**MACHINE SHOP CALCULATION - OD1640 - LESSON 1/TASK 1**

d.

*Reducing a Fraction to its Lowest Terms*.

*Rule 1*.

Divide both terms by a common factor or the greatest common

divisor.

EXAMPLE

Reduce 75/105 to its lowest terms.

Since dividing both the numerator and

the denominator by the same number does not change the value of the

fraction, both terms of the fraction may be divided by 5.

Thus 75/105 =

15/21. Now both terms of 15/21 may be divided by 3; 15/21 = 5/7. Both 5

and 7 are prime to each other (no other number except 1 can be divided into

both of then a whole number of times), so the fraction is now reduced to its

lowest terms.

e.

*Reducing Several Fractions having a Desired Common Denominator*.

*Rule 1*. Multiply both terms of each fraction by the quotient of the desired

common denominator divided by the denominator of the fraction.

Thus, the

fraction 1/2 may be changed to 6ths by multiplying both its terms by a

number which will make the denominator a 6th. This number is 3. Therefore,

1/2 becomes 3/6. Do likewise to change 1/3 to 6ths.

EXAMPLE

Reduce 1/2 and 1/3 to fractions which have 6 for a denominator.

1/2 = ?/6.

The first step is to divide 6 by 2.

It goes 3 times.

Therefore, you

multiply the numerator by 3. You then get:

Reduce 7/9, 3/8, and 5/6 to 72ds. Both terms of 7/9 are multiplied by 8,

since 72 ƒ 9 = 8. Both terms of 3/8 are multiplied by 9, since 72 ƒ 8 = 9.

Both terms of 5/6 are multiplied by 12, since 72 ƒ 6 = 12. Therefore, 7/9 =

56/72, 3/8 = 27/72, and 5/6 = 60/72.

**12**