Factor 48w + 32x - 24 using the GCF.
To factor the expression 48w + 32x - 24 using the greatest common factor (GCF), we need to find the common factors of all the terms.
Step 1: Find the GCF of the coefficients (48, 32, and 24).
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 32 are: 1, 2, 4, 8, 16, 32
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The common factors of all three numbers are: 1, 2, 4, 8
Step 2: Find the GCF of the variables (w and x).
Since w and x do not have any common factors, the GCF of the variables is 1.
Step 3: Multiply the GCF of the coefficients and the GCF of the variables.
The GCF of the coefficients is 8.
The GCF of the variables is 1.
Therefore, the GCF of the entire expression is 8w + 8x - 6.
Step 4: Divide the original expression by the GCF.
(48w + 32x - 24) ÷ 8 = 6w + 4x - 3
The factored form of 48w + 32x - 24 using the GCF is:
8(6w + 4x - 3)
Add: 5(0.5k - 1) + 2(0.4 - k) Answer should be in decimal form.
To add the expression 5(0.5k - 1) + 2(0.4 - k), we need to distribute the coefficients.
5(0.5k - 1) = 5 * 0.5k - 5 * 1 = 2.5k - 5
2(0.4 - k) = 2 * 0.4 - 2 * k = 0.8 - 2k
Now we can combine like terms:
2.5k - 5 + 0.8 - 2k
Combining the k terms, we have:
(2.5k - 2k) - 5 + 0.8 = 0.5k - 4.2
Therefore, the simplified expression in decimal form is 0.5k - 4.2.
Subtract 1/2 * (z + 4) - 3(1/4 * z + 1) . Use fractions in final form.
To subtract 1/2 * (z + 4) - 3(1/4 * z + 1), we'll first simplify the expressions inside the parentheses, and then perform the subtraction.
1/2 * (z + 4) = (1/2)z + (1/2) * 4
= (1/2)z + 2
3(1/4 * z + 1) = 3 * (1/4)z + 3 *1
= (3/4)z + 3
Now we can substitute these simplified expressions back into the original subtraction equation:
1/2 * (z + 4) - 3(1/4 * z + 1)
= (1/2)z + 2 - (3/4)z - 3
Next, let's rewrite the subtraction as addition with the negative of the second expression:
= (1/2)z + 2 + (-(3/4)z - 3)
Now, we can combine like terms:
= (1/2)z - (3/4)z + 2 - 3
To add or subtract fractions, we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4. So we'll convert both fractions to have a denominator of 4:
= (2/4)z - (3/4)z - 1
= (2z - 3z)/4 - 1
= -z/4 - 1
Therefore, the simplified expression in fraction form is -z/4 - 1.
To factor the expression 48w + 32x - 24 using the greatest common factor (GCF), we need to find the largest number that divides evenly into all three terms: 48w, 32x, and -24.
Step 1: Find the GCF of the coefficients (48, 32, -24)
The common factors of 48, 32, and 24 are 1, 2, 3, 4, 6, 8, and 12. Since we need to find the largest factor, the GCF is 8.
Step 2: Factor out the GCF
To factor out the GCF of 8, divide each term by 8:
(48w + 32x - 24) / 8 = 6w + 4x - 3
Therefore, the factored form of 48w + 32x - 24 using the GCF is 8(6w + 4x - 3).