50 Fun Facts About 7th Grade Math

A $100 jacket is marked up 10%, then put on sale at 10% off; what is the final price?

$99 is the final price because the 10% discount comes off the larger $110, removing $11 rather than $10. A rise and a fall of the same percentage never cancel out.

Sound covers roughly 343 metres a second; how far away is lightning whose thunder arrives 3 seconds later?

About 1 km is right, since 343 × 3 is 1,029 metres. Counting three seconds for every kilometre between the flash and the bang is a standard way to judge how close a storm is.

Which shape is the cross-section when an upright cylinder, like a soup can, is sliced straight down the middle?

Rectangle is the shape whenever the cut runs at right angles to the base; through the middle it is as tall as the can and as wide as its lid. Slice the same can parallel to the base and the face is a circle.

Pi Day is celebrated on which date, chosen because the month and day match the first three digits of π?

March 14 is written 3/14 in the American style, echoing 3.14. The celebration was founded in 1988 by Larry Shaw at the Exploratorium, a science museum in San Francisco.

When a billionaire walks into a small café, which measure of the customers' wealth barely changes?

Median wealth barely moves because it is simply the middle value once everyone is lined up in order. The mean would leap into the millions, dragged up by a single extreme value.

A fair coin lands heads five times in a row; what is the probability that the sixth flip is heads?

1/2 is still the chance, because a coin has no memory and every flip is independent of the last. Expecting tails to be 'due' is the mistake known as the gambler's fallacy.

What is 68% of 50, a sum made simple by swapping it for 50% of 68?

34 is the answer either way round, because 68 × 50 and 50 × 68 are the same product. Any percentage can be flipped like this, which turns an awkward sum into simple halving.

When every side of a square is made 7 times as long, the square's area is multiplied by which number?

49 is the multiplier, because area grows with the square of the change in length: 7 times as wide and 7 times as tall. Volume grows faster still, by the cube.

Hot Wheels toy cars are made at about 1:64 scale; how long is the toy of a 16-foot car?

3 inches is right: 16 feet is 192 inches, and 192 ÷ 64 = 3. The size is also called three-sixteenths scale, because 3/16 of an inch on the model stands for one foot.

Which two-word term describes a comparison such as 60 miles per hour, where the second quantity is exactly one?

Unit rate is the form that makes comparing easy: dividing 300 miles by 5 hours gives 60 miles for every single hour. A price per ounce on a shelf tag is one too.

Which name is given to k in the equation y = kx, the role speed plays when distance depends on time?

Constant of proportionality is the full name, and y is always that many times x. For a car at a steady 50 miles an hour, k is 50, so the distance is 50 times the hours driven.

When pay is always the same multiple of hours worked, a graph of the two is a straight line through which point?

(0, 0) is on every such graph because zero of one quantity always means zero of the other: no hours worked, no pay earned. A straight line that misses that point shows a fixed fee or a head start instead.

A 12-pack of soda costs $4.20; what is the price of each can, the figure shoppers use to compare pack sizes?

$0.35 comes from dividing $4.20 by 12. Stores usually post this price for a single item or ounce on the shelf tag, beside the price of the whole pack.

On a plan where 1 cm means 2 m, what is the real area of a room drawn 3 by 7 cm?

84 m² is the real area, because the room measures 6 m by 14 m. Both sides have to be scaled up: multiplying the drawing's 21 by 2 only once gives 42, half the true figure.

A recipe uses 3 cups of flour for 2 dozen cookies; how many cups do 5 dozen cookies need?

7.5 is right: each dozen takes 1.5 cups, and 5 × 1.5 = 7.5. Adding one cup for each of the 3 extra dozen, a common slip, gives 6 and leaves the dough short.

A nurse counts 18 heartbeats in 15 seconds; what is the patient's heart rate in beats per minute?

72 bpm is the rate, since a minute holds four 15-second counts and 18 × 4 = 72. That sits comfortably inside the normal resting adult span of 60 to 100.

A sprinter who runs 100 metres in 10 seconds averages which speed in kilometres per hour?

