By Mike Swarbrick Jones

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**Extra info for A Binomial Congruence**

**Example text**

A fraction whose denominator is zero is undefined. A proper fraction has a numerator that is smaller than its denominator. 1 13 99 ᎏ Examples are ᎏ2ᎏ, ᎏ2ᎏ5 , and ᎏ 100 . Improper fractions have numerators that are big5 8 99 ger than their denominators. Examples include ᎏ5ᎏ, ᎏ13ᎏ, and ᎏ2ᎏ. What if the numerator and denominator are equal (making the fraction 2 9 20 equal to 1), as is the case with ᎏ2ᎏ, ᎏ9ᎏ, and ᎏ2ᎏ0 ? Are these proper or improper fractions? The rule is that these fractions must be called improper fractions.

No, but by convention, we always reduce our fractions as much as possible. Indeed, there are mathematicians who can’t go to sleep at night unless they’re sure that every fraction has been reduced to its lowest possible terms. You probably wouldn’t want to keep these poor people up all night, so always reduce your fractions. 53 54 Express Review Guides: BASIC MATH & PRE-ALGEBRA But with Unlike Denominators . . ” You can add apples to apples; you can add oranges to oranges. But you can’t add apples to oranges.

When you figure out that the factors of 15 are 5 and 3, you are factoring. 43 44 Express Review Guides: BASIC MATH & PRE-ALGEBRA Example Factor 13 into its prime factors. Is 13 divisible by 2? No. Is 13 divisible by 3? No. Then, remember, it’s prime. FUEL FOR THOUGHT The number 15 is divisible by 3 because 15 has no remainder when divided by 3; 3 goes into 15 evenly. A number like 12 that has 2 as a factor is divisible by 2. Such a number is an even number. A number like 13 that leaves a remainder when divided by 2 is an odd number.

### A Binomial Congruence by Mike Swarbrick Jones

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