Rama has 3 5/8 metres of ribbon and Uma has 5 3/4 metres of ribbon. How many metres of ribbon do they have together?
Understand the Problem
The question is asking to calculate the total length of ribbon that Rama and Uma have combined. This involves adding two fractional amounts of ribbon.
Answer
$9 \frac{3}{8}$
Answer for screen readers
They have a total of $9 \frac{3}{8}$ metres of ribbon together.
Steps to Solve
-
Convert mixed numbers to improper fractions
For Rama:
$$ 3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8} $$For Uma:
$$ 5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} $$ -
Find a common denominator
The denominators are 8 and 4. The least common denominator (LCD) is 8.
Convert Uma's ribbon amount to eighths:
$$ \frac{23}{4} \times \frac{2}{2} = \frac{46}{8} $$ -
Add the fractions
Now we add the two fractions:
$$ \frac{29}{8} + \frac{46}{8} = \frac{29 + 46}{8} = \frac{75}{8} $$ -
Convert the improper fraction back to a mixed number
To convert $$ \frac{75}{8} $$ back to a mixed number:
$$ 75 \div 8 = 9 \quad \text{(remainder } 3) $$
So, $$ \frac{75}{8} = 9 \frac{3}{8} $$
They have a total of $9 \frac{3}{8}$ metres of ribbon together.
More Information
Converting mixed numbers into improper fractions can simplify operations like addition. The process of finding a common denominator allows for easier addition of fractions.
Tips
- Forgetting to convert mixed numbers to improper fractions before performing operations.
- Not finding the least common denominator, which can lead to incorrect addition of fractions.
- Incorrectly converting back to a mixed number, especially miscalculating the whole number and the remainder.
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