To perform the addition of 458 + 277 on an abacus with 4 spikes, let's break it down step-by-step.
Step 1: Understand the Abacus Layout
An abacus typically has several rods (or spikes) representing different place values:
- Units (1s)
- Tens (10s)
- Hundreds (100s)
- Thousands (1000s) (not used in this case)
For our calculation, we will use 4 spikes:
- Spike 1: Units (1s)
- Spike 2: Tens (10s)
- Spike 3: Hundreds (100s)
- Spike 4: Thousands (not needed in this case)
Step 2: Represent 458 on the Abacus
- Hundreds (4): 4 beads on the hundreds spike.
- Tens (5): 5 beads on the tens spike.
- Units (8): 8 beads on the units spike.
So far, the abacus looks like this:
Spike 1 (Units): ■■■■■■■■■ (8 beads)
Spike 2 (Tens): ■■■■■ (5 beads)
Spike 3 (Hundreds): ■■■■ (4 beads)
Spike 4 (Thousands): - (0 beads)
Step 3: Represent 277 on the Abacus
Now, we need to add 277 to our initial representation (458):
- Hundreds (2): 2 beads on the hundreds spike.
- Tens (7): 7 beads on the tens spike.
- Units (7): 7 beads on the units spike.
Step 4: Set Up for Addition
We will add the units, tens, and hundreds separately:
Units:
- Starting units: 8
- Adding: 7
- Total: 15 (which means we write down 5 and carry over 1 to the tens place)
Tens:
- Starting tens: 5
- Adding: 7
- Plus carry over: 1
- Total: 5 + 7 + 1 = 13 (which means we write down 3 and carry over 1 to the hundreds place)
Hundreds:
- Starting hundreds: 4
- Adding: 2
- Plus carry over: 1
- Total: 4 + 2 + 1 = 7 (no carry-over since it is less than 10)
Step 5: Final Representation on the Abacus
Now we can represent the final sum, which is:
- Hundreds (7): 7 beads on the hundreds spike.
- Tens (3): 3 beads on the tens spike.
- Units (5): 5 beads on the units spike.
The abacus now looks like this:
Spike 1 (Units): ■■■■■ (5 beads)
Spike 2 (Tens): ■■■ (3 beads)
Spike 3 (Hundreds): ■■■■■■■■ (7 beads)
Spike 4 (Thousands): - (0 beads)
Conclusion: Result of 458 + 277
Therefore, the sum of 458 + 277 is 735.