jon spent 1/2 of his study time doing math homework and 2/7 proparing for a history exam. Waht fraction of his study time remains?
1/2 + 2/7 = 7/14 + 4/14 = 11/14
Now, subtract 11/14 from 14/14.
3/14
To find the fraction of Jon's study time that remains, we need to subtract the fractions that represent the time he spent on math homework and preparing for the history exam from 1 (since 1 represents the whole study time).
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.