesis
(8 − 18) + (49 + 79)
Left Parenthesis 8 minus 18 Right Parenthesis plus Left Parenthesis Start Fraction 4 over 9 End Fraction plus Start Fraction 7 over 9 End Fraction Right Parenthesis
(18 − 8 − 9)
To make it easiest to add, we can group the terms that have the same sign or can be simplified together:
(18 − 8) + (−949 + 79)
This grouping allows us to simplify the subtraction within the parentheses (18 - 8 = 10) and the addition within the second set of parentheses (-949 + 79 = -870).
Therefore, the expression should be grouped as:
(18 − 8) + (−949 + 79)
What should you do if a place value is missing a number?(1 point)
Responses
Subtract without it.
Subtract without it.
Remove the last digit(s) in the number that has the additional place values.
Remove the last digit(s) in the number that has the additional place values.
Nothing.
Nothing.
Add a zero.
Add a zero.
To simplify the expression 12 8/15 − 7 + 7/15 + 15, we need to perform the operations in the correct order, starting with any addition or subtraction within parentheses, then any multiplication or division, and finally any addition or subtraction.
First, let's simplify the mixed number 12 8/15. To convert this to an improper fraction, we multiply the whole number (12) by the denominator of the fraction (15) and then add the numerator (8). This gives us:
12 8/15 = (12 * 15 + 8)/15 = 188/15
Now, our expression becomes:
188/15 − 7 + 7/15 + 15
Next, let's add the fractions and simplify. To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 15 and 1 is 15. Therefore, we can rewrite 7 as 7 * 15/15:
188/15 − 7/15 * 15/15 + 7/15 + 15
Simplifying further:
188/15 − 105/15 + 7/15 + 15
Now we can subtract the fractions:
(188 - 105 + 7)/15 + 15
Simplifying the numerator:
(90)/15 + 15
Dividing the numerator by the denominator:
6 + 15
Adding the whole numbers:
6 + 15 = 21
Therefore, 12 8/15 − 7 + 7/15 + 15 simplified to 21.
To simplify the expression 12 8/15 - 7 + 7/15 + 15, we need to perform the calculations in a specific order.
Step 1: Convert the mixed number 12 8/15 to an improper fraction.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, keep the same denominator.
12 8/15 = (12 x 15 + 8) / 15 = 188/15
So, our expression becomes: 188/15 - 7 + 7/15 + 15
Step 2: Find a common denominator.
To add or subtract fractions, we need to have a common denominator. In this case, the denominators are already the same, so no additional steps are needed.
Step 3: Perform the calculations.
188/15 - 7 + 7/15 + 15 = (188 - 7 + 7) / 15 + 15
= 188 / 15 + 15
Step 4: Add the fractions.
To add fractions with the same denominator, we add their numerators while keeping the denominator unchanged.
188/15 + 15 = (188 + 15 * 15) / 15
= (188 + 225) / 15
= 413/15
So, the simplified form of the expression 12 8/15 - 7 + 7/15 + 15 is 413/15.