Question

2)4 + ( - 8) - 19 - ( - 15) - 40 3)5 7/8+(3 5/12)-(-1 7/16)

Answer 1

2) 4-8-19+15-40=-48
3) 57/8+35/12+17/16=533/48

Answer 2

Let's solve the two arithmetic expressions step by step:

1. 4 + (-8) - 19 - (-15) - 40

To simplify this expression, follow the order of operations (PEMDAS):

1. Parentheses (or Brackets)
2. Exponents (or Powers)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Now, there are no exponents or multiplication/division operations in this expression. We have only addition and subtraction. So, let's start by simplifying the expression:

4 + (-8) - 19 - (-15) - 40

Step 1: Simplify inside the parentheses: 4 + (-8) = -4 -(-15) = +15

Step 2: Continue with addition and subtraction from left to right: -4 - 19 + 15 - 40

Step 3: Perform addition and subtraction: -4 - 19 = -23 -23 + 15 = -8 -8 - 40 = -48

The result of the expression is -48.

2. 5 7/8 + (3 5/12) - (-1 7/16)

To simplify this expression, let's first convert mixed numbers to improper fractions:

5 7/8 = (5 * 8 + 7) / 8 = 47/8 3 5/12 = (3 * 12 + 5) / 12 = 41/12 -1 7/16 = (-1 * 16 + 7) / 16 = -9/16

Now, the expression becomes:

47/8 + 41/12 - (-9/16)

To add and subtract fractions, we need to find a common denominator, which is 48 (the least common multiple of 8, 12, and 16):

47/8 = (47/8) * (6/6) = 282/48 41/12 = (41/12) * (4/4) = 164/48 -9/16 = (-9/16) * (3/3) = -27/48

Now, the expression becomes:

282/48 + 164/48 - (-27/48)

Now, perform the addition and subtraction:

282/48 + 164/48 = 446/48

446/48 - (-27/48) = 446/48 + 27/48 = 473/48

The result of the expression is 473/48. If you want to simplify this fraction further, you can find the greatest common divisor (GCD) of 473 and 48 and divide both the numerator and denominator by it. However, the expression is already in its simplest form.