Jon spent 1/3 of his study time doing math homework and 2/7 preparing fo a history exam what fraction of study time remains?=2/21
1/3 = 7/21
2/7 = 6/21
7/21 + 6/21 = 13/21
21/21 - 13/21 = ?
To determine the fraction of study time that remains, we need to find the fraction of time Jon spent on math homework and preparing for the history exam.
Let's start by finding the fraction of time Jon spent on math homework. We are given that Jon spent 1/3 of his study time doing math homework. Therefore, 1/3 represents the fraction of his study time spent on math homework.
Next, we need to find the fraction of time Jon spent preparing for the history exam. We are given that he spent 2/7 of his study time preparing for the history exam. So, 2/7 represents the fraction of his study time spent on preparing for the history exam.
To find the fraction of study time that remains, we need to subtract the fractions of time spent on math homework and preparing for the history exam from 1. Therefore, we subtract (1/3 + 2/7) from 1:
1 - (1/3 + 2/7)
To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 7 is 21. So, we can rewrite the expression as:
1 - ((7/21) + (6/21))
Now, we can add the numerators together since we have a common denominator:
1 - (13/21)
To subtract fractions with the same denominator, we subtract the numerators:
(21/21) - (13/21) = 8/21
Therefore, the fraction of study time that remains is 8/21.