How do you understand what happens on a fraction number line and how do you know where the fraction is. Tell me how we will be a
1 answer:
9514 1404 393
Answer:
understand what the fraction means
Step-by-step explanation:
First of all, you need to <em>understand what 2/3 means</em>. It means 1 whole has been divided into 3 equal parts, and you're concerned with 2 of those parts.
In the number line in the first attachment, the space between 0 and 1 has been divided into 3 equal parts. The decimal value (rounded) is shown at each tick mark. The point marked "2/3" is located at the second of those divisions, counting from zero.
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The same fraction is located on the same number line in the second attachment. That number line is marked with divisions at intervals of 1/10, so there are 10 of them between 0 and 1. The value 2/3 is represented by the point that is (2/3)(10) = 6 2/3 of those intervals, so is between 0.6 and 0.7 on the number line.
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If the number line were divided into 12ths, then the fraction 2/3 would be located at the 8th tick mark, counting from 0. (2/3)(12) = 8 That is shown in the third attachment.
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Answer:
2/x+1
Step-by-step explanation:
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Answer:
- 12 gallons 84%
- 8 gallons 4%
Step-by-step explanation:
I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.
Here, that means the ratio of 84% solution to 4% solution is ...
48 : 32 = 12 : 8
Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)
Mary must use ...
- 12 gallons of 84% acid solution
- 8 gallons of 4% acid solution
You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.
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<em>Check</em>
12 × 84% + 8 × 4% = 10.40 = 20 × 52%
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<em>Usual Solution</em>
A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...
0.84x + 0.04(20 -x) = 0.52(20)
0.80x + 0.8 = 10.4 . . . . simplify
0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8
x = 9.6/0.8 = 12 . . . . gallons of 84% acid
20-x = 8 . . . . . . . . . . gallons of 4% acid
