How To Add Fractions Horizontally

we want to solve the equation, x plus nine-halves equals nine-eighths. the solution to the equation is the value of x that makes the sum on the left equal to nine-eighths. in order to solve the equation for x, we need to isolate x on one side of the equation. and because x is on the left side of the equation, our solution will be in the form

How To Add Fractions Horizontally, x equals some value, or some fraction, again, that makes this sum equal to nine-eighths. now, looking at the left side of the equation, in order to isolate the variable x,

we don't want this plus nine-halves here. and therefore, to undo plus nine-halves, we need to perform the opposite, or inverse operation. and therefore to undo plus nine-halves, we will subtract nine-halves on both sides of the equation. and because we have fractions, we'll show the subtraction horizontally, rather than vertically under the equation. our next step will be x plus nine-halves, minus nine-halves equals nine-eighths, minus nine-halves. notice how again, we subtracted nine-halves on both sides of the equation.

whatever operation we perform to one side of the equation must also be performed on the other side to maintain equality. looking at the left side, subtracting nine-halves undoes the plus nine-halves, so this simplifies to zero. so, now on the left side we just have the variable x, and we have equals, this difference will be our solution. but before subtracting, we need to obtain a common denominator, hopefully the least common denominator. the least common denominator will be the least common multiple of two and eight,

which is eight, and therefore, eight is the least common denominator. and because two times four equals eight, we'll multiply the numerator and denominator of nine-halves by four. so now we know that x is equal to nine-eighths minus thirty-six eighths. now, because we have a common denominator, we can subtract the fractions. the denominator stays the same and the numerator is going to be nine minus thirty-six, which equals negative twenty-seven. if we need to, we can work this out on the side. nine minus thirty-six is equal to nine plus negative thirty-six,

which once again is equal to negative twenty-seven. so, our solution is x equals negative twenty-seven eighths, but before we go, let's check our solution by substituting negative twenty-seven eighths into the equation to make sure the sum on the left is equal to nine-eighths. so, performing this substitution we would have negative twenty-seven eighths plus nine-halves equals nine-eighths. the least common denominator on the left side is going to be eight, so multiply the numerator and denominator of nine-halves by four, just like we did below.

so, now we have negative twenty-seven eighths plus thirty-six eighths and negative twenty-seven eighths plus thirty-six eighths is nine-eighths. so we have nine-eighths equals nine-eighths, which is true, verifying our solution is correct. i hope you found this helpful.