1/2 + 2/7 = 7/14 + 4/14 = 11/14
Now, subtract 11/14 from 14/14.
Now, subtract 11/14 from 14/14.
Jon spent 1/2 of his study time doing math homework, so the fraction representing the time he spent on math homework is 1/2.
Jon also spent 2/7 of his study time preparing for a history exam, so the fraction representing the time he spent on history preparation is 2/7.
To find the remaining fraction of his study time, we can subtract these fractions from 1:
1 - 1/2 - 2/7
To subtract fractions, we need to find a common denominator. The common denominator for 2 and 7 is 14. So we convert 1/2 into an equivalent fraction with 14 as the denominator:
1/2 = 7/14
Now our expression becomes:
1 - 7/14 - 2/7
To perform the subtraction, the fractions need to have the same denominator. Since both fractions already have a denominator of 14, we can subtract the numerators directly:
1 - 7/14 - 2/7 = 1 - (7 + 4)/14
= 1 - 11/14
To subtract fractions with the same denominator, we simply subtract the numerators and keep the common denominator:
1 - 11/14 = (14 - 11)/14
= 3/14
Therefore, the fraction of Jon's study time that remains is 3/14.