Question

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.

Ms. Nellies has 2 1/2 pints of vinegar for her students to use in a science experiment.Each group of students needs 3/8 pint of vinegar.Trey draws the number line model and writes the equation below to help Ms. Nellies figure out how many 3/8-pint serving of vinegar she has.Are Trey's number line model and equation correct?

Trey's number line is _______ because it represents the expression _________.The correct equation is _______.Ms. Nellies has enough vinegar for _________ groups of students.

1st blank box: correct or incorrect

2nd blank box: 2 1/2 x 3/4,2 1/2 ÷ 3/4,2 1/2 x 3/8,or 2 1/2 ÷ 3/8.

3rd blank box: 2 1/2 ÷ 3/8= 6 2/3,2 1/2 ÷ 3/8 = 3 1/3,2 1/2 x 3/8 = 2 3/16, or 2 1/2 ÷ 3/8 = 15/16

4th blank box: 2,6,3,or 0


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Answer 1

Answers:

Trey's number line is incorrect because it represents the expression 2 1/2 ÷ 3/4.

The correct equation is 2 1/2 ÷ 3/8 = 6 2/3.

Ms. Nellies has enough vinegar for 6 groups of students.

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Step-by-step explanation:

Trey has the right idea, but made a mistake on how the tickmarks are set up. Focus on the interval from 0 to 1. This section is cut into 4 equal pieces. So each tickmark represents 1/4 of a unit.

Going 3 tickmarks across means 3/4 of a unit is represented. Since each larger arc represents 3/4 of a unit, this means we're dividing the 2 & 1/2 over 3/4 instead of 3/8

That's why Trey's model represents 2 1/2 ÷ 3/4

The value 3 & 1/3 at the end is correct. Visually we see 3 whole jumps plus an extra 1/3 of a jump to arrive at 2 & 1/2. But again, Trey didn't cut the number line up in the right way, so it doesn't matter that he arrived at the correct result of 3 & 1/3 since his initial setup is faulty.

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See the diagram below to see what Trey should have drawn. Notice each tickmark represents 1/8 instead of 1/4. Each large blue arc jump represents 3/8 of a unit. We have exactly 6 of these blue arcs plus 2 additional smaller arcs that are 1/3 of the blue arc. So that accounts for the 1/3+1/3 = 2/3 portion.

Overall, we would say that the equation is 2 1/2 ÷ 3/8 = 6 2/3

If you're curious why that equation works, check out the steps below

`2 (1)/(2) / (3)/(8) = (5)/(2) / (3)/(8)\\\\2 (1)/(2) / (3)/(8) = (5)/(2) * (8)/(3)\\\\2 (1)/(2) / (3)/(8) = (5*8)/(2*3)\\\\2 (1)/(2) / (3)/(8) = (40)/(6)\\\\2 (1)/(2) / (3)/(8) = (20)/(3)\\\\2 (1)/(2) / (3)/(8) = (18+2)/(3)\\\\2 (1)/(2) / (3)/(8) = (18)/(3)+(2)/(3)\\\\2 (1)/(2) / (3)/(8) = 6+(2)/(3)\\\\2 (1)/(2) / (3)/(8) = 6(2)/(3)\\\\`

So again, the equation is 2 1/2 ÷ 3/8 = 6 2/3

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What does this all mean? Well it means the teacher can break up the vinegar into 6 whole parts plus an additional 2/3 of a part.

In other words, 6 groups will get 3/8 of a pint each. The leftover part 2/3 isn't enough to form that 7th group. Notice in the diagram below, we have 2/8 = 1/4 of a pint which is smaller than 3/8 of a pint.

1/4 = 0.25

3/8 = 0.375

So this is another way to see that the leftovers isn't enough to form a 7th group.

Therefore, she has enough vinegar for 6 groups