Katrina rode her bicycle \(6\dfrac{1}{2}\,\text{km}\) in the morning and \(8\dfrac{3}{4}\,\text{km}\) in the evening. Find the total distance travelled that day.
\(15\dfrac{1}{4}\,\text{km}\)
Goal: Add the morning and evening distances.
Given:
Step 1: Write each mixed number as an improper fraction.
For \(6\dfrac{1}{2}\):
\(6\times 2 = 12\)
\(12 + 1 = 13\)
So, \(6\dfrac{1}{2} = \dfrac{13}{2}\).
For \(8\dfrac{3}{4}\):
\(8\times 4 = 32\)
\(32 + 3 = 35\)
So, \(8\dfrac{3}{4} = \dfrac{35}{4}\).
Step 2: Make denominators the same.
The denominators are \(2\) and \(4\). A common denominator is \(4\).
Convert \(\dfrac{13}{2}\) to a denominator of \(4\):
\(\dfrac{13}{2} = \dfrac{13\times 2}{2\times 2} = \dfrac{26}{4}\).
Step 3: Add the fractions.
\(\dfrac{26}{4} + \dfrac{35}{4} = \dfrac{26 + 35}{4} = \dfrac{61}{4}\).
Step 4: Change the improper fraction to a mixed number.
Divide \(61\) by \(4\):
\(61 \div 4 = 15\) with remainder \(1\).
So, \(\dfrac{61}{4} = 15\dfrac{1}{4}\).
Answer: \(15\dfrac{1}{4}\,\text{km}\).
Quick check with decimals (optional):
\(6\dfrac{1}{2} = 6.5\)
\(8\dfrac{3}{4} = 8.75\)
\(6.5 + 8.75 = 15.25\)
\(15.25 = 15\dfrac{1}{4}\,\text{km}\). ✔️