Byron wants to use the distributive property to rewrite the
addition problem shown so that the numbers left in the
parentheses have no common factor except 1.
(48 + 72)
Which is an equivalent expression that has numbers in the
parentheses whose only common factor is 1?
To rewrite the addition problem (48 + 72) using the distributive property so that the numbers in the parentheses have no common factors except 1, you can follow these steps:
Step 1: Find the greatest common factor (GCF) of the numbers 48 and 72.
- The prime factorization of 48: 2^4 * 3^1.
- The prime factorization of 72: 2^3 * 3^2.
- The common factors between 48 and 72 are 2^3 * 3^1, which is 24.
Step 2: Rewrite both numbers in terms of their GCF.
- 48 can be expressed as 24 * 2.
- 72 can be expressed as 24 * 3.
Step 3: Apply the distributive property.
(48 + 72) becomes (24 * 2 + 24 * 3).
Step 4: Factor out the common factor.
(24 * 2 + 24 * 3) can be simplified as 24 * (2 + 3).
Step 5: Simplify the expression.
24 * (2 + 3) equals 24 * 5.
Therefore, an equivalent expression to (48 + 72), with numbers in the parentheses having no common factor except 1, is 24 * 5.
To use the distributive property to rewrite the expression (48 + 72) so that the numbers in the parentheses have no common factors except 1, we need to find the greatest common factor (GCF) of 48 and 72.
Step 1: Find the factors of both numbers:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Step 2: Identify the common factors:
The common factors of 48 and 72 are 1, 2, 3, 4, 6, 8, 12, and 24.
Step 3: Choose the greatest common factor:
The greatest common factor (GCF) of 48 and 72 is 24.
Step 4: Rewrite the expression using the distributive property:
To rewrite the expression (48 + 72) with numbers in the parentheses whose only common factor is 1, we divide both numbers by their GCF, 24.
(48 + 72) becomes (2 * 24 + 3 * 24).
Step 5: Simplify the expression:
Using the distributive property, we can simplify the expression as follows:
(2 * 24 + 3 * 24) = (48 + 72).
Therefore, an equivalent expression that has numbers in the parentheses whose only common factor is 1 is (2 * 24 + 3 * 24).
48 = 24*2
72 = 24*3
So, 24(2+3)
read up on Greatest Common Factor