Question

A studen bought $4\frac{1}{3}$m of yellow ribbon, $6\frac{1}{6}$m of red ribbon and $3\frac{2}{9}$m of blue ribbon for decorating a room. How many meters of ribbon did he buy?

Answer 1

Step 1: Converting the given statement into a mathematical equation

Total meters of ribbon =$4\frac{1}{2}+6\frac{1}{6}+3\frac{2}{9}$

$=\frac{4\times 3+1}{3}+\frac{6\times 6+1}{6}+\frac{3\times 9+2}{9}$


$=\frac{12+1}{3}+\frac{36+1}{6}+\frac{27+2}{9}$

=$\frac{12}{3}+\frac{37}{6}+\frac{29}{9}$

Step 2: Simplifying the obtained expression to find the total quantity that he bought

=$\frac{12}{3}+\frac{37}{6}+\frac{29}{9}$
=$\frac{13\times 6+37\times 3+29\times 2}{18}$

[LCM of (3,6,9) =18]

=$\frac{78+111+58}{18}$

=$\frac{247}{18}$m

Hence, he bought $\frac{247}{18}$ or $13\frac{13}{18}$m of the ribbon.