Danny+and+Mark+I.+8-16

media type="youtube" key="1-99R09nYDs"**Background information** A vulgar fraction is said to be a **proper fraction** if the absolute value of the numerator is less than the absolute value of the denominator — that is, if the absolute value of the entire fraction is less than 1 (e.g. 7⁄9) — but an **improper fraction** (US, British or Canadian) or **top heavy fraction** (British only) if the absolute value of the numerator is greater than or equal to the absolute value of the denominator (e.g. 9⁄7). **Mixed numbers** A **mixed number** is the sum of a whole number and a proper fraction. For instance, you could have two entire cakes and three quarters of another cake. The whole and fractional parts of the number are written right next to each other: 2 + 3⁄4 = 23⁄4. An improper fraction can be thought of as another way to write a mixed number; in the "23⁄4" example above, imagine that the two entire cakes are each divided into quarters. Each entire cake contributes 4⁄4 to the total, so 4⁄4 + 4⁄4 + 3⁄4 = 11⁄4 is another way of writing 23⁄4. A mixed number can be converted to an improper fraction in three steps: Similarly, an improper fraction can be converted to a mixed number: **Equivalent fractions** Multiplying the numerator and denominator of a fraction by the same (non-zero) number results in a new fraction that is said to be **equivalent** to the original fraction. The word //equivalent// means that the two fractions have the same value. This is true because for any number //n//, multiplying by //n//⁄//n// is really multiplying by one, and any number multiplied by one has the same value as the original number. For instance, consider the fraction 1⁄2. When the numerator and denominator are both multiplied by 2, the result is 2⁄4, which has the same value as 1⁄2. To see this, imagine cutting the example cake into four pieces; two of the pieces together (2⁄4) make up half the cake (1⁄2). For example: 1⁄3, 2⁄6, 3⁄9, and 100⁄300 are all equivalent fractions. Dividing the numerator and denominator of a fraction by the same non-zero number will also yield an equivalent fraction. this is called **reducing** or **simplifying** the fraction. A fraction in which the numerator and denominator have no __factors__ in common (other than 1) is said to be **irreducible** or **in lowest** or **simplest terms.** For instance, 3⁄9 is not in lowest terms because both 3 and 9 can be evenly divided by 3. In contrast, 3⁄8 //is// in lowest terms — the only number that's a factor of both 3 and 8 is 1.
 * proper, and improper fractions**
 * 1) Multiply the whole part times the denominator of the fractional part.
 * 2) Add the numerator of the fractional part to that product.
 * 3) The resulting sum is the numerator of the new (improper) fraction, and the new denominator is the same as that of the mixed number.
 * 1) Divide the numerator by the denominator.
 * 2) The quotient (without remainder) becomes the whole part and the remainder becomes the numerator of the fractional part.
 * 3) The new denominator is the same as that of the original improper fraction.