A student bought \(\frac{4}{3}\) m of yellow ribbon, \(\frac{1}{6}\) m of red ribbon, and \(\frac{2}{3}\) m of blue ribbon for decorating a room. How many metres of ribbon did he buy?
Answer (1)
To find out the total amount of ribbon the student bought, we need to add the lengths of all the different ribbons together.
The student bought:
3 4 meters of yellow ribbon
6 1 meters of red ribbon
3 2 meters of blue ribbon
To add these fractions together, we need to find a common denominator. The fractions have denominators of 3 and 6. The least common multiple of 3 and 6 is 6.
Let's convert each fraction to have a denominator of 6:
3 4 = 3 × 2 4 × 2 = 6 8
6 1 = 6 1
3 2 = 3 × 2 2 × 2 = 6 4
Now, we can add the fractions:
6 8 + 6 1 + 6 4 = 6 8 + 1 + 4 = 6 13
The student bought a total of 6 13 meters of ribbon.
To make this easier to understand, 6 13 can also be converted to a mixed number. 6 13 is the same as 2 whole meters and 6 1 of a meter:
6 13 = 2 6 1
So, the student bought a total of 2 meters and 6 1 meter of ribbon.
