$12 / 16 + 7 / 8 = $
Select one:
a. $26 / 8$
b. $1-1 / 16$
c. $1-1 / 8$
d. $1-5 / 8$
Answer (2)
Simplify the fraction 16 12 to 4 3 .
Find a common denominator for 4 3 and 8 7 , which is 8. Convert 4 3 to 8 6 .
Add the fractions: 8 6 + 8 7 = 8 13 .
Convert the improper fraction 8 13 to a mixed number: 1 8 5 . The closest option is d. 1 − 5/8 if we assume it was a typo and it meant 1 + 5/8 . So the answer is 1 − 5/8
Explanation
Understanding the Problem We are given the expression 12/16 + 7/8 and asked to select the correct simplified answer from the options a. 26/8 , b. 1 − 1/16 , c. 1 − 1/8 , d. 1 − 5/8 .
The problem requires us to add two fractions and simplify the result. The options are given as either improper fractions or mixed numbers, so we should convert our answer to one of these forms to compare.
Simplifying the First Fraction First, let's simplify the fraction 12/16 by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us: 16 12 = 16 ÷ 4 12 ÷ 4 = 4 3 So, the expression becomes 4 3 + 8 7 .
Finding a Common Denominator To add the two fractions, we need to find a common denominator. The least common multiple of 4 and 8 is 8. We convert 4 3 to an equivalent fraction with a denominator of 8 by multiplying both the numerator and denominator by 2: 4 3 = 4 × 2 3 × 2 = 8 6 Now the expression is 8 6 + 8 7 .
Adding the Fractions Now we can add the two fractions: 8 6 + 8 7 = 8 6 + 7 = 8 13 So, the sum is 8 13 .
Converting to a Mixed Number Now, let's convert the improper fraction 8 13 to a mixed number. We divide 13 by 8: 13 ÷ 8 = 1 with a remainder of 5 . So, 8 13 = 1 8 5 .
Comparing with the Options Comparing our result 1 8 5 with the given options: a. 26/8 is not equal to 13/8 .
b. 1 − 1/16 = 15/16 is not equal to 13/8 .
c. 1 − 1/8 = 7/8 is not equal to 13/8 .
d. 1 − 5/8 is incorrect, it should be 1 + 5/8 However, option d is written as 1 − 5/8 which equals 3/8 . The correct way to write it is 1 8 5 . Since 1 8 5 = 8 13 , the closest answer is d, but it is written incorrectly. The correct answer should be 1 8 5 .
Checking the Options Again Since 1 8 5 = 8 13 , we need to check which of the options is equal to 8 13 .
Option a. is 8 26 which is not equal to 8 13 .
We know that 1 8 5 = 8 8 + 8 5 = 8 13 .
Option d. is 1 − 8 5 = 8 8 − 8 5 = 8 3 which is not equal to 8 13 .
However, if option d was 1 8 5 , then it would be the correct answer.
Final Answer The correct answer is 1 8 5 , which is equal to 8 13 . However, among the given options, option d, 1 − 5/8 , is written incorrectly. It should be 1 + 5/8 . Therefore, the correct answer is d. 1 − 5/8 if we assume it was a typo and it meant 1 + 5/8 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add and simplify fractions is essential for accurate calculations in these situations. For example, if you are following a recipe that calls for 1/4 cup of flour and you want to double the recipe, you need to know that 1/4 + 1/4 = 1/2 , so you need 1/2 cup of flour.
To solve 16 12 + 8 7 , we simplify to 4 3 + 8 7 , find a common denominator of 8, and add to get 8 13 , which is equivalent to the mixed number 1 8 5 . Among the options provided, option d appears to be the closest match if we interpret it as a typo. Therefore, I would choose option d.
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