Question

600+_____= 1,400

because both addends were rounded_____, the estimate will than the actual sum

3+___=11

___+500+700=1,300

the sum is ___

Answer 1

Let's solve each equation step by step.

1. For the first equation:
\[ 600 + x = 1,400 \]
To find \( x \):
\[ x = 1,400 - 600 \]
\[ x = 800 \]

2. The phrase "because both addends were rounded _____, the estimate will than the actual sum" seems like it might be asking for an appropriate word. A potential word could be "down," indicating that rounding down could lead the estimate to be lower than the actual sum.

3. For the equation:
\[ 3 + y = 11 \]
To find \( y \):
\[ y = 11 - 3 \]
\[ y = 8 \]

4. For the equation:
\[ z + 500 + 700 = 1,300 \]
Combining the known numbers:
\[ z + 1,200 = 1,300 \]
To find \( z \):
\[ z = 1,300 - 1,200 \]
\[ z = 100 \]

5. Lastly, the sum is to be calculated from the context we have, which could be referring to any of the previous results or summing these together. If we consider all relevant sums:
- From the first equation: \( 600 + 800 = 1,400 \)
- From the second equation: \( 3 + 8 = 11 \)
- From the fourth equation: \( 100 + 500 + 700 = 1,300 \)

If you want the sum of all unique results:
\[ 1,400 + 11 + 1,300 = 2,711 \]

Thus, the responses are:
- 600 + 800 = 1,400
- The estimate will be **lower** than the actual sum.
- 3 + 8 = 11
- 100 + 500 + 700 = 1,300
- The sum is **2,711** (if that is the intended context).

Let me know if you need any further clarification or assistance!