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addition and subtraction of fractions best video in assamese

Basic To Advanced Level Mathematics Part 7

Thursday, April 7, 2022

ভগ্নাংশৰ যোগ(Addition Of Fractions):

(i) যেতিয়া হৰবোৰ একে থাকে (সদৃশ ভগ্নাংশৰ যোগ)

[When the denominators are same (addition of like fractions)]

addition of fraction in assamese

Example:

511+411=911\frac{5}{11} + \frac{4}{11} = \frac{9}{11}

(ii) যেতিয়া হৰবোৰ একে নাথাকে (অসদৃশ ভগ্নাংশৰ যোগ)

[When the denominators are different (addition of unlike fractions)]

addition of fractions mathematics in assamese

Example 1:

14+18=1×24×2+18[LCM=8]=28+18=2+18=38\begin{aligned} & \frac{1}{4} + \frac{1}{8} \\ & = \frac{1\times2}{4\times2} + \frac{1}{8} \quad[LCM = 8] \\ & = \frac{2}{8} + \frac{1}{8} \\ & = \frac{2+1}{8} \\ & = \frac{3}{8} \\ \end{aligned}

Example 2:

34+16=3×34×3+1×26×2[LCM=12]=912+212=9+212=1112\begin{aligned} & \frac{3}{4} + \frac{1}{6} \\ & = \frac{3\times3}{4\times3} + \frac{1 \times 2}{6 \times2 } \quad[LCM = 12] \\ & = \frac{9}{12} + \frac{2}{12} \\ & = \frac{9+2}{12} \\ & = \frac{11}{12} \\ \end{aligned}

ভগ্নাংশৰ বিয়োগ(Subtraction Of Fractions):

Example 1:

14−18=1×24×2−18[LCM=8]=28−18=2−18=18\begin{aligned} & \frac{1}{4} - \frac{1}{8} \\ & = \frac{1\times2}{4\times2} - \frac{1}{8} \quad[LCM = 8] \\ & = \frac{2}{8} - \frac{1}{8} \\ & = \frac{2-1}{8} \\ & = \frac{1}{8} \\ \end{aligned}

Example 2:

34−16=3×34×3−1×26×2[LCM=12]=912−212=9−212=712\begin{aligned} & \frac{3}{4} - \frac{1}{6} \\ & = \frac{3\times3}{4\times3} - \frac{1 \times 2}{6 \times2 } \quad[LCM = 12] \\ & = \frac{9}{12}- \frac{2}{12} \\ & = \frac{9-2}{12} \\ & = \frac{7}{12} \\ \end{aligned}

Additional Examples on Fraction:

(i) 534+316=5×4+34+3×6+16=20+34+18+16=234+196=23×34×3+19×26×2=6912+3812=69+3812=11712=9912\begin{aligned} & (i) \, 5\frac{3}{4} + 3\frac{1}{6} \\ & = \frac{5\times 4+3}{4} + \frac{3 \times 6 + 1}{6} \\ & = \frac{20+3}{4} + \frac{18+1}{6} \\ & = \frac{23}{4} + \frac{19}{6}\\ & = \frac{23\times3}{4\times3} + \frac{19 \times 2}{6 \times2 } \\ & = \frac{69}{12} + \frac{38}{12} \\ & = \frac{69+38}{12} \\ & = \frac{117}{12} \\ & = 9\frac{9}{12} \end{aligned}
(ii) 534+316−312=5×4+34+3×6+16−3×2+12=20+34+18+16−6+12=234+196−72=23×34×3+19×26×2−7×62×6=6912+3812−4212=69+38−4212=69−412=6512=5512\begin{aligned} & (ii) \, 5\frac{3}{4} + 3\frac{1}{6} - 3\frac{1}{2} \\ & = \frac{5\times 4+3}{4} + \frac{3 \times 6 + 1}{6} - \frac{3 \times 2 +1}{2} \\ & = \frac{20+3}{4} + \frac{18+1}{6}- \frac{6+1}{2} \\ & = \frac{23}{4} + \frac{19}{6} - \frac{7}{2}\\ & = \frac{23\times3}{4\times3} + \frac{19 \times 2}{6 \times2 } - \frac{7 \times 6}{2\times 6}\\ & = \frac{69}{12} + \frac{38}{12} - \frac{42}{12} \\ & = \frac{69+38-42}{12} \\ & = \frac{69 - 4}{12} \\ & = \frac{65}{12}\\ & = 5\frac{5}{12} \end{aligned}

QUESTIONS:

(i)425+312(ii)513+124(iii)357+243(iv)2511+4110(v)617−21320(vi)725−319+313(vii)612−413−112(viii)−513+814(ix)−916+37(x)1111+217(i) \quad 4\frac{2}{5} + 3\frac{1}{2} \\ (ii) \quad 5\frac{1}{3} + 1\frac{2}{4} \\ (iii) \quad 3\frac{5}{7} + 2\frac{4}{3} \\ (iv) \quad 2\frac{5}{11} + 4\frac{1}{10} \\ (v) \quad 6\frac{1}{7} - 2\frac{13}{20} \\ (vi) \quad 7\frac{2}{5} - 3 \frac{1}{9} + 3\frac{1}{3} \\ (vii) \quad 6\frac{1}{2} - 4\frac{1}{3} - 1\frac{1}{2} \\ (viii) \quad -5\frac{1}{3} + 8\frac{1}{4} \\ (ix) \quad -9\frac{1}{6} + \frac{3}{7} \\ (x) \quad 1\frac{1}{11} +2 \frac{1}{7} \\