Solve: Combining (5/6)x + (7/8)x + (2/4)x Algebraic Expression

Question

$\frac{5}{6}x+\frac{7}{8}x+\frac{2}{4}x=$

00:00 Solve

00:03 Multiply each factor by its number to find the common denominator

00:09 Make sure to raise both numerator and denominator by the number

00:31 Now we have a common denominator and can group factors

00:45 Note to add the numerators and keep the denominator

00:54 Each time combine 2 numbers and then continue

01:01 Break down 53 into 48 plus 5

01:06 Break down the fraction into whole number and remainder

01:12 Convert from proper fraction to whole number

01:16 And this is the solution to the question

First, let's find a common denominator for 4, 8, and 6: it's 24.

Now, we'll multiply each fraction by the appropriate number to get:

$\frac{5\times4}{6\times4}x+\frac{7\times3}{8\times3}x+\frac{2\times6}{4\times6}x=$

Let's solve the multiplication exercises in the numerator and denominator:

$\frac{20}{24}x+\frac{21}{24}x+\frac{12}{24}x=$

We'll connect all the numerators:

$\frac{20+21+12}{24}x=\frac{41+12}{24}x=\frac{53}{24}x$

Let's break down the numerator into a smaller addition exercise:

$\frac{48+5}{24}=\frac{48}{24}+\frac{5}{24}=2+\frac{5}{24}=2\frac{5}{24}x$

$2\frac{5}{24}x$