Explain how you can mentally find the sum of 3 2/3 + 4 1/5 + 1 1/3 + 2 3/5
Add the whole numbers first to obtain 3+4+1+2 = 10
Then note that 2/3 + 1/3 = 3/3 = 1 which now makes 11. You have 1/5 + 3/5 left to make 4/5 so total is 11 4/5.
To mentally find the sum of 3 2/3 + 4 1/5 + 1 1/3 + 2 3/5, you can follow these steps:
1. Convert all the mixed fractions to improper fractions.
- 3 2/3 = (3 * 3 + 2) / 3 = 11/3
- 4 1/5 = (4 * 5 + 1) / 5 = 21/5
- 1 1/3 = (1 * 3 + 1) / 3 = 4/3
- 2 3/5 = (2 * 5 + 3) / 5 = 13/5
2. Find a common denominator for all the fractions.
The common denominator for 3, 5, and 3 is 15.
3. Convert all the fractions to have the common denominator of 15.
- 11/3 = (11/3) * (5/5) = 55/15
- 21/5 = (21/5) * (3/3) = 63/15
- 4/3 = (4/3) * (5/5) = 20/15
- 13/5 = (13/5) * (3/3) = 39/15
4. Add the fractions together.
- 55/15 + 63/15 + 20/15 + 39/15 = (55 + 63 + 20 + 39) / 15 = 177/15
5. Simplify the fraction (if possible).
- 177/15 is already in its simplest form.
So, the sum of 3 2/3 + 4 1/5 + 1 1/3 + 2 3/5 is equal to 177/15.
To mentally find the sum of 3 2/3, 4 1/5, 1 1/3, and 2 3/5, you can follow these steps:
1. Convert the mixed numbers to improper fractions:
3 2/3 = (3 × 3 + 2) / 3 = 11/3
4 1/5 = (4 × 5 + 1) / 5 = 21/5
1 1/3 = (1 × 3 + 1) / 3 = 4/3
2 3/5 = (2 × 5 + 3) / 5 = 13/5
2. Find a common denominator for all the fractions, which in this case is 15 (the least common multiple of 3 and 5).
3. Convert all the fractions to have the same denominator of 15:
11/3 = (11/3) × (5/5) = 55/15
21/5 = (21/5) × (3/3) = 63/15
4/3 = (4/3) × (5/5) = 20/15
13/5 = (13/5) × (3/3) = 39/15
4. Add the converted fractions together:
55/15 + 63/15 + 20/15 + 39/15 = 177/15
5. Simplify the fraction if necessary:
In this case, the fraction is already in its simplest form.
So, the sum of 3 2/3, 4 1/5, 1 1/3, and 2 3/5 is 177/15.