Use a known result instead of starting again
Before this page: be confident with multiplying and dividing by powers of ten and with basic multiplication and division facts.
You are told that 43 × 26 = 1,118, then asked to find 4.3 × 26. The given result is there to save you from doing another written multiplication.
Compare the new calculation with the one you know:
- What changed?43 → 4.3The first factor was divided by 10.
- What stayed the same?26 → 26The second factor did not change.
- Make the product follow1,118 → 111.8Divide the product by 10 as well.
Therefore 4.3 × 26 = 111.8. This page develops that comparison into a reliable method for related products, divisions and missing values—all without recalculating the given fact.
Scale one factor at a time
Write each change beside the number it affects. This makes the product's change visible before any decimal point is placed.
43 × 26 = 1,118, so 4.3 × 26 = 111.8 and 4.3 × 2.6 = 11.18.
Combine the scale changes
Each factor of 10 changes the product once. In 4.3 × 2.6, the first factor is one tenth of 43 and the second is one tenth of 26.
product change=first-factor change × second-factor change
An unchanged factor contributes ×1. It does not add another change to the product.
Read a product fact backwards
Every multiplication fact gives two division facts. From 43 × 26 = 1,118, it follows immediately that:
Division undoes multiplication. Once the related product 4.3 × 2.6 = 11.18 is known, make 11.18 the dividend and divide by either factor. The quotient is the other factor.
related product4.3 × 2.6 = 11.18
divide the product by 4.311.18 ÷ 4.3 = 2.6
divide the product by 2.611.18 ÷ 2.6 = 4.3
Form the related multiplication fact first, then read it in the direction the question requires.
Same product, smaller known factor
4.3 × 260 = 1,118
4.3 is one tenth of 43. To keep the product at 1,118, the other factor must be ten times 26.
1,118 ÷ 4.3 = 260
Product and divisor both smaller
43 × 2.6 = 111.8
The second factor and product are both one tenth of their original values, so the other factor remains 43.
111.8 ÷ 2.6 = 43
Rewrite a missing value with an inverse
First use an inverse operation to make the missing value the subject. Then replace each changed number with its relationship to the given calculation.
Find the missing factor in ? × 2.6 = 111.8
Use the given fact 43 × 26 = 1,118.
Missing factor
? = 43
Find the missing dividend in ? ÷ 4.3 = 260
Use the same given fact 43 × 26 = 1,118.
Missing dividend
? = 1,118
Find the missing factor in ? × 2.6 = 11.18
Use the same given fact 43 × 26 = 1,118.
Missing factor
? = 4.3
Explore the related fact family
Select the value to calculate, then scale the other two. The selected scale and related equation update from the given fact.
Given43 × 26 = 1,118
The first factor is divided by 10 and the second factor is unchanged, so the product is divided by 10. The related fact is 4.3 times 26 equals 111.8.
Check the relationship, not the original arithmetic
Use an inverse
From 4.3 × 2.6 = 11.18, check that 11.18 ÷ 2.6 = 4.3.
Check the scale
Both factors are one tenth of the originals, so 11.18 must be one hundredth of 1,118.
These checks confirm that the new statement is consistent with the given fact. They do not repeat the multiplication.
Common mistakes
- Changing the product only onceIf both factors are divided by 10, the product is divided by 10 twice: overall, it is divided by 100.
- Moving every decimal point the same wayCompare the role of each number first. In 1,118 ÷ 4.3, a smaller divisor produces the larger quotient 260.
- Recalculating the given productTreat 43 × 26 = 1,118 as known. Only apply the stated powers-of-ten changes.
- Forgetting the inverse factRewrite a missing factor as division or a missing dividend as multiplication before tracking the changes.
Summary
- Start from the stated calculation and do not recalculate it.
- Write how each factor has changed: ×10, ÷10, ×100, ÷100 or unchanged.
- Combine the two factor changes to find the product's scale change.
- Use inverse operations to turn the related fact into the form needed for a quotient or missing value.
- Check with the inverse operation and confirm that the new values have the expected scale.