Question

Connor has an envelope that is 3 inches tall. The envelope is 4 9/10 times as long as it is tall. How long is his envelope?

Write your answer as a fraction or as a whole or mixed number.

Answer 1

To find the length of the envelope, we can multiply the height of the envelope by the factor that gives the length in relation to the height.

Given:
- Height of the envelope = 3 inches
- Length is given as 4 9/10 times the height

First, we convert 4 9/10 to an improper fraction:

\[
4 \frac{9}{10} = \frac{40}{10} + \frac{9}{10} = \frac{49}{10}
\]

Now we can calculate the length of the envelope:

\[
\text{Length} = \text{Height} \times \text{Factor}
\]

We substitute the values:

\[
\text{Length} = 3 \times \frac{49}{10}
\]

We convert 3 to a fraction:

\[
3 = \frac{30}{10}
\]

Now we can multiply the fractions:

\[
\text{Length} = \frac{30}{10} \times \frac{49}{10} = \frac{30 \times 49}{10 \times 10} = \frac{1470}{100}
\]

Next, we simplify \(\frac{1470}{100}\):

Both the numerator and denominator can be divided by 10:

\[
\frac{1470 \div 10}{100 \div 10} = \frac{147}{10}
\]

We can convert this improper fraction into a mixed number:

\[
\frac{147}{10} = 14 \frac{7}{10}
\]

So, the length of Connor's envelope is:

\[
\boxed{14 \frac{7}{10}} \text{ inches}
\]