Question

5 8/12 + 1 8/3, 6 6/50 - 3 9/75, 2 1/7 * 2 4/5, 2 2/16 : 1 2/32

Answer 1

58/12 + 18/3 = 76/42

66/50 - 39/75 = 27/35

21/7 × 24/5 = 531/65

22/16 : 12/32 = 1/7

Answer 2

To perform the given arithmetic operations involving mixed numbers, follow these steps for each operation:

1. Convert mixed numbers to improper fractions.
2. Perform the required operation (addition, subtraction, multiplication, or division) with the improper fractions.
3. If necessary, simplify the result back to a mixed number.

Let's go through each of the given operations:

1. Addition: 5 8/12 + 1 8/3

Step 1: Convert mixed numbers to improper fractions. 5 8/12 = (5 * 12 + 8) / 12 = 68 / 12 1 8/3 = (1 * 3 + 8) / 3 = 11 / 3

Step 2: Add the improper fractions. 68 / 12 + 11 / 3 = (68 * 3 + 11 * 12) / (12 * 3) = (204 + 132) / 36 = 336 / 36

Step 3: Simplify the result. 336 / 36 = 9 (remainder: 12/36, which simplifies to 1/3)

So, 5 8/12 + 1 8/3 = 9 1/3.

2. Subtraction: 6 6/50 - 3 9/75

Step 1: Convert mixed numbers to improper fractions. 6 6/50 = (6 * 50 + 6) / 50 = 306 / 50 3 9/75 = (3 * 75 + 9) / 75 = 234 / 75

Step 2: Subtract the improper fractions. 306 / 50 - 234 / 75 = (306 * 3 - 234 * 2) / (50 * 3) = (918 - 468) / 150 = 450 / 150

Step 3: Simplify the result. 450 / 150 = 3 (remainder: 0, no simplification needed)

So, 6 6/50 - 3 9/75 = 3.

3. Multiplication: 2 1/7 * 2 4/5

Step 1: Convert mixed numbers to improper fractions. 2 1/7 = (2 * 7 + 1) / 7 = 15 / 7 2 4/5 = (2 * 5 + 4) / 5 = 14 / 5

Step 2: Multiply the improper fractions. (15 / 7) * (14 / 5) = (15 * 14) / (7 * 5) = 210 / 35

Step 3: Simplify the result. 210 / 35 = 6 (remainder: 0, no simplification needed)

So, 2 1/7 * 2 4/5 = 6.

4. Division: 2 2/16 : 1 2/32

Step 1: Convert mixed numbers to improper fractions. 2 2/16 = (2 * 16 + 2) / 16 = 34 / 16 1 2/32 = (1 * 32 + 2) / 32 = 34 / 32

Step 2: Divide the improper fractions. (34 / 16) : (34 / 32) = (34 / 16) * (32 / 34) [Dividing is the same as multiplying by the reciprocal] = (34 * 32) / (16 * 34) = 32 / 16 = 2

Step 3: Simplify the result (no simplification needed).

So, 2 2/16 : 1 2/32 = 2.

Final results:

1. 5 8/12 + 1 8/3 = 9 1/3
2. 6 6/50 - 3 9/75 = 3
3. 2 1/7 * 2 4/5 = 6
4. 2 2/16 : 1 2/32 = 2