Answered

1. Haven bought [tex]6 \frac{2}{3} \, \text{m}[/tex] of cloth. She used [tex]4 \frac{3}{5} \, \text{m}[/tex] for 3 skirts. How much cloth remained?

A. [tex]\frac{1}{15} \, \text{m}[/tex]
B. [tex]1 \frac{2}{15} \, \text{m}[/tex]
C. [tex]2 \frac{1}{15} \, \text{m}[/tex]
D. [tex]2 \frac{2}{15} \, \text{m}[/tex]



Answer :

GinnyAnswer
Certainly! Let's solve the problem step-by-step:

1. Convert Mixed Numbers to Improper Fractions:
- Haven bought [tex]\(6\frac{2}{3}\)[/tex] meters of cloth.
- Haven used [tex]\(4\frac{3}{5}\)[/tex] meters of cloth.

To work with these amounts, we first convert them to improper fractions.

For [tex]\(6\frac{2}{3}\)[/tex]:
- The whole number part is 6.
- The fractional part is [tex]\(\frac{2}{3}\)[/tex].
- Convert [tex]\(6\frac{2}{3}\)[/tex] to an improper fraction:
[tex]\[ 6\frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \][/tex]

For [tex]\(4\frac{3}{5}\)[/tex]:
- The whole number part is 4.
- The fractional part is [tex]\(\frac{3}{5}\)[/tex].
- Convert [tex]\(4\frac{3}{5}\)[/tex] to an improper fraction:
[tex]\[ 4\frac{3}{5} = 4 + \frac{3}{5} = \frac{20}{5} + \frac{3}{5} = \frac{20 + 3}{5} = \frac{23}{5} \][/tex]

2. Calculate Remaining Cloth:
- Subtract the amount of cloth used from the amount of cloth bought.
[tex]\[ \text{Remaining cloth} = \frac{20}{3} - \frac{23}{5} \][/tex]

To subtract these, find a common denominator:
- The least common multiple (LCM) of 3 and 5 is 15.
- Convert each fraction to have the denominator of 15.
[tex]\[ \frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15} \][/tex]
[tex]\[ \frac{23}{5} = \frac{23 \times 3}{5 \times 3} = \frac{69}{15} \][/tex]

Now subtract the fractions:
[tex]\[ \frac{100}{15} - \frac{69}{15} = \frac{100 - 69}{15} = \frac{31}{15} \][/tex]

3. Convert the Remaining Cloth Back to a Mixed Number:
- [tex]\(\frac{31}{15}\)[/tex] can be converted to a mixed number.
- Divide 31 by 15.
[tex]\[ 31 \div 15 = 2 \text{ remainder } 1 \][/tex]
- So, [tex]\(\frac{31}{15}\)[/tex] is equivalent to:
[tex]\[ 2 \frac{1}{15} \][/tex]

4. Match to the Given Choices:
- The remaining cloth is [tex]\(2 \frac{1}{15}\)[/tex] meters.
- The correct choice is [tex]\(C: 2 \frac{1}{15} \text{ m}\)[/tex].

In conclusion, the remaining cloth is [tex]\(2 \frac{1}{15}\)[/tex] meters, which corresponds to option [tex]\(C: 2 \frac{1}{15} \text{ m}\)[/tex].

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