Question

При каких значениях 5\16а-1\12 в 4 раза больше значения выражения 5\16+5\12?

Answer 1

5/16a-1/12=(5/16+5/12)×4
5/16a-1/12=1 1/4+1 2/3
5/16a=1 3/12+1 8/12+1/12
5/16x=3:5/16
x=48/5=9 3/5=9,6

Answer 2

Calculation of Expressions

To find the values of the given expressions, let's start by calculating each expression step by step.

The given expressions are: 1. \(5/16a - 1/12\) 2. \(5/16 + 5/12\)

Calculation 1: \(5/16a - 1/12\)

First, let's calculate the value of \(5/16a - 1/12\).

Given that \(5/16a - 1/12\) is 4 times the value of \(5/16 + 5/12\), we can set up the equation as follows:

\[5/16a - 1/12 = 4 \times (5/16 + 5/12)\]

Now, let's solve for the value of \(a\).

Solving for \(a\)

To solve for \(a\), we'll first simplify the expression on the right-hand side of the equation and then solve for \(a\).

First, let's simplify \(4 \times (5/16 + 5/12)\):

\[4 \times (5/16 + 5/12) = 4 \times (5/16 + 10/24)\] \[= 4 \times (5/16 + 5/12)\] \[= 4 \times (15/48 + 20/48)\] \[= 4 \times (35/48)\] \[= 35/12\]

So, the equation becomes:

\[5/16a - 1/12 = 35/12\]

Now, let's solve for \(a\).

\[5/16a = 35/12 + 1/12\] \[5/16a = 36/12\] \[5/16a = 3\]

Now, solving for \(a\):

\[a = \frac{3}{5/16}\] \[a = 3 \times \frac{16}{5}\] \[a = 3 \times 3.2\] \[a = 9.6\]

Calculation 2: \(5/16 + 5/12\)

Now, let's calculate the value of \(5/16 + 5/12\).

\[5/16 + 5/12 = \frac{5 \times 3 + 5 \times 4}{16 \times 3}\] \[= \frac{15 + 20}{48}\] \[= \frac{35}{48}\]

So, the value of \(5/16 + 5/12\) is 35/48.

Conclusion

The value of \(5/16a - 1/12\) when \(a = 9.6\) is 4 times the value of \(5/16 + 5/12\), which is 35/48.