36 km/h is the answer: 10 metres a second, times the 3,600 seconds in an hour, is 36,000 metres. Multiplying metres per second by 3.6 always converts to kilometres per hour.

What is a 20% tip on a $65 restaurant bill, found quickly by doubling one-tenth of the total?

$13 is the tip: one-tenth of $65 is $6.50, and doubling that gives $13. Sliding the decimal point one place to the left finds 10% of any amount.

An $80 pair of sneakers is sold where sales tax is 6%; what is the total at the register?

$84.80 is the total: 6% of $80 is $4.80, added to the shelf price. Multiplying $80 by 1.06 does both steps at once.

After a 20% discount a pair of running shoes costs $96; what was the price before the sale?

$120 was the original price: the $96 is the 80% left after the discount, and 96 ÷ 0.80 = 120. Adding 20% of $96 back on gives only $115.20, because that 20% is taken from a smaller amount.

A phone's price falls from $200 to $150; what is the percent decrease, measured against the original price?

25% is the decrease: the $50 drop is one quarter of the original $200. Measured against the new price of $150, the same $50 would be about 33%, which is why the starting value matters.

63 is 45% of which number, found by dividing 63 by 0.45 rather than multiplying?

140 is the whole: 63 ÷ 0.45 = 140, and 45% of 140 is 63 as a check. Multiplying instead gives 28.35, an answer smaller than the part it is supposed to contain.

How much simple interest does $500 earn in 3 years at 4% a year, with no interest reinvested?

$60 is the interest: 4% of $500 is $20 a year, for three years. Simple interest is always worked out on the starting amount alone, which bankers call the principal.

Which word describes numbers such as π and the square root of 2, whose decimals never end or repeat?

Irrational numbers cannot be written as one whole number over another. In one legend the Greek Hippasus was thrown overboard at sea by fellow Pythagoreans for discovering them.

Which name, from the Latin for 'whole', covers zero, the counting numbers and the negatives of those numbers?

Integers have no fractional part, so −3, 0 and 8 qualify but 2.5 does not. Mathematicians label the set with a Z, from Zahlen, the German word for numbers.

Which two-word term names a number's distance from zero on the number line, written with vertical bars?

Absolute value is never negative, so −7 and 7 share the same one: 7. The vertical-bar notation was introduced by the German mathematician Karl Weierstrass in 1841.

Which term names a number's opposite, such as −9 for 9, the partner that brings the sum to zero?

Additive inverse pairs sit equally far from zero on opposite sides of the number line. Zero is the only number that is its own.

Which word describes a decimal such as 0.375 that stops, unlike 0.333… which goes on forever?

Terminating decimals come only from fractions whose simplest-form denominator has no prime factors other than 2 and 5. That is why eighths end neatly while thirds never do.

What is the value of 8 − (−11)?

19 is the result, because taking away a debt of 11 is the same as gaining 11: 8 + 11 = 19. Dropping one of the minus signs gives −3 instead.

What is (−4) × (−3) × (−2), a product whose sign depends on there being three negative factors?

−24 is the product: the first two negatives multiply to a positive 12, and the third flips the sign back. An odd count of negative factors always leaves a negative result.

What is 5/8 written as a decimal, found by dividing 5 by 8 until the remainder disappears?

0.625 is exact, because one eighth is 0.125 and five of them make 0.625. Eighths never need more than three decimal places, since 8 is 2 × 2 × 2.

A student measures a 50 cm table as 46 cm; what is the percent error, judged against the true length?

8% is the error: the measurement is off by 4 cm, and 4 is 8% of the true 50 cm. Dividing by the measured 46 instead gives about 8.7%, but the accepted value is always the yardstick.

Four test scores average 80; what must a fifth test score be to lift the overall mean to 83?

95 is needed: five scores averaging 83 total 415, and the first four supply only 320. A single new score has to sit well above the target to drag the mean up.

Team A scores 10, 12 and 14; Team B scores 2, 12 and 22; which measure shows Team B is less consistent?

Range is 4 for Team A but 20 for Team B, though both average exactly 12. Measures of spread show what an average hides: how tightly the values cluster.

