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A piece of ribbon is [tex]$8 \frac{1}{3}$[/tex] feet long. How many pieces [tex]$1 \frac{2}{3}$[/tex] feet in length could be cut from the longer piece?

[tex]\square[/tex] pieces

Sagot :

GinnyAnsweridn
To solve the problem, we need to determine how many pieces each [tex]$1 \frac{2}{3}$[/tex] feet long can be cut from a longer ribbon that is [tex]$8 \frac{1}{3}$[/tex] feet long.

Let's break down the steps:

1. Convert the mixed numbers to improper fractions:
- The length of the longer piece of ribbon is [tex]$8 \frac{1}{3}$[/tex] feet. Convert this to an improper fraction:
[tex]\[ 8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3} \text{ feet} \][/tex]
- The length of the smaller pieces is [tex]$1 \frac{2}{3}$[/tex] feet. Convert this to an improper fraction:
[tex]\[ 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} \text{ feet} \][/tex]

2. Divide the total length of the ribbon by the length of one piece:
- To find how many [tex]$1 \frac{2}{3}$[/tex] foot pieces can be cut from [tex]$8 \frac{1}{3}$[/tex] feet of ribbon, divide [tex]$\frac{25}{3}$[/tex] by [tex]$\frac{5}{3}$[/tex]:
[tex]\[ \frac{25}{3} \div \frac{5}{3} = \frac{25}{3} \times \frac{3}{5} = \frac{25 \times 3}{3 \times 5} = \frac{75}{15} = 5 \][/tex]

3. Result:
- The number of [tex]$1 \frac{2}{3}$[/tex] foot pieces that can be cut from the larger piece of ribbon is:
[tex]\[ 5 \text{ pieces} \][/tex]

So, you can cut [tex]\(\boxed{5}\)[/tex] pieces of [tex]$1 \frac{2}{3}$[/tex] feet in length from a ribbon that is [tex]$8 \frac{1}{3}$[/tex] feet long.
Hi1315idn

Answer:

5

Step-by-step explanation:

1. Convert the mixed numbers to improper fractions:

[tex]8 \frac{1}{3}\: \text{becomes}\: \frac{25}{3} .\\\\1 \frac{2}{3} \: \text{becomes}\: \frac{5}{3}[/tex]

2. Divide the lengths:

 [tex]\frac{25}{3} \div \frac{5}{3}[/tex]

3. Dividing by a fraction is the same as multiplying by its reciprocal:

[tex]\frac{25}{3} \times \frac{3}{5} \\\\\frac{25 \times 3}{3 \times 5} \\\\ \frac{75}{15} = 5[/tex]

[tex]\text{So, you can cut 5 pieces}[/tex]  

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