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kirill [66]
3 years ago
8

Without doing the math, determine which is greater, 40. 1/4 or 40÷ 1/4. Explain your reasoning.

Mathematics
2 answers:
nevsk [136]3 years ago
8 0

When you divide by a fraction, in this case 40 divided by 1 over 4, you multiply by the reciprocal of what you're dividing by, so:

\frac{40}{1} ÷ \frac{1}{4}

turns into...

\frac{40}{1} · \frac{4}{1}, or 40 * 4, which equals 160.

With this knowledge, whenever given a set of numbers like you were given, we know that 40 ÷ \frac{1}{4} must be the larger, and 40 · \frac{1}{4} must be the smaller.

Therefore, 40 ÷ \frac{1}{4} is the greater number.

<em>Hope this helps! :)</em>

maw [93]3 years ago
4 0

40 ÷ \frac{1}{4} is greater

multiplying a whole number by a fraction  reduces the size of the whole number

dividing a whole number by a fraction increases the size of the number


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3x + 1 = 5X-13 if anyone knows what to do can they please help ​
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Answer:

  x = 7

Step-by-step explanation:

First, you look at the equation. Identify the locations of variable terms (both sides of the equal sign) and the constant terms (both sides of the equal sign).

If there are any parentheses, it is a good idea to use the distributive property to eliminate them. Here, there are none.

I like to start by subtracting <em>the variable term with the smallest coefficient</em>. Here, that is 3x, so we add -3x to both sides of the equation.

  3x -3x +1 = 5x -3x -13

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Now, we have the only variable term on one side of the equal sign. We want it by itself, so we need to make the -13 go away. We do that by adding its opposite to both sides of the equation:

  1 +13 = 2x -13 +13

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Finally, we want the coefficient of 2 in the x-term to disappear. We make that happen by multiplying both sides of the equation by 1/2, the reciprocal of that coefficient.

  (1/2)(14) = (1/2)(2x)

  7 = x . . . . the solution

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It is generally a good idea to <em>check your work</em> by seeing if your solution value satisfies the equation:

  3(7) +1 = 5(7) -13 . . . . put 7 where x is in the original equation

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_____

<em>Additional comment</em>

By subtracting 3x from 5x, the result is 2x with a positive coefficient. We could solve the equation just as easily by subtracting 5x from 3x. That result would be ...

  -2x +1 = -13

Subtracting 1 would give

  -2x = -14

and you would multiply by -1/2 to get x=7. I personally like to avoid having this many minus signs show up in the problem. That is why I choose to subtract the x-term with the smallest coefficient.

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