Totals & comparisons — cards that total numbers and compare two of them

The four cards on the left are input cards. "Plan A" and "Plan B" are Summary cards, each adding up two costs. The Delta card "A vs B" at the bottom right shows the change from "Plan A", connected first, to "Plan B" as ▲ +60 and +9%. The Split the bill card at the top right splits Plan A's $700 between 3 people. It rounds each share up to a multiple of 10, so it shows 240 each, 720 collected and 20 left over.

With "A: hotel" changed from 400 to 460, Plan A becomes $760 and the Delta card shows 0 and 0%. The split changes to 260 each, 780 collected.

Result

The Result card shows the total of the numbers on the cards connected to it. With nothing connected it shows "Connect a card". Its main job is "Keep this total" in its ⋯ menu: the total is fixed, and when one number changes the other cards adjust. How to fix a total, how a change is spread, limits and splitting in whole numbers are covered in the usage guide's Keep a total and split it.

A Result card has no ○ handle to connect it onward. To use a total in further calculations, use a Summary card.

Summary

The Summary card turns the numbers on the connected cards into one value. The menu at the top of the card chooses SUM, AVG, MEDIAN, MODE, MAX, MIN or STDEV, and the card shows how many cards are connected ("5 cards"). Unlike a Result card, a Summary card's value can be connected onward from its ○ handle; the Split the bill card on Board 1 takes its total from a Summary card.

• STDEV — the standard deviation that divides by the number of values. For 20, 50 and 80 it is 24.494897.
• MODE — the value that appears most often. When several values appear equally often, the smallest is shown. When every value appears once, the card says "Every value appears once, so there is no mode".
• With a List card connected — the Summary card uses the single value the List card shows (the aggregate chosen on the list), not each row.
• Keep the average — with AVG chosen, the ⋯ menu has "Keep the average". The average at that moment is fixed; changing one connected input card makes the others adjust so the average stays the same. The ways to spread the change are the same as for "Keep this total" on a Result card.

Board 2 summarises five people's commute times with four Summary cards: max, min, mean and median. Right now the mean and the median are both 60 min.

With Person B changed from 90 to 180, the max becomes 180 min and the mean 78 min, while the median stays at 60 min. One large value pulls the mean up; the median is the middle value in order, which this change does not move.

A board that adds three values, 20, 30 and 50, to give 100. More value cards can be connected to the Summary card.

Open the total board ↗

A board that compares the plain average of A, B and C (20, 50, 80) from a Summary card with a weighted average using weights 1, 2 and 7. The Summary card shows 50; the weighted average is 68.

Open the weighted average board ↗

A board that splits 100 in the ratio 2 : 3 : 5. A Summary card adds the weights to 10, and 100 × weight ÷ 10 gives 20, 30 and 50.

Open the ratio split board ↗

Reference

The Reference card brings one value from another board saved on this device. The value has to be offered by the board that holds it: with a calculation card selected and the calculator below open, the "Result settings" button shows "Board output"; turning it on and pressing "Done" offers that card's value. An "Output label (optional)" can be given too.

On the board that uses the value, choosing "Reference" opens "Reference another board", where you pick the board and the output. After "OK", the Reference card appears with 🔗, the label and the value. Its value can be connected onward from its ○ handle.

• When the value changes on the other board, the new value appears the next time this board is opened. With both boards open in the same browser, it changes right away.
• ↻ reads the saved value again; → opens the referenced board.
• When the referenced board cannot be found, the card shows ⚠ and keeps the last value.

A Reference card needs a board saved on the reader's own device, so this page has no example board for it.

Before & after

The eight cards from Before & after to Time to double take numbers typed into fields on the card. They have no ○ handle, so the numbers they show cannot be used in another card's formula, and connecting another card to them brings the notice "This card can't take a value". The exception is the Total field of Split the bill, which can take a value from other cards. Board 3 shows Before & after, Percentage, Ratio and Min / current / max.

Given a Before and an After value, the Before & after card shows the change and the percentage change relative to Before. "Price rise" on Board 3 goes from 1,200 to 1,380, so it shows "Change +180 (+15%)". With Before set to 1,500 it shows "Change −120 (−8%)". The percentage has at most one decimal place. When Before is 0, only the change is shown.

Selecting the card and pressing "Visualize" offers "See the difference", a Delta card that reads these two numbers.

XY point

Given X and Y, the XY point card shows the point, such as "Point (3, 4)". Selecting two or more XY point cards and pressing "Visualize" makes a scatter plot. With only one selected, the "Visualize" button does not appear.

Min / current / max

Given three numbers, the Min / current / max card shows where the current value lies between min and max. "Food this month" on Board 3 is 360 on a range of 0 to 600, so it shows "60% of the way from min". With Current set to 660 it shows "60 above the max". Below the min it says how far below; it also says so when min is larger than max, or when they are the same.

Selecting the card and pressing "Visualize" offers "Number line" and "Position in range" (a gauge).

Percentage

The Percentage card has three fields, Whole, Part and Rate %, and works out one from the other two. Changing Whole or Rate % recalculates Part; changing Part recalculates Rate %. The bar and the figure below show the rate.

"Seats booked" on Board 3 is 30 of 40, so 75%. With Whole set to 50, the rate stays at 75% and Part becomes 37.5. Setting Part back to 30 then makes the rate 60%. When Whole is 0 the card shows "—".

Ratio

Given A, B and C, the Ratio card shows D such that A : B = C : D, which is B × C ÷ A. "Sugar and flour" on Board 3 shows "2 : 3 = 100 : 150": 100 g of sugar goes with 150 g of flour. With C set to 160 it shows "2 : 3 = 160 : 240". When A is 0, D is "—".

