Algebra: Chapter 3, Lesson 9, page 148.
Proportions
A ratio of 2 quantities is a comparison, often expressed as a fraction. An equation that states that 2 ratios are equal is called a proportion. I prefer to just criss-cross, or cross multiply proportional problems, but the book’s way is OK too.
For example,
`x/63=2/9`, I solve by criss-crossing. That becomes
`x*9=2*63` or `9x=63*2` or `9x=126`
and dividing both sides by 9 to clear the x, gives us `x=14`.
Here is a link from purplemath.com that has some more examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 2, Lessons 5 and Lesson 6, pages 77 and 81
Multiplication and Division of Rational Numbers
Today is easy because the rules for multiplication and division are simple.
- When multiplying 2 numbers AND if the SIGNS are the same, the product is ALWAYS positive.
- If the signs are different, them the product is ALWAYS negative. This is pretty straightforward.
Division follows the same rules as multiplication.
2 rational numbers whose product is 1 are called multiplicative inverses or reciprocals of each other. Just flip the rational expression over and keep the same sign. For example, the reciprocal of `2/3` or `m/n` is `3/2 ` and `n/m` respectively.
Remember too, to divide rational numbers, sometimes its easier to express them as improper fractions, then convert the 2nd term to its reciprocal and change the `/` to a `⋅`.
Two of tonight’s homework problems solved by MrE are here! Just click it!
Purplemath.com has these tutorials about multiplying and dividing rational numbers, check it out!