Question

Will someone help me with both of these I have to solve for the unknown portions please

Answer 1

Answer:

• h = 5/2
• p = 6

Step-by-step explanation:

c) Multiply by the denominator under the variable, then simplify.

$\dfrac{10}{8}=\dfrac{h}{2}\\\\\dfrac{2\cdot 10}{8}=h\\\\\dfrac{5}{2}=h$

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d) Simple observation shows you the denominator of each fraction is half the numerator, so p = 6.

If you want to solve this algebraically, you can multiply by p and divide by the value on the left of the equal sign (2).

$\dfrac{4}{2}=\dfrac{12}{p}\\\\\dfrac{p}{2}\cdot\dfrac{4}{2}=\dfrac{p}{2}\cdot\dfrac{12}{p}\\\\p=6$

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For an "upside down" proportion such as this (with the variable in the denominator), you can rewrite it by inverting both fractions:

  $\dfrac{2}{4}=\dfrac{p}{12}$

Now, solve as for (c), by multiplying by the denominator under the variable:

  $\dfrac{12\cdot 2}{4}=p=6$

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Comment on this last solution method

In general, you can use equation solving methods to solve inequalities. However, taking a reciprocal is an order-reversing process:

  3 > 2

  1/3 < 1/2

So, if you want to solve an inequality with the variable in the denominator of a proportion, be careful to observe any order-changing behavior of your solution method.

Answer 2

Answer:

b=2.5

p=6

Step-by-step explanation:

Take the fraction and simplify it. So 10/8 would be 5/4

You multiply the 2 by 2, giving you h/4

So now you have 5/4=h/4

h=5 but now you have to divide both by 2 again so it can go back to the original fraction.

5÷2=2.5 and 4÷2=2

Second Problem! 4/2 is equal to 2/1

You can also multiply 4 by 3 to get the numerator as 12. Multiply the 4 by 3 and the 2 by 3

Now you have 12/6= 12/p

So p is 6