50 Fun Facts About 6th Grade Math

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

Multiplication ranks above addition, so the answer is 14, not 20.

What is (2 + 3) × 4?

The parentheses force the addition to happen first: 5 × 4 = 20.

A bowl holds 8 oranges and 6 lemons. What is the ratio of oranges to lemons in simplest form?

Divide both parts of 8:6 by 2; the ratio of oranges to all the fruit would be 8:14, or 4:7.

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

Solving proportions is how you scale a recipe up or read a map.

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

So 45% is the fraction 45/100, or 0.45 as a decimal.

If 50% of a class of 500 students are boys, how many boys are there?

50 out of every 100 means half, and half of 500 is 250.

A price of $2.50 goes up by $0.15. What percentage increase is that?

Divide the change by the original price: 0.15 ÷ 2.50 = 0.06.

Which of these is an integer?

Integers are whole numbers and their negatives, plus zero; fractions and decimals are not.

What is the absolute value of −3?

Absolute value is a number's distance from zero, so it is never negative.

In the expression 2⁵, what is the 5 called?

The 2 is the base; the exponent tells you how many times to multiply the base by itself.

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

It looks odd, but it keeps the pattern going: 2³ = 8, 2² = 4, 2¹ = 2, 2⁰ = 1.

Why is b² called 'b squared'?

In the same way, b³ is 'b cubed' because it is the volume of a cube with side b.

What is the least common multiple of 4 and 6?

Multiples of 4 are 4, 8, 12, 16...; multiples of 6 are 6, 12, 18...; the earliest number on both lists is 12.

What is the greatest common factor of 8 and 12?

The factors of 8 are 1, 2, 4, 8 and of 12 are 1, 2, 3, 4, 6, 12; the biggest one they share is 4.

When adding fractions, the smallest number both denominators divide into is called what?

Rewriting 1/4 and 1/6 as 3/12 and 2/12 makes them easy to add.

Every whole number above 1 is prime or a unique product of primes. What is this fact called?

It is why prime factorisation trees always end up with the same primes no matter which branch you split first.

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

It is the point where the x-axis and y-axis cross.

The two axes of a coordinate plane divide it into how many quadrants?

They are numbered counter-clockwise, starting from the top right.

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

Counting goes counter-clockwise from there: the second quadrant has a negative x and positive y.

How do you find the area of a triangle?

A triangle is exactly half of a four-sided shape with the same base and height.

A triangle has a base of 10 cm and a height of 6 cm. What is its area?

Multiply base by height and halve it: 10 × 6 ÷ 2 = 30.

A quadrilateral with two pairs of parallel sides is called what?

Its opposite sides are equal in length and its opposite angles are equal too.

In North American English, a quadrilateral with at least one pair of parallel sides is called what?

The parallel sides are the bases and the other two are the legs; British books call the same shape a trapezium.

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

For a box that is 2 by 3 by 4, that is 6 × 4 = 24 cubic units.

How many edges does a rectangular box (cuboid) have?

It also has 6 faces and 8 corners, the same counts as a cube.

How much the outside of a solid object covers, adding up every face, is called what?

For a box, you find it by adding up the areas of its six rectangular faces.

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

Pi is about 3.14159, and its decimals never end or settle into a repeating pattern.

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

22 ÷ 7 = 3.142857..., close to pi's 3.14159 but not exact, because pi cannot be written as a fraction at all.

What is the distance around the outside of a circle called?

It is the circle's version of perimeter; you find it with pi times the diameter.

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

Add them up to get 25 and divide by how many there are: 25 ÷ 5 = 5.

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

It is not thrown off by one huge or tiny value, which is why median income is often reported instead of average income.

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

In the list 3, 5, 5, 8, 9 the mode is 5.

In algebra, a letter that stands for an unknown or changeable number is called what?

In 3x + 2, the x is the variable, the 3 is its coefficient and the 2 is a constant.

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

You spread the multiplying over each part of the sum; both sides equal 8.

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

Every integer counts too, since −5 is the same as −5/1.

What do you multiply 5 by to get exactly 1?

Any number times its 'flip' gives 1; 0.25 pairs with 4 in the same way.

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

Dividing by 1/2 is the same as multiplying by 2, which is why the answer gets bigger.

What is the square root of 16?

4 × 4 = 16; strictly speaking −4 is a square root too, but the principal square root is the positive one.

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

Each number is the sum of the two before it: 8 + 13 = 21.

How many cubic centimetres are in one litre?

A litre is a cube 10 cm on each side, and 10 × 10 × 10 = 1,000.

How many centimetres are in a metre?

'Centi' means a hundredth, just as a cent is a hundredth of a dollar.

How many yards are in a mile?

5,280 is the number of feet in a mile; divide by 3 to get yards.

A rectangle has an area of 24 square units and a width of 4. What is its length?

Area equals length times width, so length is 24 ÷ 4.

Which number is a perfect square?

7 × 7 = 49; the perfect squares run 1, 4, 9, 16, 25, 36, 49, 64...

An integer is even if it can be divided evenly by which number?

Zero counts as even, and so do negatives like −4.

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

That is why knowing two angles of a triangle always lets you work out the third.

What is an angle smaller than a right angle called?

An angle between 90 and 180 degrees is obtuse, from a word meaning blunt.

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

For a circle or ellipse the same measurement gets a special name: the circumference.

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

Students often remember it with the sentence "Please Excuse My Dear Aunt Sally".

What sign does the product of two negatives have?

This rule is needed so that multiplication keeps obeying the distributive law.