A rope is 6 3/4 meter along is cut into 3/4 meters pieces and thea 1/2 all those pieces
are used for a project how many meters of rope were used
Answer (2)
I. Convert the total rope length to an improper fraction[tex]\[\mathsf{6\frac{3}{4} = \frac{27}{4}}\][/tex]II. Divide the total length by the length of each piece[tex]\[\mathsf{\frac{27}{4} \div \frac{3}{4} = \frac{27}{4} \times \frac{4}{3} = \frac{108}{12} = 9}\][/tex]III. Multiply the number of pieces used by the length of each piece:[tex]\[\mathsf{\frac{9}{2} \times \frac{3}{4} = \frac{27}{8} = 3\frac{3}{8}}\][/tex]IV. Final answer[tex]\[\boxed{\mathsf{3\frac{3}{8}\ \text{meters}}}\][/tex]Therefore, the total length of rope used is 3 3/8 meters
27/8 meters or 3.375 meters of rope were usedDivide first to find how many pieces are used. Convert to improper fraction to divide. Then we get the reciprocal and multiply to find the quotient.[tex]6\frac{3}{4} \div\frac{3}{4}[/tex][tex]\frac{27}{4} \div\frac{3}{4}[/tex][tex]\frac{27}{4} \times \frac{4}{3}[/tex][tex]\frac{27\times4}{4\times3} =\frac{108}{12}[/tex]Simplify by getting the GCF (Greatest Common Factor) In this case, it's 12[tex]\frac{108\div12}{12\div12} =\frac{9}{1} =9[/tex]Therefore, there is 9 pieces cut into 3/4 metersIt says that 1/2 is used, so we can just divide the pieces by 2[tex]9\div2 = 4.5[/tex]Therefore, 4.5 pieces of rope were usedNow, to get how many meters were used we multiply 4.5 by 3/4First, we convert 4.5 to fraction [tex]\frac{9}{2}\times\frac{3}{4}[/tex]Multiply the numerator and the denominator[tex]\frac{9\times3}{2\times4} =\frac{27}{8}[/tex]The decimal representation of 27/8 is 3.375.To convert the fraction 27/8 to a decimal, you can divide 27 by 8. This results in 3 with a remainder of 3. Then, you can express the remainder as a decimal by dividing it by 8, which is 3/8, or 0.375. Combining the whole number part (3) with the decimal part (0.375) gives you the final decimal representation of 3.375. Therefore, the meters of rope used is 27/8 meters or 3.375 meters
