1 Answer

Vennsoh · Answer 1 · 2021-07-11T12:55:59+0000

Answer:

1

Explanation:

There's a lot to unwrap here, but thankfully we have a set of rules for unwrapping an expression like this called the order of operations. It starts with looking at any parts of the expression that are clearly grouped with parentheses. Our expression has the complex grouping

$\left(((2.4-0.5)\cdot1(3)/(4))/((6.4-2.6)/(4)/(70))+0.875\right)$

With the groupings
(2.4-0.5) and
(6.4-2.6) nested inside. Let's handle those first:

$2.4-0.5=1.9\\6.4-2.6=3.8$

Taking these back to the larger grouped expression, we now have

$\left((1.9\cdot1(3)/(4))/(3.8/(4)/(70))+0.875\right)$

Since dividing by a fraction is the same as multiplying by its reciprocal, we can rewrite
3.8/(4)/(70) as
$3.8\cdot(70)/(4)$ . Let's also rewrite
1(3)/(4) as the improper fraction
(7)/(4) . The fraction in the parenthesis now becomes

$(1.9\cdot(7)/(4))/(3.8\cdot(70)/(4))$

We can split this up into the expression

$(1.9)/(3.8)\cdot((7)/(4))/((70)/(4))$

1.9 is half of 3.8, so
(1.9)/(3.8)=(1)/(2) , and
$(7)/(4) /(70)/(4) =(7)/(4) \cdot(4)/(70)=(7)/(70)=(1)/(10)$ , so we can finally simplify the big parentheses to read:

$((1)/(2)\cdot(1)/(10) +0.875)$

Next down from grouped expressions in the order of operations are exponents, and after that multiplication and division, which we handle from left to right. Handling the multiplication
$(1)/(2)\cdot(1)/(10)$ gives us
(1)/(20) =0.05 , letting us finally solve the big parentheses expression to get

(0.05+0.875)=0.925 .

Pulling back out to the larger expression and bringing back in the last two operations, we now have the expression
0.925/1(17)/(20) +0.5 . We can rewrite
in decimal form as
1.85 , making our expression read: