Unit 2: Division
Topic D: Dividing by Two and Three Digit Divisors
Finding Trial Quotients:
When dividing by 2-digit numbers, you will need to estimate the quotient. This guess is called a trial quotient.
Example A
[latex]624 \div 24[/latex]
Rewrite as [latex]24\enclose{longdiv}{624}[/latex]
Step 1: Divide
- Think: [latex]2\enclose{longdiv}{6}[/latex] is [latex]3[/latex]. So [latex]24\enclose{longdiv}{62}[/latex] is about [latex]3[/latex].
Step 2: Multiply and subtract.
- [latex]\begin{array}{r}3 \ \ \ \\ 24\enclose{longdiv}{624}\\72 \ \ \ \\ \hline \end{array}[/latex]
- Since 72 > 62, 3 is too large.
Step 4: Finish the problem.
Example B
[latex]630 \div 15[/latex]
Rewrite as [latex]15\enclose{longdiv}{630}[/latex]
Step 1: Divide
- 15 rounds to 20. Think: [latex]2\enclose{longdiv}{6}[/latex] is [latex]3[/latex]. So [latex]15\enclose{longdiv}{63}[/latex] is about [latex]3[/latex].
Step 3: Try a larger number, multiply and subtract.
- [latex]\begin{array}{r}4 \ \ \ \\ 24\enclose{longdiv}{630}\\60 \ \ \\ \hline 3 \ \ \end{array}[/latex]
- Since 3 < 15, 4 is correct.
Step 4: Finish the problem.
Exercise 1
In each question, the trial quotient is either too large or too small. Multiply. Write too large or too small on the line. Then, write the correct trial quotient beside.
Example D
[latex]27\enclose{longdiv}{2205}[/latex]
Since 27 rounds to 30, think [latex]3\enclose{longdiv}{22}[/latex] . 3 goes into 22 ≈ 7. 7 would be a good trial quotient.
[latex]\begin{array}{r}7\ \ \ \\ 27\enclose{longdiv}{2205}\\189\ \ \ \\ \hline 31\ \ \ \end{array}[/latex]
Since 31 > 27, so 7 is too small. A better trial quotient would be 8.
Exercise 2
Find the first digit in the trial quotient. Check your work using the answer key at the end of the exercise.
- [latex]43\enclose{longdiv}{1772}[/latex] [latex]\begin{array}{r}4\\ 4\enclose{longdiv}{17}\\16\\ \hline 1\end{array}[/latex]. 1 < 4
- [latex]64\enclose{longdiv}{3276}[/latex]
- [latex]28\enclose{longdiv}{6008}[/latex]
- [latex]33\enclose{longdiv}{2731}[/latex]
- [latex]59\enclose{longdiv}{4164}[/latex]
- [latex]75\enclose{longdiv}{2420}[/latex]
- [latex]54\enclose{longdiv}{3316}[/latex]
- [latex]38\enclose{longdiv}{2759}[/latex]
- [latex]46\enclose{longdiv}{387}[/latex]
- [latex]35\enclose{longdiv}{3316}[/latex]
- [latex]83\enclose{longdiv}{7237}[/latex]
- [latex]77\enclose{longdiv}{6763}[/latex]
- [latex]93\enclose{longdiv}{3724}[/latex]
- [latex]52\enclose{longdiv}{4690}[/latex]
- [latex]86\enclose{longdiv}{2089}[/latex]
- [latex]26\enclose{longdiv}{1417}[/latex]
- [latex]72\enclose{longdiv}{1462}[/latex]
- [latex]27\enclose{longdiv}{6939}[/latex]
- [latex]32\enclose{longdiv}{7840}[/latex]
- [latex]24\enclose{longdiv}{7605}[/latex]
- [latex]16\enclose{longdiv}{8640}[/latex]
- [latex]45\enclose{longdiv}{3060}[/latex]
- [latex]38\enclose{longdiv}{2158}[/latex]
- [latex]42\enclose{longdiv}{1491}[/latex]
Answers to Exercise 2
- 4
- 5
- 2
- 8
- 7
- 3
- 6
- 7
- 8
- 4
- 8
- 8
- 4
- 9
- 2
- 5
- 2
- 2
- 2
- 3
- 5
- 6
- 5
-