How do you evaluate #\frac { a } { 7} + \frac { 5} { 7} = \frac { 3} { 7}#?

Question

HIX Tutor · Accepted Answer

undefined Let's solve the equation step by step.

1. Start with the equation:
   $$
   \frac{a}{7} + \frac{5}{7} = \frac{3}{7}
   $$

2. Combine the fractions on the left side. Since both fractions have the same bottom number (denominator), we add the tops:
   $$
   \frac{a + 5}{7} = \frac{3}{7}
   $$

3. Now, since the denominators are the same, we can set the tops (numerators) equal to each other:
   $$
   a + 5 = 3
   $$

4. Next, we want to find $a$. To do that, we subtract 5 from both sides:
   $$
   a = 3 - 5
   $$

5. Calculate $3 - 5$:
   $$
   a = -2
   $$

So, the answer is:
$$
a = -2
$$

Julia Adams · Answer

#a=-2#

It is equally true to write: since all of the denominators (bottom numbers) are the same.

#a+5=3#

If someone were a purist, they would have said to multiply both sides by 7

~

Now consider: #a+5=3#

Subtract #color(red)(5)# from both sides

#color(green)(a+5=3 color(white)("dddd")->color(white)("dddd")a+5color(red)(-5)color(white)("d")=color(white)("d")3color(red)(-5))#

#color(green)(color(white)("dddddddddddd")->color(white)("dddd")a+color(white)("d")0color(white)("d")=color(white)("d")-2#

#color(green)( color(white)("dddddddddddd")-> color(white)("dddd") acolor(white)("dddd.d")=color(white)("d")-2)#

Isaiah Anthony · Answer

undefined To evaluate the expression $ \frac { a } { 7} + \frac { 5} { 7} = \frac { 3} { 7} $, we first recognize that both fractions have the same denominator, which is 7. Thus, to combine them, we can add their numerators while keeping the denominator the same.

$$
\frac { a } { 7} + \frac { 5} { 7} = \frac { a + 5} { 7}
$$

Now, we equate this expression to $ \frac { 3} { 7} $ and solve for $ a $:

$$
\frac { a + 5} { 7} = \frac { 3} { 7}
$$

To solve for $ a $, we multiply both sides by 7:

$$
7 \cdot \frac { a + 5} { 7} = 7 \cdot \frac { 3} { 7}
$$

$$
a + 5 = 3
$$

Now, subtract 5 from both sides:

$$
a + 5 - 5 = 3 - 5
$$

$$
a = -2
$$

Thus, the value of $ a $ that satisfies the equation is $ -2 $.