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Multiplying and dividing Fractions and Decimals with Positive and Negative Values

MIXED NUMBERS:

Multiplying Fractions:

IMPROPER FRACTIONS:

Mixed Numbers and Improper Fractions

Mixed Numbers:

  • contain a RATIONAL number and a IRRATIONAL number
  • To turn this into and improper fraction multiply the whole number by the denominator and add it to the numerator
  • this will be the new numerator and the current denominator will stay the same

Improper Fractions:

  • a fraction where the numerator is larger than the denominator
  • equals a whole number and sometimes a whole number and a fraction
  • To turn this into a mixed number divide the denominator into the numerator
  • However many times it can go in equally is the whole number in the mixed fraction
  • the remainder will become the numerator
  • the current denominator will stay

Mixed and Improper Fractions:

Mixed Numbers are numbers that contain a RATIONAL number and a IRRATIONAL number. This is where there is a whole number and fraction together. To turn this into and improper fraction, you must multiply the whole number by the denominator and add it to the numerator, this will be the new numerator and the current denominator will stay the same.Example 2 3/4.

Improper Fractions are fractions where the numerator is larger than the denominator. An improper fraction equals a whole number and sometimes a whole number and a fraction. To turn this into a mixed number, you must divide the denominator into the numerator. However many times it can go in equally is the whole number in the mixed fraction. Whatever the remainder is will become the numerator and the current denominator will stay. Example 15/3.

Homework:

How to...

  • convert mixed numbers to improper fractions
  • multiply the two numerators
  • multiply the two denominators
  • Simplify

Complete the multiplying and dividing positive and negative fractions and decimals worksheet at home and bring to class tomorrow. This assignment will be graded. DUE OCTOBER 16TH.

Practice

Answer Key:

Annawesley: 15/32

Gabe: -5/6

Nathan: 5/12

Landon: -49/36

Carleigh: 21/64

Kyndal: -2/21

Now in order come up and do this on the board.

When multiplying two fractions, you multiply the two numerators and the two denominators. Simplify. The fractions can't be a mixed number, you must copnvert mixed numbers to improper fractions.

To divide fractions you have to simplify. Then, flip the second fraction, putting the original denominator on top and the original numerator on the bottom. Then, you multiply the fraction like normal.

When you multiply decimals, multiply them like a whole number, with out a decimal. Then, add the decimal point at the end of the number, after you are done multiplying and move the decimal over to the left however many numbers are behind the decimal in total in the problem.

When you divide decimals you just divide as you normally would except move the decimal to the right in the divisor until the divisor turns to a whole number. Then, you move the decimal in the dividend over as many spaces as you moved the decimal in the divisor. Then, you divide as if there were no decimal and you carry the decimal to the same place over on the quotient.

The same rules for whole numbers applies for fractions and decimals. If you multiply or divide numbers with the same signs, it will be a positive answer and if you multiply or divide numbers with opposite signs, it will be a negative answer.

Annawesley: -15/8 × -6/24

Gabe: -1/3×15/6

Nathan: 5/8×6/9

Landon: 7/6 ÷ -6/7

Carleigh: 6/8 ÷ 16/7

Kyndal: 1/7 × -2/3

Examples

Here is an example of multiplying a positive fraction by a positive fraction

Here is a positive decimal times a negative decimal

1/3 * 4/5 = 4/15

6.3 * - 2.6 = - 16.38

Here is a positive decimal times a positive decimal

Here is an example of a negative decimal times a negative decimal

5.2 * 6.8 = 35.36

Here is a positive fraction times a negative fraction

-6.3 * -4.7 = 29.61

Here is a negative fraction times a negative fraction

3/6 * -3/7 = (-.21)

-6/9 * -3/4 = 0.5

By: Brenna Curtis, Samuel Briones, and Johnathan Owens

By the end of this lesson you will be able to multiply and divide fractions and decimals with positive and negative values. In this lesson we will teach you how to...

  • multiply decimals
  • divide decimals
  • multiply fractions
  • divide fractions
  • the rules of multiplying/ dividing with negative and positive numbers

Dividing Fractions

Lesson Plan:

Dividing Decimals:

  • move the decimal in the divisor to the right until the divisor turns to a whole number
  • move the decimal in the dividend to tdhe right as many spaces as you moved the decimal in the divisor
  • divide like normal, as if there were no decimal
  • carry the decimal to the same place over on the quotient
  • simplify the fractions as much as possible
  • flip the second fraction, putting the original denominator on top and the original numerator on the bottom
  • multiply the fraction

Multiplying Decimals:

Rules:

  • multiplying/dividing numbers with the same signs= positive answer
  • multiplying/dividing numbers with opposite signs=negative
  • multiply like normal
  • add the decimal point at the end of the number after you are done multiplying
  • move the decimal over to the left however many numbers are behind the decimals in total in the problem
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