Problem
Rounding is an up or a down
A division with a missing digit rounds to a given whole number. We need the largest the missing digit can be.
Number systemExpressionsBase-ten numbers
Your answer
How to solve
Strategy Work Backwards — Only the upper end matters, because a larger digit makes a larger dividend and so a larger quotient. So find the dividend that would push the quotient to exactly 4.5 and step back from it.
1STEP 1
Turn the rounded value back into a range
A quotient rounds to 4 exactly when it is at least 3.5 and below 4.5.
3.5 ≤ (quotient) ＜ 4.5
The blank is limited by the top end.
5.NBT.A.4Convert To Algebra2STEP 2
Find the dividend at the top of the range
Multiply the upper boundary by the divisor to see how big the dividend may get.
4.5 × 1.7 = 7.65
The dividend has to stay below 7.65.
6.NS.B.3Work BackwardsThe dividend has to stay below .
Why?
A quotient rounds to only while it is under , and times is the dividend that would put it exactly there.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
A bigger digit in the tenths place makes a bigger dividend, so once the dividend passes no digit above it can work either.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
3STEP 3
Read the largest digit that fits
With ■ = 5 the dividend is 7.58, still under 7.65; with ■ = 6 it is 7.68, which is over.
7.58 ＜ 7.65 ＜ 7.68
The largest digit is 5.
6.EE.B.8Guess And CheckAnswer
5
Divide it out: 7.58 ÷ 1.7 ≈ 4.46, which rounds to 4, while 7.68 ÷ 1.7 ≈ 4.52 rounds to 5.
Takeaway
When you want the largest digit, work from the top of the rounding range back down.
- Turn the rounded value back into a range
- Find the dividend at the top of the range
- Read the largest digit that fits