Split the bill

From Total, People and Round up to, the Split the bill card works out each person's share. The share is rounded up to a multiple of Round up to; the card also shows the amount collected and how much it exceeds the total (left over). With Board 1 at its starting values it shows "240 each × 3 = 720 (left over 20)".

• With Round up to set to 0, the share is not rounded: 10,000 for 3 people shows "3,333.33 each (10,000 ÷ 3)".
• When People is not a whole number, the card says "Enter a whole number of people".
• Other cards can be connected to the Total field. The field then holds the total of the connected cards and cannot be edited. On Board 1, the Summary card "Plan A" is connected.

Mix (concentration)

The Mix (concentration) card works out how much of A and B to mix to make a given amount at a given concentration. Its fields are A conc. %, B conc. %, Target % and Amount. Making 500 at 20% from 10% and 30% shows "A 250 + B 250".

• When the target is not between the two concentrations, the card shows "—".
• When A, B and the target all have the same concentration, such as 10%, the card shows "Any ratio gives 10%".

Board 4 of Concentration uses it for two salt solutions.

Time to double

From Change per period % and Times the start, the Time to double card works out how many periods it takes. Growing 5% per period, doubling takes "14.21 periods (rule of 72: 14.4)". The rule-of-72 figure appears only for 2 times or 0.5 times.

• Shrinking works too: at −5% per period, halving takes 13.51 periods.
• With a change of 0 the card says "Never gets there (no change)". Combinations that never arrive, such as growth with 0.5 times, show "—".

Compound interest uses it for the years to double at a yearly rate.

Check (two answers)

With two cards connected, the Check (two answers) card shows whether their values match: "✓ Match", or "✗ Off by …" with the difference. Below that it shows the two values and the names of the two cards. Values are compared to six decimal places: 80 and 80.0000001 match, while 80 and 80.000001 are "Off by 0.000001".

The next board works out a price with 10% tax in two ways, "Price × 1.1" and "Price + Price × 0.1", and compares them. Both give $132, so the card shows "✓ Match". With the price set to 98, both give 107.8 and still match.

Open the board that checks two tax formulas ↗

Delta

With two cards connected, the Delta card shows the change from the card connected first to the card connected second: ▲ in green when it goes up, ▼ in red when it goes down, with the difference and the percentage change. The percentage is rounded to a whole number. Below, the two names appear as "(A → B)"; long names are cut short with "…".

• With only one card connected, the card says "Connect two cards". A third card and any after it are not used.
• A Delta card made from a Before & after card through "Visualize" → "See the difference" reads that card's two fields.

On a board with A = 80 and B = 100 connected, it shows "▲ +20" and "+25%".

Open the before and after board ↗

Another board has the same formula x × y twice with different inputs. Case ① is 3 × 4 = 12 and case ② is 5 × 2 = 10, so the Delta card shows "▼ −2" and "−17%". With y₂ set to 3, case ② becomes 15 and the card shows "▲ +3" and "+25%".

Open the two cases board ↗

Check

The Check card checks an answer against the correct value. When a card is connected to it, you choose whether it is the answer or the correct value. Pressing "Check answer" shows "✓ Correct", "△ Close" or "✗ Try again". With the answer blank, it shows the notice "Enter your answer". While the board is being edited, the card also shows the correct value, such as "Correct: 204".

Board 4 asks for the sale price of a $240 item at 15% off. The correct value is the "Sale price" card, $204, and the "Off" card, $36, is a step on the way. Typing a number into "Your answer" and pressing "Check answer" gives:

• 204 → "✓ Correct"
• 205 → "△ Close". On this board, close means within 1% of the correct value, so up to 206 is close and 207 is "✗ Try again".
• 276 → "✗ That adds the amount off to the price", a value registered as a common mistake.
• 36 → "✗ That is the in-between “Off” (36 $). One more step"
• 200 → "✗ Try again"

"⚙ Settings" opens these options:

• How to compare — with "Exact number", the answer is correct when it equals the correct value. "Within tolerance" adds a "Tolerance (±)" field (0.01 at first); the answer is correct when it is within that distance.
• Hint 1 to 3 — for each hint written, a "Hint (1/2)" button shows one more hint per press.
• Close within — a number and how to measure it: "± (by that much)" or "% (of the answer)". An answer that is not correct but falls in this range gets "△ Close".
• Common mistake 1 to 3 — a wrong value and the message to show for it. When the answer equals that value, the message appears after "✗".
• Messages when correct, wrong and close — text shown instead of "Correct", "Try again" and "Close".

Without any settings, when the answer equals the value of a card used on the way to the correct value, the card names it. On Board 4, answering 240, the list price, also gives "in-between “Price”". The checks run in this order: correct, common mistake, in-between value, close. A value registered as a common mistake shows its message even when it is also close.

"Show answer" shows "Answer: 204". Answering correctly after that shows "✓ Correct (after seeing the answer)". An input card used for the answer can be left blank with "Allow blank (for quizzes)" in its ⋯ menu; "Your answer" on Board 4 starts blank.

Articles that use these cards

• Compound interest — the future value from an annual rate and a number of years — the Time to double card gives the years to double and the rule-of-72 estimate.
• Concentration — finding it, diluting and mixing — the Mix (concentration) card gives the amounts of two salt solutions for a target concentration.

Read next — Charts. The cards that turn number cards into bar charts, pie charts, gauges, scatter plots and other pictures.

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