Which term names a data value, like one 2 among test scores in the 80s, that sits far from the rest?

Outlier values can drag an average a long way from where most of the data sits. They are worth a second look, since some turn out to be measurement or recording errors.

Which kind of sample gives every student in a school an equal chance of being picked for a survey?

Random sampling lets a small group stand in fairly for a whole population. Asking only the students in the lunch line, by contrast, would tilt the results towards whoever eats there.

Which graph shows a data set's five-number summary, with whiskers reaching out to the lowest and highest values?

Box plot displays, also called box-and-whisker plots, were introduced by the American statistician John Tukey in 1970. The box itself holds the middle half of the data.

A spinner has 8 equal sections numbered 1 to 8; what is the probability of landing on a number above 5?

3/8 is the chance, because three of the eight equally likely sections (6, 7 and 8) count as a win. Probability is the number of winning outcomes divided by the number of possible ones.

What is the probability that two fair dice total exactly 4, a sum made by rolling 1-3, 2-2 or 3-1?

1/12 is the chance: three of the 36 equally likely pairs add up to 4, and 3/36 simplifies to 1/12. A total of 7 is the most likely of all, with six ways to roll it.

Which name is given to pieces of an expression such as 3x and 5x, which combine into 8x because the variable matches?

Like terms are combined by adding their number parts, much as 3 apples plus 5 apples make 8 apples. A pair such as 3x and 5y has to stay separate.

Which expression equals 3(x + 4) − x once the bracket is expanded and everything is simplified?

2x + 12 is the simplified form: the bracket expands to 3x + 12, and taking away one x leaves 2x. Forgetting to multiply the 4 by 3 gives 2x + 4, the usual slip.

A gym charges a $40 joining fee plus $25 a month; after how many months has a member paid $465 in total?

17 is right: taking off the $40 fee leaves $425, and 425 ÷ 25 = 17. As an equation it is 25m + 40 = 465, solved by undoing the addition before the multiplication.

Notebooks cost $8 each and a teacher has $190 to spend; what is the greatest number the teacher can buy?

23 is the most, leaving $6 in change. The inequality 8n ≤ 190 gives n ≤ 23.75, but notebooks only come whole, so the answer rounds down instead of up.

The angles of a triangle are in the ratio 3:4:5; how many degrees is the largest of the three angles?

75° is the largest: the ratio has 12 parts, each worth 15°, giving angles of 45°, 60° and 75°. A triangle whose sides are in that ratio is another matter, since it contains a 90° corner.

Which expression is 6x + 18 written as a product, with the greatest common factor outside the bracket?

6(x + 3) is the factored form, since 6 divides both 6x and 18. Multiplying it back out is a quick check: 6 times x plus 6 times 3 returns the original expression.

A circle has a circumference of 31.4 cm; using 3.14 for π, what is the area of the circle?

78.5 cm² is the area: dividing 31.4 by 3.14 gives a diameter of 10 cm, so the radius is 5 cm, and 3.14 × 5 × 5 = 78.5. Squaring the diameter instead produces 314.

A fish tank measures 50 cm by 40 cm by 40 cm inside; how much water fills the tank to the brim?

80 litres fills the tank: 50 × 40 × 40 is 80,000 cubic centimetres, and every 1,000 of those make one litre. That much water weighs about 80 kilograms.

Which word describes two angles that add up to 90°, as the two sharp corners of every right triangle do?

Complementary angles fit together to make a right angle. The word has nothing to do with praise: it traces back to the Latin complere, meaning to fill up.

Two sides of a triangle measure 4 cm and 9 cm; which of these lengths could the third side be?

8 cm works because any two sides of a triangle must add up to more than the third, and 4 + 8 beats 9. With 5 cm or 13 cm the three sides would only fold flat into a straight line.

Dividing by 2/3 gives the same result as multiplying by 3/2, a flipped fraction known by which name?

Reciprocal pairs always multiply to 1, which is why 'flip and multiply' works for dividing fractions. Zero is the only real number without one.