Solve Complex Fraction: 10÷(7÷(9/2)) Step-by-Step Solution

Question

$10/(7/(9/2))=\text{?}$

00:06 Let's solve this problem step by step.

00:10 First, we write the division as a fraction. This helps us see the relationship clearly.

00:18 Remember, division is the same as multiplying by the reciprocal. That's the flipped version of a fraction.

00:29 Now, move the multiplication to the numerator. Keep it clear and organized.

00:38 Again, division is like multiplying by the reciprocal. This is an important concept.

00:50 Next, let's factor 10. It can be broken down into 2 and 5.

00:59 Reduce or simplify what you can. This makes the numbers easier to work with.

01:07 Break down 45. Think of it as 42 plus 3.

01:12 Now, separate the fraction into a whole number and the remainder. This simplifies understanding.

01:19 And there you have it. That's the solution to our problem!

We rewrite the innermost parentheses in fraction form:

$10/(7:\frac{9}{2})=$

We convert the parentheses into a multiplication exercise through inverting the fraction:

$10/(7\times\frac{2}{9})=$

We add the 7 to the numerator for the multiplication exercise:

$10/(\frac{7\times2}{9})=10:\frac{7\times2}{9}$

We convert the exercise into a multiplication by inverting the fraction:

$10\times\frac{9}{7\times2}=$

We add the 10 to the numerator for the multiplication exercise:

$\frac{10\times9}{7\times2}=$

We break down the 10 into a simpler multiplication exercise:

$\frac{5\times2\times9}{7\times2}=$

We simplify the 2 in the numerator and denominator:

$\frac{5\times9}{7}=\frac{45}{7}$

We convert the fraction's numerator into a sum exercise:

$\frac{42+3}{7}=\frac{42}{7}+\frac{3}{7}=6+\frac{3}{7}=6\frac{3}{7}$

$6\frac{3}{7}$