Sum and Multiple Problems Calculator

Online sum-and-ratio word problem solver. Enter the sum and the multiple relation to find the larger and smaller numbers, with steps—ideal for elementary word problems.

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Smaller=sum/(k+1); Larger=smaller×k

Sum

Sum of both

How many times larger

Positive multiple

📖 Tutorial | Sum and Multiple

1. Definition

Given the sum and how many times one number is, find both.

2. Formula & Notation

k	Multiple
Parts	Smaller 1, larger k

3. Properties & Laws

k+1 parts total;
Smaller=sum/(k+1);
Larger=smaller×k;
Multiple may be decimal.

4. Steps

Enter sum s and k;
Click "Calculate";
Or click "Load Example".

5. Worked Examples

Example: sum 48, k=3.
Solution: smaller 12, larger 36.

6. Common Pitfalls

Divide by k+1;
Smaller is 1 part;
k positive.

❓ FAQ | Sum and Multiple

Sum-multiple problem?

Given sum and times, find both.

Sum48 k3?

12 and 36.

Why k+1?

k+1 parts.

Non-integer?

Works.

Verify?

Sum 48, ratio 3.

Larger?

Smaller×k.