Determine the following (convert to a mixed number where relevant).
a) 20 + 10 × (-½) ÷ 5
b) 16 ÷ (3 + 5) × -1 + 2³
c) ½ + ⅓ + ⅜
d) 3⅝ + 4 × -2
e) -1 × -1 ÷ -2 + 3 + 2°
789
A)19
B)6
C)1 (5/24)
D)4,37
E)3,5
To determine the value of each expression and convert them to mixed numbers where relevant, we'll follow the order of operations (PEMDAS/BODMAS).
a) 20 + 10 × (-½) ÷ 5:
Start by calculating the multiplication and division from left to right:
10 × (-½) = -5
Then, divide -5 by 5:
-5 ÷ 5 = -1
Finally, add 20 and -1:
20 + (-1) = 19
So, the answer is 19.
b) 16 ÷ (3 + 5) × -1 + 2³:
Inside the parentheses, calculate the addition:
3 + 5 = 8
Now divide 16 by 8:
16 ÷ 8 = 2
Calculate 2³:
2³ = 2 × 2 × 2 = 8
Finally, multiply 8 by -1 and add 8:
8 × -1 + 8 = -8 + 8 = 0
So, the answer is 0.
c) ½ + ⅓ + ⅜:
To add these fractions, we need to find a common denominator. The lowest common denominator for 2, 3, and 8 is 24 (since 24 is divisible by 2, 3, and 8).
Now, let's convert each fraction to have a denominator of 24:
½ becomes 12/24 (multiplied the numerator and denominator by 12).
⅓ becomes 8/24 (multiplied the numerator and denominator by 8).
⅜ remains 9/24.
Now, add the fractions:
12/24 + 8/24 + 9/24 = 29/24
To convert this improper fraction to a mixed number, divide the numerator by the denominator:
29 ÷ 24 = 1 remainder 5
So, the answer is 1 + 5/24.
d) 3⅝ + 4 × -2:
Multiply 4 by -2:
4 × -2 = -8
Now, add 3⅝ and -8:
3⅝ + (-8) = (3 + (-8)) + ⅝ = -5 + ⅝
So, the answer is -5 + ⅝.
e) -1 × -1 ÷ -2 + 3 + 2°:
First, calculate the multiplication and division from left to right:
-1 × -1 = 1
Then, divide 1 by -2:
1 ÷ -2 = -½
Next, add -½ and 3:
-½ + 3 = 2½
To express 2½ as a mixed number, note that the whole number is 2 and the fraction is ½.
So, the answer is 2 + ½.