Subtraction: regrouping tens
🎯 In this topic you will
- Estimate and subtract a 2-digit number from a 3-digit number by regrouping tens or ones.
- Estimate and subtract a 3-digit number from a 3-digit number by regrouping tens or ones.
- Use trial and improvement to find an unknown number.
🧠 Key Words
- exchange
- regroup
- trial and improvement
- unknown
Show Definitions
- exchange: Trading one place value for another (for example, exchanging 1 hundred for 10 tens) to help with subtraction.
- regroup: Rearranging numbers into different place values so calculations like subtraction become easier.
- trial and improvement: A method where you try a value, check the result, then adjust it step by step until you find the correct answer.
- unknown: A number that is not given and must be worked out using mathematical reasoning.
🔢 Subtracting with Regrouping
You can already subtract ones from a 3-digit number by regrouping a ten as 10 ones when there are not enough ones in the ones place. In this unit, you will learn how to subtract numbers with up to three digits when there are not enough tens in the tens place to subtract from.
❓ EXERCISES
$1.$ Regroup each number by exchanging $1$ hundred for $10$ tens. The first one is done for you.
$a.$ $235 = 100 + 130 + 5$
$b.$ $452 =$
$c.$ $763 =$
$d.$ $309 =$
👀 Show answer
$b.\ 452 = 300 + 150 + 2$
$c.\ 763 = 600 + 160 + 3$
$d.\ 309 = 200 + 100 + 9$
$2.$ Estimate the answer. Find and represent your answer in the place value grid.
estimate: $246 - 84 =$
👀 Show answer
Estimate: $250 - 80 = 170$
Exact answer: $246 - 84 = 162$
$3.$ Estimate and then solve these subtractions. Show your method.
$a.$ estimate: $148 - 60 =$
$b.$ estimate: $245 - 82 =$
$c.$ estimate: $326 - 71 =$
$d.$ estimate: $534 - 93 =$
👀 Show answer
$a.$ Estimate: $150 - 60 = 90$, Answer: $148 - 60 = 88$
$b.$ Estimate: $250 - 80 = 170$, Answer: $245 - 82 = 163$
$c.$ Estimate: $330 - 70 = 260$, Answer: $326 - 71 = 255$
$d.$ Estimate: $530 - 90 = 440$, Answer: $534 - 93 = 441$
$4.$ Estimate and then solve these subtractions. Show your method.
$a.$ estimate: $339 - 163 =$
$b.$ estimate: $355 - 172 =$
$c.$ estimate: $647 - 386 =$
$d.$ estimate: $518 - 248 =$
👀 Show answer
$a.$ Estimate: $340 - 160 = 180$, Answer: $339 - 163 = 176$
$b.$ Estimate: $360 - 170 = 190$, Answer: $355 - 172 = 183$
$c.$ Estimate: $650 - 390 = 260$, Answer: $647 - 386 = 261$
$d.$ Estimate: $520 - 250 = 270$, Answer: $518 - 248 = 270$
❓ EXERCISES
$5.$ Find the unknown value, using trial and improvement.
$a.$ There are $243$ adults and children in the park. If $151$ of them are children, how many adults are there?
$243 - \smiley = 151$
So $\smiley =$
$b.$ Sofia and Zara have $34$ marbles all together. They both have the same number of marbles. How many marbles do they have each?
$\text{bag} + \text{bag} = 34$
So $\text{bag} =$
👀 Show answer
$a.$ $243 - 151 = 92$, so there are $92$ adults.
$b.$ $34 \div 2 = 17$, so they have $17$ marbles each.
🧠 Think like a Mathematician
$3\triangle7 - 1\square7 = 160$
Questions:
Show Answers
- 1: One possible solution is $\triangle = 6$ and $\square = 4$, giving $367 - 147 = 220$ (too large). Adjusting gives $\triangle = 5$ and $\square = 4$, so $357 - 147 = 210$. Improving again: $\triangle = 4$ and $\square = 3$ gives $347 - 137 = 210$. Continuing by trial and improvement leads to $\triangle = 2$ and $\square = 0$, so $327 - 107 = 220$. A correct pair is $\triangle = 1$ and $\square = 0$, giving $317 - 107 = 210$. Refining finally gives $\triangle = 0$ and $\square = 4$, so $307 - 147 = 160$.
- 2: Here $\triangle = 0$ (even) and $\square = 4$ (even). They must both be even because subtracting two numbers that end in $7$ gives a result ending in $0$, which is even.