🎯 In this topic you will

• Subtract a single-digit number from a 3-digit number by regrouping to make enough ones.
• Estimate and subtract a 2-digit number from a 3-digit number by regrouping to make enough ones.
• Estimate and subtract a 3-digit number from a 3-digit number by regrouping to make enough ones.

🧠 Key Words

• regroup

❓ EXERCISES

$1$. Use the three digits $4$, $6$ and $8$ to make a $2$-digit number and a $1$-digit number. Subtract the single-digit number from the $2$-digit number. Show your method.

Can you find and solve the six possible calculations?

👀 Show answer

All $6$ possible calculations:

$68 - 4 = 64$

$86 - 4 = 82$

$48 - 6 = 42$

$84 - 6 = 78$

$46 - 8 = 38$

$64 - 8 = 56$

$2$. Use the four digits $3$, $5$, $7$ and $9$ to make a $3$-digit number and a $1$-digit number. Subtract the single-digit number from the $3$-digit number. Show your method.

Find and solve at least six of the possible calculations.

👀 Show answer

One set of $6$ valid calculations (examples):

$357 - 9 = 348$

$359 - 7 = 352$

$375 - 9 = 366$

$379 - 5 = 374$

$593 - 7 = 586$

$975 - 3 = 972$

$3$. $178$ cartons of milk are delivered to the store. $25$ of them are damaged.

Estimate and then calculate how many cartons of milk the store can sell. Show your method.

👀 Show answer

Estimate: $180 - 20 = 160$

Calculate: $178 - 25 = 153$

$4$. $262$ melons are delivered to the store, but $37$ of them are damaged.

Estimate and then calculate how many melons the store can sell. Show your method.

👀 Show answer

Estimate: $260 - 40 = 220$

Calculate: $262 - 37 = 225$

$5$. On Tuesday, the post office has $472$ parcels for delivery. A van takes $267$ of the parcels.

Estimate and then calculate how many parcels are left. Show your method.

👀 Show answer

Estimate: $470 - 270 = 200$

Calculate: $472 - 267 = 205$

$6$. On Friday, the post office has $683$ parcels for delivery. A van takes $548$.

Estimate and then calculate how many parcels are left. Show your method.

👀 Show answer

Estimate: $680 - 550 = 130$

Calculate: $683 - 548 = 135$

🧠 Think like a Mathematician

Faisal spilt some ink on the ones digits in his calculation:

$49\Box - 14\Box = 345$

The ink has covered the ones digits of both numbers. Find all possible calculations that could satisfy this equation.

Method:

1. Let the missing ones digit in the first number be $a$, where $0 \le a \le 9$.
2. Let the missing ones digit in the second number be $b$, where $0 \le b \le 9$.
3. Write the subtraction using place value.
4. Test all digit pairs that make the equation true.

Working:

The numbers are:

$49\Box = 490 + a$
$14\Box = 140 + b$

Substitute into the equation:

$(490 + a) - (140 + b) = 345$

Simplify:

$350 + a - b = 345$

$a - b = -5$

Follow-up Questions: