Answer:
1⅞ - 1½ ≈ ½
Step-by-step explanation:
Estimation is mental arithmetic. Practice until you can do this in your head.
Here's one way to estimate with mxed numbers.
Step 1. Separate into whole number and fractional parts
1⅞ - 1½ = 1 + ⅞ - 1 - ½
Step 2. Solve the whole number parts
1 - 1 = 0
Step 3. Solve the fraction parts by estimating.
We will round to the nearest ½, so we should round up a number greater than ¾.
(a) ⅞ is greater than ⁶/₈ (¾), so we round it up to ⁸/₈:
⅞ - ½ ≈ ⁸/₈ - ½
(b) Convert each fraction to a common denominator.
We can write ⁸/₈ as ²/₂
⁸/₈ - ½ = ²/₂ - ½
(c) Solve the fraction part
²/₂ - ½ = ½
Step 4. Combine the whole and fraction parts
0 + ½ = ½
So, 1⅞ - 1½ ≈ ½
The solution of the system of the equations shown is where the equations intersect
--> <u>(-7, 1)</u>
Hope that helps!
<span> Use the rational root theorem to find the possible rational roots. The rational roots theorem says that possible rational roots are +/- factors the constant term (36 here) divided by factors of the leading coefficient (1 here). Possible rational roots are
+/- 1, 2, 3, 4, 9, 12, 18, 36
Test each zero using the rational root test. To do this, use synthetic division to test the roots. I won't show the work here, but the roots that work are -2 and -3. As factors, this is x+2 and x+3.
From the synthetic division, we have x^2-4x+6 left over, which is irreducible.
In factored form:
f(x) = (x+2)(x+3)(x^-4x+6)
You could also use a graphing calculator to find the roots and work backwards to get the factored form too. A TI-89 Titanium would factor the polynomial and give you the above answer.</span>
