Topic C: Estimating Products
Before you practice estimating products, look at the easy multiplication that can be done when the factors end in zeros.
You already know how to quickly multiply by 10, 100, 1000, etc…
You can find the products in questions like these using regular multiplication:
But here is a shortcut:
- Count all the zeros at the end of the numbers in both factors.
- Write down that many zeros at the end of the product.
- Multiply the other digits in the usual way and put them before the zeros.
Example A
30 × 500 =
- How many zeros at the end of the factors? 3
- Write them down. 000
- Multiply the other digits and put them before the zeros. 3 × 5 = 15
30 × 500 = 15000
Example B
400 × 3000 =
- How many zeros at the end of the factors? 5
- Write them down: 00000
- Multiply the other digits and put them before the zeros. 4 × 3 = 12
400 × 3000 = 1200000
Exercise 1
Find the products using the shortcut. Check your work using the answer key at the end of the exercise.
- [latex]\begin{array}{rr}&300\\\times&20\\\hline&6000\end{array}[/latex]
- [latex]\begin{array}{rr}&6000\\\times&200\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&210\\\times&20\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&800\\\times&600\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&400\\\times&500\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&6000\\\times&90\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&50000\\\times&6000\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&80000\\\times&30\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5000\\\times&50\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&70\\\times&80\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&3000\\\times&700\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&50000\\\times&900\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&9000\\\times&8000\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&60000\\\times&90\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&90000\\\times&2000\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&600\\\times&600\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&40000\\\times&800\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&2400\\\times&70\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&390\\\times&40\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&7200\\\times&5000\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&7000\\\times&7000\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&61000\\\times&400\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5200\\\times&300\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&40\\\times&60\\\hline\\\end{array}[/latex]
Answers to Exercise 1
- 6 000
- 1 200 000
- 4 200
- 480 000
- 200 000
- 540 000
- 300 000 000
- 2 400 000
- 250 000
- 5 600
- 2 100 000
- 45 000 000
- 72 000 000
- 5 400 000
- 180 000 000
- 360 000
- 32 000 000
- 168 000
- 15 600
- 36 000 000
- 49 000 000
- 24 400 000
- 1 560 000
- 2 400
To find an estimated product, round the factors before you multiply. If a factor has only one digit, do not round it.
Example C
[latex]\begin{array}{rr}&6258\\\times&3\\\hline\end{array}[/latex]
6258 rounds to 6000. Leave 3 as is.
[latex]\begin{array}{rr}&6000\\\times&3\\\hline&18000\end{array}[/latex]
18000 is the estimated product.
Example D
[latex]\begin{array}{rr}&491\\\times&24\\\hline\end{array}[/latex]
491 rounds to 500. 24 rounds to 20.
[latex]\begin{array}{rr}&500\\\times&20\\\hline&10000\end{array}[/latex]
10000 is the estimated product.
Topic C: Self-Test
Mark /18 Aim 15/18
A. Multiply these numbers.
- [latex]\begin{array}{rr}&600\\\times&70\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&9000\\\times&30\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&5000\\\times&600\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&3000\\\times&500\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&400\\\times&50\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&8000\\\times&1000\\\hline\end{array}[/latex]
B. Find an estimated product.
- [latex]\begin{array}{rr}&87\\\times&23\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&268\\\times&25\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&9421\\\times&75\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&2632\\\times&49\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&365\\\times&455\\\hline\end{array}[/latex]
- [latex]\begin{array}{rr}&7264\\\times&590\\\hline\end{array}[/latex]
Answers to Topic C Self Test
A. Multiply these numbers.
- 42000
- 270000
- 3000000
- 1500000
- 20000
- 8000000
B. Find an estimated product.
- 90 × 20 = 1800
- 300 × 30 = 9000
- 9000 × 80 = 720000
- 3000 × 50 = 150000
- 400 × 500 = 200000
- 7000 × 600 = 4200000