1. What is \( \frac{2}{3} - \frac{1}{5} \)?
2. What is \( \frac{3}{4} - \frac{4}{8} \)?
3. What is the value of \( N \) in \( \frac{3}{6} - \frac{1}{5} = -N \)?
4. Find the difference between \( 2 \frac{2}{9} \) and \( \frac{2}{3} \).
Answer (1)
To find 3 2 − 5 1 , we need to have a common denominator. The least common multiple of 3 and 5 is 15.
Convert 3 2 to have a denominator of 15. 3 2 = 3 × 5 2 × 5 = 15 10 .
Convert 5 1 to have a denominator of 15. 5 1 = 5 × 3 1 × 3 = 15 3 .
Now subtract: 15 10 − 15 3 = 15 7 .
To find 4 3 − 8 4 , we first simplify 8 4 because it is equivalent to 2 1 .
Convert 4 3 and 2 1 to have a common denominator of 4: 4 3 − 2 1 .
2 1 = 4 2 .
Now subtract: 4 3 − 4 2 = 4 1 .
To solve for N in 6 3 − 5 1 = − N , first simplify 6 3 to 2 1 .
Convert 2 1 and 5 1 to have a common denominator of 10.
2 1 = 10 5 and 5 1 = 10 2 .
Now subtract: 10 5 − 10 2 = 10 3 .
So, N = − 10 3 .
To find the difference between 2 9 2 and 3 2 :
First, convert 2 9 2 to an improper fraction. 2 9 2 = 9 18 + 9 2 = 9 20 .
Convert 3 2 to have a denominator of 9. 3 2 = 9 6 .
Now subtract: 9 20 − 9 6 = 9 14 .
Therefore, the differences are 15 7 , 4 1 , N = − 10 3 , and 9 14 .
