Natural numbers

Build the number from billions, millions, thousands and units. Give every group except the first three digits, adding leading zeros when necessary. For example, 2 billion 5 million 7 thousand 9 = 2 005 007 009.

Find the place to which you must round and look at the next digit to its right. If it is 0–4, keep the rounding digit; if it is 5–9, increase it by 1. Replace lower whole-number places with zeros.

Follow the order of operations: multiplication comes before addition and subtraction, even when it is not written first.

1. First multiply the numbers joined by the “×” sign.
2. Then add the remaining number to the product or subtract it from the product, as the expression requires.
3. Check that you did not add or subtract before multiplying.

To make the order clearer, imagine parentheses around the multiplication.

A divisor is a positive whole number that divides the given number without a remainder. Add all the divisors; do not merely count them.

1. Look for divisors in pairs: when a candidate divides the number, the quotient is its partner.
2. Write down both members of each pair and continue until the pairs begin to repeat. Remember the pair containing 1 and the number itself.
3. If the two members of a pair are equal, include that divisor only once.
4. Add all the distinct divisors you found.

Check each divisor by confirming that the division leaves no remainder.

This expression contains division and addition. The order of operations requires division first and addition second.

1. Find the division and divide the first number by the second.
2. Add the last number to the quotient.
3. Check that you did not add the second and third numbers first.

If helpful, imagine parentheses around the division: calculate it first, then add.

Build the number from billions, millions, thousands and units. Give every group except the first three digits, adding leading zeros when necessary. For example, 2 billion 5 million 7 thousand 9 = 2 005 007 009.

A divisor is a positive whole number that divides the given number without a remainder. Add all the divisors; do not merely count them.

1. Look for divisors in pairs: when a candidate divides the number, the quotient is its partner.
2. Write down both members of each pair and continue until the pairs begin to repeat. Remember the pair containing 1 and the number itself.
3. If the two members of a pair are equal, include that divisor only once.
4. Add all the distinct divisors you found.

Check each divisor by confirming that the division leaves no remainder.

Digits are symbols used to write numbers. The decimal number system uses these digits:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Counting them gives 10 digits. Infinitely many different numbers can be formed from these ten digits.

This test defines natural numbers as 1, 2, 3, ...: the positive whole numbers used for counting objects. Under this convention, 0 is not natural. Other sources may use a convention that includes 0.

This expression contains division and addition. The order of operations requires division first and addition second.

1. Find the division and divide the first number by the second.
2. Add the last number to the quotient.
3. Check that you did not add the second and third numbers first.

If helpful, imagine parentheses around the division: calculate it first, then add.