To multiply by 125, divide by 8, and call it thousands, because 125 is 1/8 of a thousand.

To multiply by 12 1/2, divide by 8; call it hundreds.

To multiply by 1 1/4, divide by 8; call it tens.

To multiply by 62 1/2, divide by 16, and call it thousands.

To multiply by 6 1/4, divide by 16, and call it hundreds.

To multiply by 31 1/4, divide by 32, and call it thousands.

To multiply by 333 1/3, divide by 3, and call it thousands.

To multiply by 33 1/3, divide by 3, and call it hundreds.

To multiply by 3 1/3, divide by 3 and call it tens.

'To multiply by 50, divide by 2, and call it hundreds.

To multiply by 66%, divide by 15, and call it thousands.

To multiply by 833 1/3, divide by 15, and call it ten thousands, by annexing four ciphers.

To multiply by 83 1/3, divide by 12, and call it thousands.

To multiply by 8 1/3, divide by 12, and call it hundreds, because 8 1/3 is 1-12 of a hundred. The reason is similar in each case.

To multiply by 166 2/3, divide by 6, anu call it thousands.

To multiply by 16 2/3, divide by 6, and call it hundreds.

To multiply by 1 2/3, divide by 6, and call it tens.

To multiply by 37 1/2, take 3/8 of the number, and call it hundreds; 87 1/2, 7/8 of the number, and call it hun-areds, etc.

We simply reverse these methods to divide. To divide by 10,100, 1,000, etc., we remove the point one, two and three places to the left.

To divide by 25, remove the decimal point two places to the left, and multiply by 4.

Removing the point two places divides by one hundred; hence the quotient is four times too small; hence we remove the point two places, and multiply by 4.

To divide by 2 1/2, remove the point one place to the left, and multiply by 4.

To divide by 125, remove the point three places to the left, and multiply by 8.

To divide by 12 1/2, remove the point two places to the left, and multiply by 8.

To divide by 1 1/4, remove the point one point to the left, and multiply by 8. There are about 1% cubic feet in one bushel. Hence dividing the number of cubic feet by 1 1/4 gives the number of bushels nearly.

To divide by 133 1/3, remove the point three places to the left, then multiply by 3 and divide by 4.

To divide by 8 1/3, remove the point two places to the left, and multiply by 12.

## Contractions In Multiplication

To multiply by 25 add 2 ciphers and divide by 4. To multiply by 33 1/3 add 2 ciphers and divide by 3. To multiply by 125 add 3 ciphers and divide by 8. To multiply by 175 add 2 ciphers and divide by 5, and multiply result by 7.