Question

Nora's car weighs 6 2/3 tons and Ling's car weighs 2 1/4 tons. How much more does Nora's car weigh than Ling's car? Write your answer as a fraction or as a whole or mixed number.

Answer 1

To find out how much more Nora's car weighs than Ling's car, we need to subtract Ling's car weight from Nora's car weight.

Nora's car weight: \(6 \frac{2}{3}\) tons
Ling's car weight: \(2 \frac{1}{4}\) tons

First, we will convert both mixed numbers to improper fractions.

For Nora's car:
\[
6 \frac{2}{3} = 6 \cdot 3 + 2 = 18 + 2 = \frac{20}{3}
\]

For Ling's car:
\[
2 \frac{1}{4} = 2 \cdot 4 + 1 = 8 + 1 = \frac{9}{4}
\]

Now we need to subtract \(\frac{9}{4}\) from \(\frac{20}{3}\).

To do this, we need a common denominator. The least common multiple of 3 and 4 is 12.

Now, convert both fractions to have a denominator of 12:

For Nora's car:
\[
\frac{20}{3} = \frac{20 \cdot 4}{3 \cdot 4} = \frac{80}{12}
\]

For Ling's car:
\[
\frac{9}{4} = \frac{9 \cdot 3}{4 \cdot 3} = \frac{27}{12}
\]

Now we can subtract:
\[
\frac{80}{12} - \frac{27}{12} = \frac{80 - 27}{12} = \frac{53}{12}
\]

Now, we can convert \(\frac{53}{12}\) back to a mixed number:
\[
53 \div 12 = 4 \quad \text{remainder } 5
\]
So,
\[
\frac{53}{12} = 4 \frac{5}{12}
\]

Therefore, Nora's car weighs \(4 \frac{5}{12}\) tons more than Ling's car.