Fractions Trivia Quiz

Answer: Broken

The Latin word "fractus" is also the root for the English word "fracture". Many mathematical terms are originated from Latin and Greek words.

Answer: Solidus

Besides, a vinculum can also be used to represent a fraction. It is the "horizontal line" that separates the numerator and the denominator of a fraction. It has other uses as well. For example, 1/3 = 0.333333... can be written as 0.3 (which a vinculum above the value 3 in 0.3) to indicate that the value 3 repeats itself infinitely.

It is used in Boolean algebra (AND, OR, NOT), too. For example, A (with a vinculum above the letter A) means NOT A.

Answer: Denominator

The number on the top is the numerator while the number at the bottom is the denominator.

Answer: Improper fraction

Only improper fractions can be converted into mixed numbers. For an improper fraction, the value of the numerator is greater than that of the denominator. For example, 9/7 can be converted into 1 2/7. On the other hand, a proper fraction is a fraction where its numerator's value is lower than that of the denominator.

Answer: False

This type of series is called a divergent series, where the sum is not a constant. We notice that 1/1 =1, 1/2 = 0.5, 1/3 = 0.333..., 1/4 = 0.25, 1/5 = 0.2 and so on. On the other hand, for a convergent series, the sum converges to a constant. For example, 1/2 + 1/(2^2) + 1/(2^3) + 1/(2^4) + 1/(2^5) + ... converges to 1. We can test whether a given series is convergent or divergent by using many tests, including ratio test, root test, integral test, alternating series test, limit comparison test, etc.

This series (1/1 + 1/2 + 1/3 + 1/4 +...) is called a harmonic series. The values for all the numerators are the same, namely 1.

1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 +...
=1/1 + (1/2) + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8)+ (1/9 + 1/10+...
Notice that (1/3 + 1/4) is greater than 1/2, and 1/5 + 1/6 + 1/7 + 1/8 is also greater than 1/2, and so does 1/9 + 1/10 + ... + 1/16.
So the series is greater than an infinitely multiple of 1/2. So we can conclude that the sum of 1/1 + 1/2 + 1/3 + 1/4 1/5 does not approach to a certain number and it is a divergent series.

Answer: 1

This is just multiplication of fractions. (1/2) x (1/4) x (1/8) x 64 = 1.

Answer: 3.141... (pi)

Pi is an irrational number. The fraction of 22/7 is only an approximation to the real value of pi and it is only correct for the first few decimal places.

It is obvious that 0.5 equals to 1/2. Repeating decimal numbers can be converted into fractions. For example, 0.123123123... We can write it as 0.123 + 0.000123 + 0.000000123 + ... The first term is 0.123, followed by 0.000123, 0.000000123 and so on, with a geometric ratio of 0.0001. This is a geometric progression. So, by using the formula a/(1-r), 0.123123123... = 0.123/(1-0.0001) = 41/333 .

The number 0.111111111... can also be written in fraction form, which is 1/9. Irrational numbers such as 3.141... (pi) and surd 2 cannot be expressed in fractions, since their decimal numbers do not appear in repeating patterns.

Answer: Pythagoras

The square root of 2 (the number 1.414...) is also known as the Pythagoras constant. It is the first known irrational number. The irrationality of surd 2 can be proved by various methods, including infinite descent, unique factorization and geometry.

Answer: For a fraction a/b, both a and b can take the value of 0.

The value of the nominator in a/b can be 0, but not the denominator, since it is impossible to divide a thing into 0 equal parts.

Answer: True

Fractions were used as early as 2800 BC in the ancient Indus Valley civilization. Amazingly, the bricks that were used to build the Great Bath were in perfect 4:2:1 ratio.