Solve: 3⅚ × 5⅚ × ⅓x Mixed Number Multiplication

Question

Solve the following problem:

$3\frac{5}{6}\times5\frac{5}{6}\times\frac{1}{3}x=$

00:00 Solve

00:03 We want to convert from a mixed number to a fraction only

00:06 We'll do this by multiplying the whole number by the denominator

00:10 We'll use the same method for this fraction

00:19 Always solve multiplication and division before addition and subtraction

00:33 Make sure to multiply numerator by numerator and denominator by denominator

00:46 We'll use long multiplication to calculate

00:59 This is the numerator multiplication

01:06 Now we'll use long multiplication to calculate the denominator multiplication

01:20 This is the denominator multiplication

01:23 And this is the solution to the question

First, let's convert all mixed fractions to simple fractions:

$\frac{3\times6+5}{6}\times\frac{5\times6+5}{6}\times\frac{1}{3}x=$

Let's solve the exercises with the eight fractions:

$\frac{18+5}{6}\times\frac{30+5}{6}\times\frac{1}{3}x=$

$\frac{23}{6}\times\frac{35}{6}\times\frac{1}{3}x=$

Since the exercise only involves multiplication, we'll combine all the numerators and denominators:

$\frac{23\times35}{6\times6\times3}x=\frac{805}{108}x$

$\frac{805}{108}x$