Math 4

MATHEMATICS 8 UNIT 4 SUBTRACTING FRACTIONS MULTIPLYING FRACTIONS DIVIDING FRACTIONS FRACTIONS AND DECIMALS ORDER OF OPERATIONS

SUBTRACTING FRACTIONS _

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When the denominators of the fractions are the same, simply subtract one numerator from the other and place your answer over the original denominator.

When the denominators are not the same, you will have to find a common denominator before you can begin subtraction.

To find a common denominator for these two fractions, you need to find the lowest common multiple for 5 and 3

The lowest common multiple of 5 and 3 is 15

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Look at the relationship between the original denominators of the fractions and the new common denominator. What number would you have to multiply the old denominator by to get the new one? Whatever that number is, multiply the old numerator by it as well and place your answer over the new common denominator. Do this for both fractions. Subtract the second numerator from the first and put your answer over the new denominator.

Multiply the two Numerators

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Multiply the two Denominators

MULTIPLYING FRACTIONS The Simplest of the Operations

DIVIDING FRACTIONS DIVIDED BY

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This is easier than it seems. You simply change the second fraction to its reciprocal, change the operation sign to multiplication, then follow the rules for multiplying fractions.

Reciprocal A reciprocal of a fraction is obtained by flipping the original fraction over so that the original numerator becomes the new denominator and the original denominator becomes the new numerator Each of these fractions is the reciprocal of the other

INVERT AND MULTIPLY =

DIVIDED BY

BECOMES

X CHANGE OPERATION SIGN TO MULTIPLICATION

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RECIPROCAL

LOWEST TERMS Sometimes fractions can be broken down into equivalent fractions with the smallest possible numerators and denominators. This is called reducing to lowest terms. To reduce a fraction to lowest terms, you must find the greatest common factor for both the numerator and denominator. You then divide both the top and bottom by the greatest common factor.

The greatest common factor for 6 and 8 is Divide both top and bottom 6 divided by 2 = 3 by 2. Its the largest Lowest Terms number that will divide 8 divided by 2 = 4 evenly into 6 and 8

FRACTIONS TO DECIMALS As indicated before, the line dividing the numerator and the denominator is a division line. This fraction can be read “5 divided by 8”

Tenths Hundredths Thousandths

Mixed Numbers to Decimals Two and five sixths

5 6

Keep the whole number and do the division for the fraction. Place the decimal point between the whole number and the decimal you get after doing the division.

5 divided by 6 = 0.83333

Decimal Point.

This seperates the whole number from the fractional number.

Another Way... 5 6 5 6

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Turn the mixed number into an improper fraction. 17 6

Then divide the top number by the bottom number.

17 divided by 6 = 2.8333

ORDER OF OPERATIONS BEDMAS APPLIES TO FRACTIONS TOO!

P Brackets P Exponents P Division P Multiplication P Addition P Subtraction

In the order of appearance from left to right In the order of appearance from left to right