Question

Model 458+277 on an abacus with 4 spikes then find the sum.
Show your workings bit by bit

Answer 1

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:

1. **Units (1s)**
2. **Tens (10s)**
3. **Hundreds (100s)**
4. **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
1. **Hundreds (4)**: 4 beads on the hundreds spike.
2. **Tens (5)**: 5 beads on the tens spike.
3. **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):
1. **Hundreds (2)**: 2 beads on the hundreds spike.
2. **Tens (7)**: 7 beads on the tens spike.
3. **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**.