49 Fun Facts About 6th Grade Math

In the expression 2 + 3 × 4, which operation do you do first?

The multiplication comes first, which makes the answer 14; without an agreed order the same string of symbols could mean two different numbers, so everyone follows one convention.

What is (2 + 3) × 4?

20: the grouping symbols send 2 + 3 to the front of the queue, making 5 × 4, because such symbols overrule the usual order.

What is the ratio of oranges to lemons, in simplest form, in a bowl of 8 oranges and 6 lemons?

4:3 comes from dividing both parts of 8:6 by 2; the order matters, because 3:4 would describe a bowl with more lemons than oranges.

A statement that two ratios are equal, such as 6:8 = 3:4, is called what?

A proportion lets you find a missing number by multiplying across the known corners and dividing by the third, which is how a recipe is scaled up or a distance read off a map.

The word 'percent' literally means 'by' what number?

One hundred is the 'cent' in percent, from the Latin per centum, 'by the hundred'; the same root gives a century its hundred years and a dollar its hundred cents.

What is 50% of 500?

250: fifty percent is just another name for a half, and the same shortcut turns 10% into a tenth, a quick way to work such percentages out in the head.

What percentage increase is a price rise from $2.00 to $2.50?

25%: divide the 50-cent rise by the starting price of $2.00; measured against the new price it would be only 20%, which is why a 25% rise is wiped out by a 20% cut.

Which of these is an integer?

−7 is an integer because integers are the whole numbers, their negatives and zero; the word is Latin for 'untouched' or 'whole', a number with no broken-off fractional part.

Which number has the greatest absolute value?

−8 sits eight steps from zero, farther than 7 does, and absolute value measures only that distance and never the direction, which is why it can never come out negative.

In the expression 2⁵, what is the 5 called?

The exponent counts how many copies of the base get multiplied together, so 2⁵ is 2 × 2 × 2 × 2 × 2 = 32, a long way from the 10 you get from 2 times 5.

Any nonzero number raised to the power of 0 equals what?

1: each step down in power divides by the base, so 2³ = 8, 2² = 4, 2¹ = 2 and 2⁰ = 1; it is the pattern, not a special rule, that forces the answer.

Why is b² called 'b squared'?

It gives a square's area: a square with side b covers b × b, just as b³ is 'b cubed' because a cube with that side has a volume of b × b × b.

What is the least common multiple of 6 and 8?

24: it is the first number to show up in both times tables, 6, 12, 18, 24 and 8, 16, 24; multiplying the pair gives 48, a common multiple but not the least one.

What is the greatest common factor of 18 and 27?

9: it is the largest number that divides both exactly, which is why 18/27 shrinks to 2/3 in a single step when you divide top and bottom by it.

When adding fractions, the smallest number that both bottom numbers divide into is called what?

The lowest common denominator of 1/2 and 1/3 is 6, so they become 3/6 and 2/6 and add up to 5/6; slices can only be counted together once they are all the same size.

Which theorem says every whole number above 1 is prime or a unique product of primes?

The fundamental theorem of arithmetic is why a factor tree always ends in the same primes however you split it, and why 1 is not counted as prime, since tacking on extra 1s would spoil the uniqueness.

On a coordinate plane, what are the coordinates of the origin?

(0, 0) marks the spot where the two axes cross, and every other point is measured from it; pinning points to numbers this way let René Descartes describe curves with equations, which joined geometry to algebra.

Which ordered pair names the point 5 units up and 3 units to the right of the origin?

(3, 5): the across move is always written first and the up-or-down move second, whichever way the directions are read out, which is why it is called an ordered pair and why (5, 3) is a different point.

In which quadrant of a coordinate plane are both the x and y values positive?

The first quadrant is the top right one, and the numbering then runs counter-clockwise, so the second sits at top left, where x turns negative while y stays positive.

How do you find the area of a triangle?

Half of base times height works because two identical copies of any triangle fit together into a four-sided shape with that same base and height, so one copy covers exactly half of it.

If 4 pens cost $6, what do 10 pens cost at the same price each?

$15: find the price of one pen first, $1.50, then multiply by ten; that price for a single unit is what supermarket shelf labels print so that different pack sizes can be compared.

What is the name for any four-sided shape whose opposite sides would never meet, however far they were extended?

A parallelogram also has opposite sides of equal length, which means every rectangle, square and rhombus belongs to the family; push a rectangle sideways and it stays one.

In North American English, which name covers every quadrilateral that has at least one pair of parallel sides?

A trapezoid is the American name; British books call the same shape a trapezium, and to add to the muddle each country has used the other's word for a four-sided shape with no parallel sides at all.

For a box shape (a rectangular prism), how do you find the volume?

Area of the base times the height gives the volume because a box is a stack of layers: one that is 2 by 3 by 4 has 6 unit cubes in its bottom layer and 4 such layers, so 24 in all.

What are the 12 lines where the faces of a rectangular box meet called?

