Question

Which addition problem matches the multiplication problem:
2/3 x 4
A
2 + 4 + 32\ +\ 4\ +\ 32 + 4 + 3
B
23+23+23+23\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{2}{3}
3
2
​
+
3
2
​
+
3
2
​
+
3
2
​

C
34+34+23\frac{3}{4}+\frac{3}{4}+\frac{2}{3}
4
3
​
+
4
3
​
+
3
2
​

Answer 1

To find the addition problem that matches the multiplication problem \( \frac{2}{3} \times 4 \), we'll first compute the multiplication:

1. \( \frac{2}{3} \times 4 = \frac{2 \times 4}{3} = \frac{8}{3} \).

Now, we need to look for an addition problem that also results in \( \frac{8}{3} \).

Let's evaluate each option to see if it sums up to \( \frac{8}{3} \).

**A:**
\[ 2 + 4 + 32 + 4 + 32 + 4 + 3 \]
This sum is clearly much larger than \( \frac{8}{3} \).

**B:**
\[ 23 + 23 + 23 + 23\frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} \]
This sum amounts to:
- 4 groups of 23: \( 4 \times 23 = 92 \)
- plus \( 4 \times \frac{2}{3} = \frac{8}{3} \)
So we get \( 92 + \frac{8}{3} \), which does not equal \( \frac{8}{3} \) but a much larger number.

**C:**
\[ 34 + 34 + 23\frac{3}{4} + \frac{3}{4} + \frac{2}{3} \]
Again this sum adds up to:
- 2 groups of 34: \( 2 \times 34 = 68 \)
- plus \( 23\frac{3}{4} \), which converts to \( \frac{95}{4} \)
- plus \( \frac{3}{4} + \frac{2}{3} \), which is also a complex fraction.

This sum easily exceeds \( \frac{8}{3} \).

After evaluating the options, none of the addition problems appear to add up to \( \frac{8}{3} \). Therefore, based on calculations above, none of the options (A, B, or C) match the multiplication problem \( \frac{2}{3} \times 4 \).

However, a direct representation of \( \frac{2}{3} \times 4 \) would yield the addition equivalent \( \frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = \frac{8}{3} \), which is not provided among your options.

If you need clarification or additional options checked, please let me know!