Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 44324 by Rio Michael last updated on 26/Sep/18

5 2 a + 3 5 ___ the addition on the left is in base 6.find a. 1001

$$\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{2}\:{a} \\ $$$$\:\:\:\:+\:\:\:\:\mathrm{3}\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\_\_\_\:\:\:\:\:{the}\:{addition}\:{on}\:{the}\:{left}\:{is}\:{in}\:{base}\:\mathrm{6}.{find}\:{a}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1001} \\ $$

Answered by MJS last updated on 27/Sep/18

in base 6 similar to what we learned in primary school: 1001−0035=? 5+2=11, write 2, keep 1 in mind 1001−0035=2 3+1=4 4+2=10, write 2, keep 1 in mind 1001−0035=22 0+1=1 1+5=10, write 5, keep 1 in mind 1001−35=522 0+1=1 1+0=1, so we′re ready a=2

$$\mathrm{in}\:\mathrm{base}\:\mathrm{6}\:\mathrm{similar}\:\mathrm{to}\:\mathrm{what}\:\mathrm{we}\:\mathrm{learned}\:\mathrm{in} \\ $$$$\mathrm{primary}\:\mathrm{school}: \\ $$$$\mathrm{1001}−\mathrm{0035}=? \\ $$$$\mathrm{5}+\mathrm{2}=\mathrm{11},\:\mathrm{write}\:\mathrm{2},\:\mathrm{keep}\:\mathrm{1}\:\mathrm{in}\:\mathrm{mind} \\ $$$$\mathrm{1001}−\mathrm{0035}=\mathrm{2} \\ $$$$\mathrm{3}+\mathrm{1}=\mathrm{4} \\ $$$$\mathrm{4}+\mathrm{2}=\mathrm{10},\:\mathrm{write}\:\mathrm{2},\:\mathrm{keep}\:\mathrm{1}\:\mathrm{in}\:\mathrm{mind} \\ $$$$\mathrm{1001}−\mathrm{0035}=\mathrm{22} \\ $$$$\mathrm{0}+\mathrm{1}=\mathrm{1} \\ $$$$\mathrm{1}+\mathrm{5}=\mathrm{10},\:\mathrm{write}\:\mathrm{5},\:\mathrm{keep}\:\mathrm{1}\:\mathrm{in}\:\mathrm{mind} \\ $$$$\mathrm{1001}−\mathrm{35}=\mathrm{522} \\ $$$$\mathrm{0}+\mathrm{1}=\mathrm{1} \\ $$$$\mathrm{1}+\mathrm{0}=\mathrm{1},\:\mathrm{so}\:\mathrm{we}'\mathrm{re}\:\mathrm{ready} \\ $$$$ \\ $$$${a}=\mathrm{2} \\ $$

Answered by MrW3 last updated on 27/Sep/18

(52a)_6 =5×6^2 +2×6^1 +a×6^0 =192+a (35)_6 =3×6^1 +5×6^0 =23 (1001)_6 =1×6^3 +0×6^2 +0×6^1 +1×6^0 =217 192+a+23=217 ⇒a=2

$$\left(\mathrm{52}{a}\right)_{\mathrm{6}} =\mathrm{5}×\mathrm{6}^{\mathrm{2}} +\mathrm{2}×\mathrm{6}^{\mathrm{1}} +{a}×\mathrm{6}^{\mathrm{0}} =\mathrm{192}+{a} \\ $$$$\left(\mathrm{35}\right)_{\mathrm{6}} =\mathrm{3}×\mathrm{6}^{\mathrm{1}} +\mathrm{5}×\mathrm{6}^{\mathrm{0}} =\mathrm{23} \\ $$$$\left(\mathrm{1001}\right)_{\mathrm{6}} =\mathrm{1}×\mathrm{6}^{\mathrm{3}} +\mathrm{0}×\mathrm{6}^{\mathrm{2}} +\mathrm{0}×\mathrm{6}^{\mathrm{1}} +\mathrm{1}×\mathrm{6}^{\mathrm{0}} =\mathrm{217} \\ $$$$\mathrm{192}+{a}+\mathrm{23}=\mathrm{217} \\ $$$$\Rightarrow{a}=\mathrm{2} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com