3.) To add these fractions, we need to first convert the mixed number to an improper fraction:
2 5/8 = (2 x 8 + 5) / 8 = 21/8
Now we can add the fractions:
2 5/8 + 32/7 = (21/8) + (32/7)
To add these fractions, we need to find a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite the fractions with this denominator:
2 5/8 + 32/7 = (21/8) x (7/7) + (32/7) x (8/8) = 147/56 + 256/56
Now we can add the numerators:
2 5/8 + 32/7 = (147 + 256) / 56 = 403/56
We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor of 403 and 56, which is 1:
2 5/8 + 32/7 = 403/56 (fully simplified)
4.) 3/8 + 5/8 = (3 + 5) / 8 = 8/8 = 1
5.) To add these mixed numbers, we need to first convert them to improper fractions:
7 3/4 = (7 x 4 + 3) / 4 = 31/4
1 1/8 = (1 x 8 + 1) / 8 = 9/8
Now we can add the fractions:
7 3/4 + 1 1/8 = (31/4) + (9/8)
To add these fractions, we need to find a common denominator. The least common multiple of 4 and 8 is 8, so we can rewrite the fractions with this denominator:
7 3/4 + 1 1/8 = (31/4) x (2/2) + (9/8) x (1/1) = 62/8 + 9/8
Now we can add the numerators:
7 3/4 + 1 1/8 = (62 + 9) / 8 = 71/8
We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor of 71 and 8, which is 1:
Answers & Comments
2.) -4/9 + 3/9 = (-4 + 3) / 9 = -1/9
3.) To add these fractions, we need to first convert the mixed number to an improper fraction:
2 5/8 = (2 x 8 + 5) / 8 = 21/8
Now we can add the fractions:
2 5/8 + 32/7 = (21/8) + (32/7)
To add these fractions, we need to find a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite the fractions with this denominator:
2 5/8 + 32/7 = (21/8) x (7/7) + (32/7) x (8/8) = 147/56 + 256/56
Now we can add the numerators:
2 5/8 + 32/7 = (147 + 256) / 56 = 403/56
We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor of 403 and 56, which is 1:
2 5/8 + 32/7 = 403/56 (fully simplified)
4.) 3/8 + 5/8 = (3 + 5) / 8 = 8/8 = 1
5.) To add these mixed numbers, we need to first convert them to improper fractions:
7 3/4 = (7 x 4 + 3) / 4 = 31/4
1 1/8 = (1 x 8 + 1) / 8 = 9/8
Now we can add the fractions:
7 3/4 + 1 1/8 = (31/4) + (9/8)
To add these fractions, we need to find a common denominator. The least common multiple of 4 and 8 is 8, so we can rewrite the fractions with this denominator:
7 3/4 + 1 1/8 = (31/4) x (2/2) + (9/8) x (1/1) = 62/8 + 9/8
Now we can add the numerators:
7 3/4 + 1 1/8 = (62 + 9) / 8 = 71/8
We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor of 71 and 8, which is 1:
7 3/4 + 1 1/8 = 71/8 (fully simplified)