Question
Using the distributive property, an expression equivalent to 48 + 30 is
5 (6 + 8).
(6) (8) + (3) (10).
(3) (16) + (6) (5).
6 (8 + 5).
5 (6 + 8).
(6) (8) + (3) (10).
(3) (16) + (6) (5).
6 (8 + 5).
Answers
Answered by
GPT-4o mini
To find an expression equivalent to \(48 + 30\) using the distributive property, let's first evaluate \(48 + 30\):
\[
48 + 30 = 78.
\]
Now, let's check the provided options to see which one equals \(78\).
1. **Option 1: \(5(6 + 8)\)**
\[
= 5 \cdot 14 = 70\quad \text{(not equal to 78)}
\]
2. **Option 2: \( (6)(8) + (3)(10) \)**
\[
= 48 + 30 = 78\quad \text{(equal to 78)}
\]
3. **Option 3: \( (3)(16) + (6)(5) \)**
\[
= 48 + 30 = 78\quad \text{(equal to 78)}
\]
4. **Option 4: \(6(8 + 5)\)**
\[
= 6 \cdot 13 = 78\quad \text{(equal to 78)}
\]
Upon examination, **Options 2, 3, and 4 are all equivalent to \(48 + 30\)** (i.e., \(78\)). However, if you are looking for direct use of the distributive property on \(48 + 30\), then one representation would be:
\[
6(8 + 5).
\]
Thus, all the options are technically correct representations; options 2, 3, and 4 are derived directly from the distributive property, while option 1 is not.
\[
48 + 30 = 78.
\]
Now, let's check the provided options to see which one equals \(78\).
1. **Option 1: \(5(6 + 8)\)**
\[
= 5 \cdot 14 = 70\quad \text{(not equal to 78)}
\]
2. **Option 2: \( (6)(8) + (3)(10) \)**
\[
= 48 + 30 = 78\quad \text{(equal to 78)}
\]
3. **Option 3: \( (3)(16) + (6)(5) \)**
\[
= 48 + 30 = 78\quad \text{(equal to 78)}
\]
4. **Option 4: \(6(8 + 5)\)**
\[
= 6 \cdot 13 = 78\quad \text{(equal to 78)}
\]
Upon examination, **Options 2, 3, and 4 are all equivalent to \(48 + 30\)** (i.e., \(78\)). However, if you are looking for direct use of the distributive property on \(48 + 30\), then one representation would be:
\[
6(8 + 5).
\]
Thus, all the options are technically correct representations; options 2, 3, and 4 are derived directly from the distributive property, while option 1 is not.