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1. If thereâ€™s any parentheses ( ) then do them first.
2. Then do exponents xn and powers 103 and radicals.
3. Then do multiplication Ã— and division Ã·.
4. And then do any addition + and subtraction - from left to right.
It may help to remember them as P.E.M.D.A.S. using their first letters.
Thus in the example 4 + 5 Ã— 2, we would multiply first.
8 - 4 - 1 =?
What if we wanted to tell someone to do the subtraction in a different order? Use parentheses to change the natural order. Expressions in parentheses are always done first. Note: Singular is parenthesis, and plural is parentheses.
8 - (4 - 3) =?
What about nested parentheses? Evaluate the innermost parentheses first.
( 8 - (4 + 2))2 =?
Suppose you have an expression with both subtraction and exponents. You should do the exponent first (unless commanded otherwise by parentheses).
2 Ã—3 + 4 Ã— 5 =?
So be sure to understand how your own calculator handles its order of operations!
By the way, most calculators that follow the natural order (multiplication first) also have parentheses keys so you can change the order, if needed. If you see parentheses on a calculator, thatâ€™s a good clue that it was designed to handle the natural order of operations. If in doubt, use the parentheses keys â€œ(â€œ and â€œ)â€ to ensure it follows the order you want.
a + 6 - b =?
a / 2 Ã— b =?
b - a / 2 =?
What about cascading fractions such as? This can be either or which give different results. The writer must be clear when putting it on paper! This is another great reason to love parentheses.
Use the implied parentheses around each fraction, then start with the innermost and work your way out.There is nothing worse than a slow WordPress website and Headway Digital get as frustrated as the next person. There are many reasons why a WordPress Website could be slow and while there are WordPress plugins that can help optimise files and attempt to make the site faster, invariably it is just another plugin. For this reason, we provide a professional WordPress Website Speed Optimisation service.
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Recall last week, each index bottomed within two points of its 20-day moving average.
And after a strong two-day spike, each index topped Tuesday right around multi-year highs.
That means for the time being, each index is crammed between its near-term uptrend as support and its multi-year range top as resistance.
After pulling back to three-week lows, the S&P has rallied sharply over the past two sessions.
In Tuesday's action, the index topped at 1,388 -- just a point under its five-year high -- before pulling in modestly to close at 1,382.
From current levels, modest support holds around 1,382 followed by a firmer floor in the 1,370-to-1,372 area.
Meanwhile, the Dow Jones Industrial Average has also staged a steep two-day spike.
On Tuesday, it briefly notched another all-time high, before pulling in modestly to close at 12,156.
Its all-time closing high, established on Oct. 26, rests at 12,163 -- just seven points above Tuesday's close.
That leaves the Nasdaq as a hybrid of the Dow and the S&P.
Like the Dow, the Nasdaq briefly notched five-year highs intraday on Tuesday.
Yet like the S&P, the Nasdaq closed essentially on its five-year range top. Indeed, Tuesday's close of 2,375 precisely matched the April high.
As the chart illustrates, the Nasdaq's been working on the April high for about three weeks now.
On Tuesday, it topped intraday at 2,391 -- marking a five-year high -- before pulling in to close at 2,375.
Meanwhile, the Dow Jones Industrial Average remains the strongest major benchmark.
After holding its 20-day moving average last week, it briefly notched all-time highs Tuesday.
Yet on a closing basis, Tuesday's close missed an all-time high by seven points.
Like the other benchmarks, the S&P 500 has also successfully tested its near-term uptrend.
It bottomed Friday just a point under its 20-day before spiking Tuesday within a point of five-year highs.
Over the past two sessions, each major U.S. benchmark has challenged significant resistance while rallying from near-term support.
The downside support points held at each benchmarks' uptrend, which roughly tracks its 20-day moving average. Recall each index bottomed last week within two points of its 20-day.
The Nasdaq closed precisely on the 2,375 resistance -- matching the April high.
The S&P 500 topped at 1,388 -- just a point under its five-year high.
The Dow closed at 12,156, missing an all-time closing high by just seven points.
So that's where the tension rests technically: Each index is crammed between its uptrend and multi-year highs.
The area that gives way first will likely open the way to the next meaningful near-term move.
Yet until that tension is resolved, the established uptrend remains in play. Until proven otherwise, the path of least resistance is higher.
Last profiled Oct. 17, the Telecom Index XTC remains among the stronger technology sectors.
After breaking out in mid-August, the group has notched five-year highs, establishing a tight, three-month ascending channel.
Last week, it pulled back to observe the early-October high as support, rising from that area over the past two sessions.
The five charts below illustrate related names positioned to rise: Telecom iShares IYZ, Millicom International Cellular MICC, Leap Wireless LEAP, NII Holdings NIHD and SBA Communications SBAC.
Initially profiled Aug. 28, Infosys Technologies INFY has returned 21.2% and remains well positioned.
Tuesday, it challenged six-year highs on increased volume, positioning the shares to build on the stock's mid-October spike marked by strong volume.
China-based online-media company Sina Corp. SINA spiked last week after posting strong third-quarter results.
Since then, it's sustained its gains, pulling in on lighter volume toward a more attractive entry near the breakout point.
Initially profiled Aug. 2, Akamai Technologies AKAM has returned 29.7% and remains well positioned.
After notching six-year highs in early October, it's pulled back to successfully test the 50-day moving average as support.
In Tuesday's action, it rallied from support on strong volume, positioning Akamai to retest the October high.
Fair Isaac FIC is a mid-cap software vendor positioned to rise.
After recently observing its 50-day moving average as support, it spiked last week on its fourth-quarter results.
The subsequent consolidation has come on lighter volume, with the shares extending their gains again Tuesday. Recent strength places Fair Isaac above its 200-day moving average for the first time since March.
Novell NOVL spiked last week after announcing a software partnership with Microsoft.
The subsequent pullback has been orderly, bringing the shares to more attractive levels 11% under last week's high.
PLX Technology PLXT is a small-cap semiconductor name positioned to rise.
In mid-October, it spiked above its 200-day, an area it had observed as resistance since July.
After a shallow pullback, it rallied Tuesday driven by another volume uptick, positioning the shares to challenge a five-month range top.
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As the end of