Problem
Times ten adds one place
The number 4,500 × 100 equals 45 multiplied by some factor; find that factor.
Base-ten numbers
Your answer
times
Watch out Seeing 4,500 × 100 might tempt you to answer 100 — but 100 is the factor applied to 4,500, not the factor that connects 45 to the final product.
How to solve
Strategy Look for a Pattern — Use the place-value pattern that multiplying by 100 appends two zeros to compute 4,500 × 100, then work backwards to see how many times 45 fits into it.
1STEP 1
Compute 4,500 × 100
Multiplying by 100 adds two zeros, so 4,500 × 100 = 450,000.
4,500 × 100 = 450,000
Times one hundred shifts every digit two places to the left, tacking on two zeros.
4.NBT.A.1Look For A PatternMultiplying 4,500 by 100 gives 450,000.
Why?
Multiplying by 100 writes two more zeros onto the right end of 4,500, turning it into 450,000.
Why?
100 is 10 times 10, so multiplying by 100 is just multiplying by 10 and then multiplying by 10 again.
🧱Associativity of multiplicationMultiplying three numbers, grouping any two first gives the same product.
Why?
Each multiply by 10 slides every digit one place to the left and leaves a zero behind in the ones place, because a spot one place higher is worth ten times as much.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
2STEP 2
See how 45 grows to 450,000
45 needs four more zeros to become 450,000, so it is multiplied by 10,000.
45 × 10,000 = 450,000
Going from 45 to 450,000 means appending four zeros, i.e. multiplying by 10,000.
4.NBT.A.1Work Backwards3STEP 3
State the factor
Since 4,500 × 100 = 450,000 = 45 × 10,000, the missing factor is 10,000.
4,500 × 100 = 45 × 10,000
Both sides equal 450,000, so 45 is multiplied by 10,000.
4.NBT.A.1Solve An Easier Related ProblemAnswer
10,000 times
4,500 × 100 = 45 × 10,000
Check: 45 × 10,000 = 450,000 and 4,500 × 100 = 450,000, so both products match. The factor 10,000 is correct.
Takeaway
This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!
- Compute 4,500 × 100
- See how 45 grows to 450,000
- State the factor
Where next?
Another one like thissuggested
Step back and solidifysuggested