Evaluating without a calculator

Question

Given that $31 \times 417 = 12927$ , without using a calculator , evaluate

$31 \times 0.417 + 12927/4170 $

I'm stuck at how to solve this ...

First I deal with $12927/4170$

From the given equation ,

$ 310 \times 4170 = 129270 $ Therefore .. $12927/4170 = 310$

Then I'm not sure how to deal with $31 \times 0.417 $

Can I get help ? Thanks in advance !

Answer 1

Note 1: You made a little mistake on what you did with your factors of $10$ in

$$\frac{12927}{4170}$$

See if you can figure it out.

Note 2: We know that

$$31\times 0.417 = \frac{1}{1000}\times (31\times 417)$$

Can you take it from there?

Answer 2

Observe that:

• $31\times417=12927\implies\color\red{31\times0.417}=\color\red{12.927}$
• $31\times417=12927\implies\color\green{12927/4170}=\color\green{3.1}$

Therefore: $\color\red{31\times0.417}+\color\green{12927/4170}=\color\red{12.927}+\color\green{3.1}=16.027$