Start adding from the highest position. If you want to add if the layers are misaligned, try to do the math orally.

division

A number × 1.5 is equal to itself + half of itself

A number × 1.1 is equal to this number and you want to add it

A number × 0.9 is equal to the misalignment of this number.

Look ahead option If large, cut off two digits If small, cut to three digits One-step denominator Cut off multiple steps

Magnitude: consider decimal point, percent sign, unit

1. The options are very different (cut off by two digits). The first positions are all different. The first positions are the same. The difference between the second positions is > the first position.

2. The difference between the options is small (cut off to three digits). The first place is the same, and the difference between the second place ≤ the first place.

There is a big gap between the options, it’s about 100 percent.

The gap between the options is small and must be an accurate percentage.

1/2=50% 1/4=25% 1/8=12.5% 1/16=6.25%

1/3=33.3% 1/6=16.7% 1/12=8.3%

Core: option, first split out the special percentage, and the remaining number is how many times a point in the denominator is

If the numerator is close to the denominator, you can subtract it by 1

If the numerator is greater than 50%, split 50% first

If the numerator is less than 50%, it can be reduced by 50%

135%=1 0.35

The numerator and denominator take the first three significant figures respectively.

Stagger the same bits, add and subtract the same times (the multiples should be as small as possible)

Get results quickly

Directly divide vertically, compare quotient

Comparing multiples horizontally, whoever has a higher multiple will listen to whoever has it

stare

If possible, eliminate first, then compare.

None of the four can be ruled out, except vertically.

Current pit

structural reading method

Heavy header

Sweep vertically

Note traps: unit, magnitude, accumulation (time)

Look at the title

to the legend

Note special

Classification

Look separately

Pay attention to the connections between different types of materials

Base period = current period – growth amount

Base period = current period/1 r

two steps

Different subjects

The options are different, use the elimination method to directly stare at

What's the ranking?

(A/1+a)±(B/1 b)

Base period difference≈A-B/1 a

Let’s first look at the current pitfalls Analyze and stare

Let’s first look at the current pitfalls Analyze and stare

Let’s first look at the current pitfalls Look at the positive and negative again

First look at the current pitfalls, and then analyze them in detail or take advantage of growth Base period difference = (A-B)-(△A-△B)

Let’s first look at the current pitfalls Then mix thoughts and stare

Current period = base period + growth amount

Current period = base period × (1 r)

Current period = base period + n × growth amount Keep the increment unchanged If it is exceeded for the first time, convert the units first and then calculate

Current period = Base period × (1 r) Growth rate is unknown

Current period = base period × (1 r)² Keep growth rate unchanged substitution method, square numbers

If you ask about the current period, pay attention to the traps Current period=base period growth amount

The actual current period is slightly smaller than the nominal current period (direct glare)

Percentage and percentage point high minus low plus

Given the growth rate, find the multiple - how many times is it = growth rate 1

Number: How many percent is it? Double: n times = 2ⁿ times

Growth rate: Ratio with sign

Decline: compare absolute values

Range of change: compare absolute values

Known percentages and percentage points: high minus low plus (direct glare)

The specific amount is known: r = growth amount / current period - growth amount = (current period - base period) ÷ base period = current period / base period - 1 Growth amount/base period

First add the base period and current period, and then calculate the growth rate

Special test method: class growth rate A is more or less than B? %

How many have r>10%?

The fastest (slowest) growth/decline is

Line chart problem

Sorting problems

There is one year between the two times. If the growth rate is known, find the growth rate.

Formula: r1＋r2＋r1×r2

Given r and r1, find r2 r2＝r-r1/1＋r1

Calculate the interval r first (the product is ignored) Interval multiple = r space + 1

Base period = current period/1+r period

Time period + annual average..., highest/lowest growth rate (sorting)

Formula: (1 r)ⁿ=current amount/base period amount (n is the year difference between the current period and the base period)

Formula: (1 r)ⁿ=current amount/base period amount (n is the year difference between the current period and the base period)

Calculation: When |r|≤10%, then (1+r)ⁿ≈1+nr When |r|＞10%, then (1＋r)ⁿ＞1+nr, combined with substitution verification (centered substitution)

Quick calculation tool: square numbers 11²=121 12²=144 13²=169 14²=196 15²=225 16²=256 17²=289 18²=324 19²=361

Quick calculation tool: Power numbers 1.2³=1.7 1.2⁴=2.0 1.1⁵=.161 1.3³=2.2 1.3⁴=2.9 1.4³=2.7 1.4⁴=3.8

Subject mix: export + import = import and export Time mix: January-February + March = 1 quarter

Mix the main body and find the parts (subtractive transformation) Surplus + Expenditure = Revenue

Mix the main bodies and find the total amount (distance and amount are inversely proportional) Import + Export = Import and Export

Time mixing, find the part (large bias vector) January-February + March = January-March

Surplus = Exports – Imports Exports = Imports + Surplus

Method One: Three Carrots and Three Pitfalls The center is not centered after mixing (minimum growth rate < total growth rate < maximum growth rate) Prefer those with large base period volume

Method 2: Line segment method calculation Tip: Write both sides before mixing, write the middle after mixing, distance is inversely proportional to quantity (essentially, quantity is the denominator)

Mixed growth rate inverse operation

Mixed growth rate extension①

Mixed growth rate extension②

The core is a product relationship, find the growth rate Three-quantity relationship: A=B×C Features of the question: Given the growth rate b of B and the growth rate c of C, find the growth rate a of A. a=b c b×c（r1＋r2＋r1×r2）

Growth + unit (specific amount) Test method ①: The current period and base period are known: Growth amount = current period - base period (glare, underline subtraction) Special: average annual growth = current period - base period/year difference (the selection of the base period is consistent with the average annual growth rate) Test method ②: The current period and r are known: 100 percent growth = base period × r = current period / (1 + r) × r The first step: centigrade, |r|=1/n Step 2: Growth amount = current period/n+1 Decrease = current period/n-1

Given the current period, r, find the increment r＝4.2% is smaller (<5%) The growth amount is slightly less than the current period × r

Given the current period, r, find the increment r＝87% is larger (>50%) formula glare Current period/(1+r)×r

Given the current period, r, find the increment exceeding a certain number Growth amount > 120 (popular test method) Give priority to choosing the right one, neither too big nor too small. Combined with comparing stares and counting ticks

Given the increment of A, find the increment of non-A Non-A growth = overall increase – A increase

100% speed calculator

Growth + most or least (sort) Test method ① The current period and base period are known: Growth amount = current period - base period (glare, underline division) Column chart, line chart, directly see the height difference

Test method ② Known current period sum r: hundred percent Growth amount=base period×r=current period/(1+r)×r The formula: if it is big, it will be big - if the current period is big and the growth rate is big, the growth will be big. If the current period is large and the decline is large, the reduction will be large (note the negative number) One large and one hundred cents (multiples) Draw an arrow and listen to whoever gets the bigger multiple.