Remainders

Remainder problems will generally either be: simple or pattern-based reminders.

Simple

Simple remainder questions will provide some kind of division problem, which will leave some remainder. The student will then generally have to find  whatever whole number is left over when the nearest factor of the denominator is taken away from our original number.

For example: what is the remainder when 2387 is divided by 38?

238738=62.816 This means that the nearest factor of 38 to the original number is 38 * 62 = 2356

The remainder is therefore: 2387 − 2356 = 21

Pattern-Based

For pattern-based remainder questions, the question will provide some kind of repeating decimal, and will then ask for a large-numbered digit of that repeating decimal: for example, the 4567th digit after the decimal point. A repeating decimal means that there is an infinite string of digits after the decimal, which repeat in a set pattern.

The repetition often starts next to the decimal, or after the first two digits of the decimal. For example, 1/12 = .08, so the first two numbers after the decimal point are not a part of the repeating pattern.

• Key takeaway: not all numbers after the decimal point have to repeat for there to be a pattern.

Just like with patten-based remainder questions, factors are still key. However, instead of being interested in the factors of the denominator in a fraction/ratio, pattern-based remainder questions are more about how many digits repeat in the decimal pattern.

Common Repeating Decimals

Repeating-decimal questions can create or provide any decimal or pattern, but there are some common repeating decimals that might show up. The most common repeating decimals to show up on these questions (or even other questions) are:

1/6 =.1666

1/9 = .111 For any fraction with 9 as the denominator, the repeating decimal is simply equal to the numerator repeating after the decimal point (2/9 = .222)

1/11 = .090909 For any fraction with 11 as the denominator, the repeating decimal is simply equal to the numerator multiplied by 9 (expressed in two digits) after the decimal point (2/11 = .181818)

1/12 = .08333