Edges: a box has 12 of them along with 6 faces and 8 corners, and for every convex solid with flat faces the faces plus the corners come to exactly two more than that count.

Which measurement tells you how much wrapping paper would exactly cover a box?

Surface area is found for a box by adding the areas of its six faces, and since they come in three matching pairs, only three products are needed before doubling.

The number pi is the ratio of the distance around a circle to what?

Its diameter: divide the distance around any circle, whether a coin or a Ferris wheel, by the distance across and you always get the same number, about 3.14159, whose decimals never end or repeat.

Which fraction is commonly used as a rough approximation of pi?

22/7 comes to 3.142857..., right to two decimal places; the better 355/113 is right to six, yet no fraction at all can hit pi exactly.

What is the distance once around the rim of a wheel called?

The circumference comes from the Latin for 'carry around'; cut it open and straighten it out and you have the length of string that would wrap exactly once around the circle.

What is the mean of the numbers 2, 3, 4, 7 and 9?

5: add the numbers to get 25, then share that total equally among the five values, which is all a mean is, the fair share each would get if they were levelled out.

The middle value of a data set when the numbers are put in order is called what?

The median barely moves when one value is extreme, which is why typical incomes are reported this way: a billionaire moving to town drags the average up but leaves the middle where it was.

The value that appears most often in a data set is called what?

The mode of 3, 5, 5, 8, 9 is 5, and it is the one kind of average that still works when the data are not numbers at all, such as the most popular colour of car.

In algebra, a letter that stands for a number you do not yet know is called what?

A variable is the x in 3x + 2, where the 3 is its coefficient and the 2 a constant; the letter is only a placeholder, so the expression is worth 8 when x is 2 and 11 when x is 3.

Which property says that 2 × (1 + 3) equals (2 × 1) + (2 × 3)?

Distributive: the multiplying is handed out to each part of the sum, which is the trick behind mental arithmetic, since 6 × 204 is just 6 × 200 plus 6 × 4.

A number that can be written as a fraction of two integers, like 3/7 or −5, is called what?

Rational numbers include every integer, since −5 is just −5/1, and written as decimals they always either stop or settle into a repeating pattern, as 1/9 does with 0.111...

What do you multiply 5 by to get exactly 1?

1/5: any number times its flipped-over form makes 1, so 4 pairs with 0.25 and 2/3 pairs with 3/2; only zero has no such partner.

To divide by a fraction, you multiply by its what?

Reciprocal means the fraction turned upside down, so dividing by 1/2 becomes multiplying by 2; that is why dividing by a fraction smaller than 1 makes a number bigger.

What is the square root of 900?

30: a square root asks which number multiplied by itself gives 900; that one comes out whole, whereas the square root of 2 is a decimal that never ends or repeats.

In the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, ... what number comes next?

21: each term is the sum of the two before it, 8 + 13; Fibonacci met the pattern in a puzzle about breeding rabbits, and it turns up in the spirals of pine cones and sunflower heads.

How much water exactly fills a cube measuring 10 cm on each side?

1 litre is defined as the space inside exactly such a cube, which is 1,000 cubic centimetres, and that much water weighs almost exactly one kilogram.

Which unit of length is equal to 1,760 yards?

A mile is 1,760 yards or 5,280 feet, awkward numbers until you count in furlongs: a statute of 1593, under Elizabeth I, fixed the mile at eight furlongs, and a furlong is 220 yards.

What is the length of a rectangle with an area of 24 square units and a width of 4?

6: area is length times width, so dividing 24 by 4 undoes the multiplying, the same move that solves 4 × ? = 24 in algebra.

Which number is a perfect square?

49 is 7 × 7; perfect squares can only end in 0, 1, 4, 5, 6 or 9, so a number ending in 2, 3, 7 or 8 can be ruled out at a glance.

What kind of number do you always get by adding two odd numbers?

An even number: each odd number is a set of pairs with one left over, and when two of them are added the two leftovers make a pair of their own, so 3 + 5 = 8 and 7 + 9 = 16.

What do the three interior angles of any triangle add up to?

180°: set the three corners of any triangle side by side and they make a straight line, a half turn, which is why knowing two of the angles always gives you the third.

What is an angle smaller than a right angle called?

Acute comes from the Latin for 'sharpened', a cousin of the word for needle, while obtuse, the name for angles between a right angle and a straight line, means blunt.

What is the name for the total length of the boundary around a two-dimensional shape?

Perimeter comes from the Greek for 'measure around', and it is what you need to know to fence a field, whereas the amount of grass inside is a separate question.

In the order-of-operations acronym PEMDAS, what does the P stand for?

Parentheses come first, but the acronym misleads further along: addition does not outrank subtraction, the two rank equally and run left to right, so 10 − 3 + 2 is 9, not 5.

What sign does the product of two negatives have?

It is positive: multiplying by a negative reverses direction on the number line, so doing it twice points you forwards again, as with turning around twice.