Question

PLZ help thanks!!!! A shipment of 10 tons of sugar is separated into containers of equal size. If the shipment fills 3 3/4 containers, how much sugar can one container hold?

Answer 1

Answer: 5/66 (I'm so sorry if this is wrong)

Explanation: First you divide 10 and 3 3/4. 10 ÷ 3 3/4 = 0.0757575757575.

To turn that back into to a fraction, let X equal the decimal number

Equation 1:

X = 0.0757575757575 (1)

With 12 digits in the repeating decimal group,

create a second equation by multiplying

both sides by 1012 = 1000000000000

Equation 2:

1000000000000X = 75757575757.5757575757575 (2)

Subtract equation (1) from equation (2)

1000000000000X = 75757575757.5757575757575...

X = 0.0757575757575...

999999999999X = 75757575757.5

We get

999999999999X = 75757575757.5

Solve for X

X = 75757575757.5/999999999999

Multiply to eliminate 1 decimal places.

Here you multiply top and bottom by 1 10's

= 101 = 10

75757575757.5/999999999999 × 10/10 = 757575757575/9999999999990

Find the Greatest Common Factor (GCF) of 757575757575 and 9999999999990, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 151515151515,

757575757575/9999999999990 ÷ 151515151515/151515151515 = 5/66

Therefore

X = 5/66

In conclusion,

0.0757575757575 = 5/66