Simplify negative 7 and 1 over 8 − negative 9 and 1 over 2 . (5 points)
negative 2 and 3 over 8
negative 16 and 5 over 8
16 and 5 over 8
2 and 3 over 8
To simplify negative 7 and 1/8 - negative 9 and 1/2, first we need to convert both mixed numbers into improper fractions.
Negative 7 and 1/8 is equal to -7 + 1/8 = -56/8 + 1/8 = -55/8.
Negative 9 and 1/2 is equal to -9 + 1/2 = -18/2 + 1/2 = -17/2.
Now that both numbers are in the form of improper fractions, we can subtract them:
-55/8 - (-17/2)
= -55/8 + 17/2
Next, we need to find a common denominator for the fractions -55/8 and 17/2. The least common multiple of 8 and 2 is 8.
Therefore, we need to rewrite -55/8 as an equivalent fraction with a denominator of 8:
-55/8 = -55/8 * (1/1) = -55/8 * (2/2) = -110/16.
Now we can subtract the fractions:
-110/16 + 17/2
= -110/16 + 136/16
= (136 - 110)/16
= 26/16.
Lastly, we can simplify 26/16 by dividing both the numerator and denominator by their greatest common divisor, which is 2:
26/16 = (26 ÷ 2) / (16 ÷ 2)
= 13/8.
Therefore, the simplified form of negative 7 and 1/8 - negative 9 and 1/2 is 13/8 or 1 and 5/8.
To simplify the expression -7 and 1/8 - (-9 and 1/2), you can follow these steps:
1. Simplify each mixed number separately by converting them into improper fractions:
-7 and 1/8 = -7 + 1/8 = -56/8 + 1/8 = -55/8
-9 and 1/2 = -9 + 1/2 = -18/2 + 1/2 = -17/2
2. Now subtract the two fractions:
-55/8 - (-17/2) = -55/8 + 17/2
3. To add or subtract fractions, you need a common denominator. The least common multiple of 8 and 2 is 8.
4. Convert each fraction to have a common denominator of 8:
-55/8 + 17/2 = -55/8 + (17/2)(4/4) = -55/8 + 68/8
5. Combine the numerators and keep the common denominator:
-55/8 + 68/8 = (-55 + 68)/8 = 13/8
Therefore, the simplified form of -7 and 1/8 - (-9 and 1/2) is -2 and 3/8.
To simplify the expression -7 1/8 - (-9 1/2), you can follow these steps:
1. First, convert the mixed numbers (-7 1/8 and -9 1/2) into improper fractions.
The improper fraction form of -7 1/8 is (-7 * 8 + 1)/8 = -57/8.
The improper fraction form of -9 1/2 is (-9 * 2 + 1)/2 = -17/2.
2. Next, subtract the two fractions after finding a common denominator. In this case, the common denominator is 8.
(-57/8) - (-17/2) = (-57/8) + (17/2)
3. To add the fractions, perform the necessary operations:
To add fractions with different denominators, you need to find a common denominator. The common denominator for 8 and 2 is 8.
The first fraction needs to be multiplied by 1 in the form of 2/2 to change the denominator to 8.
((-57/8) * (2/2)) + (17/2) = (-114/16) + (17/2)
4. Find a common denominator for the fractions and perform the subtraction:
(-114/16) + (17/2) = (-114/16) + (136/16) = 22/16
5. Finally, simplify the fraction if possible:
22/16 can be simplified to 11/8.
Therefore, the simplified form of -7 1/8 - (-9 1/2) is -2 3/8.