Question

A carpenter is cutting a 15 1/4 foot piece of lumber into smaller pieces.
The length of each piece is 4 3/4 feet.
Use the drop-down menus to answer each question.

Answer 1

Answers:

• Expression is $15 \frac{1}{4} \div 4 \frac{3}{4}$
• whole number = 3
• fractional part = 4/19

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Explanation:

Let's convert the mixed number $15 \frac{1}{4}$ to an improper fraction

$a \frac{b}{c} = \frac{a*c+b}{c}\\\\15 \frac{1}{4} = \frac{15*4+1}{4}\\\\15 \frac{1}{4} = \frac{61}{4}$

Do the same for the other mixed number.

$a \frac{b}{c} = \frac{a*c+b}{c}\\\\4 \frac{3}{4} = \frac{4*4+3}{4}\\\\4 \frac{3}{4} = \frac{19}{4}$

We'll divide those two improper fractions to find the number of pieces

$15 \frac{1}{4} \div 4 \frac{3}{4}\\\\\frac{61}{4} \div \frac{19}{4}\\\\\frac{61}{4} \times \frac{4}{19}\\\\\frac{61}{19}$

Then let's convert that to a mixed number like so:

$\frac{61}{19}=\frac{57+4}{19}\\\\\frac{61}{19}=\frac{57}{19}+\frac{4}{19}\\\\\frac{61}{19}=3+\frac{4}{19}\\\\\frac{61}{19}=3\frac{4}{19}$

Or you could note that 61/19 leads to 3 remainder 4.

The carpenter is able to get 3 whole pieces out, then the extra fractional part is 4/19 of a foot.

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Here's another way to look at it.

Grab a footlong ruler and split it into 4 equal smaller lengths. I'll refer to these smaller pieces as "quarters" from now on.

1 ruler = 4 quarters

15 rulers = 15*4 = 60 quarters

15 rulers + 1 quarter = 60+1 = 61 quarters

So this is another way to see how the mixed number $15 \frac{1}{4}$ is the same as the improper fraction $\frac{61}{4}$

The same idea would apply to $4 \frac{3}{4} = \frac{19}{4}$

The overall entire board is 61 quarters long, and each piece is 19 quarters long. So that means 61/19 = 3 & 4/19 represents the number of pieces we can cut.

Answer 2

The carpenter is able to get 3 whole pieces out and then extra fractional part is 4/19 of a foot.

What is fraction?

A fraction is a number is expressed as a "quotient and a numerator is divided by denominator".

According to the question,

A carpenter is cutting a 15 1/4 foot piece of lumber into smaller pieces.

The length of each piece is 4 3/4 feet.

Convert mixed fraction into improper fraction  

15 1/4 = 61/4

4 3/4 = 19/4

In order to find the whole piece and the fractional part divide 61/4 and 19/4

61/4 ÷ 19/4

= 61/19

= $\frac{57+4}{19}$

= $\frac{57}{4}$ + $\frac{4}{19}$

= 3 + $\frac{4}{19}$

= $3\frac{4}{19}$.

Hence, the carpenter is cutting 3 whole piece lumber and 4/19 fractional part.

Learn more about Fraction here

https://brainly.com/question/18270600

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