Steps for multiplying any two fractions are: Go across the top and multiply the numerators, then go across the bottom and multiply the denominators. Reduce your answer to its simplest form. Multiplication is multiple addition as in the example from the Multiplication section. The first number is the multiplier and tells how many times to add the second number. The second number is the multiplicand and is added the number of times stated by the first number, the multiplier. In the problem 1/2 X 1/2 = 1/4, we are saying to add a half of 1/2. We have an illustration below showing this.
In the second part of the picture you will notice the dotted line cutting the 1/2 shaded area of our multiplicand in two, showing the size set we are adding. We are saying to add 1/2 of 1/2.
Another example problem. 1/4 X 4 We would chop 4 up into 4 equal parts and take one of those 4 parts which is 1. 4 and 4/1 are the same value since 4 divided by 1=4. You would set the problem up as 1/4 X 4/1. Go across the top and multiply the numerators getting 4 as a product. Go across the bottom and multiply the denominators getting 4 as a product and 4/4 as an answer. 4 Divided by 4 is 1. 1 Is the final reduced answer. Note how the multiplier 1/4 is telling you how many times to add the multiplicand 4 or 4/1. If it were not a fraction multiplication problem and say one like 2x4=? The multiplier 2 is telling us to add 4 twice for a product of 8. If the problem was 1x4=? The multiplier 1 is telling us to add the multiplicand 4 once for a product of 4. As with whole number multiplication you can reverse the order of the multiplier and multiplicand when multiplying fractions and you will still get the same answer.
Working with whole numbers gets us use to seeing the product larger than the multiplier and multiplicand or factors in our problem, but when we start multiplying fractions our product will be smaller than our factors lots of the time. Fraction means part of a number and for a fraction to be proper it has to be less than 1 or unity weather it be -1 or 1. Unity is when the numerator is equal to the denominator as in 2/2 or -5/5. Since these cases represent a whole number 1 and -1 and not a part of a number they are considered improper fractions. Improper fraction include unity as mentioned above and all cases where the numerator is lager that the denominator. 5/4, -7/3 and 6/2 are all improper fractions. 5/4 Is greater than 1 whole and reduces down to 1 1/4, which is called a Mixed Number. -7/3 Reduces down to -2 1/3 and 6/2 reduces down to 3. When you multiply 2 improper fractions you will get products that are greater than or equal to 1 or -1, depending on if one of your terms is negative.
Above when you reduce and improper fraction like 5/4, all you do is divide 5 by 4, which goes 1 time and leaves 1 for a remainder, the remainder stays over the 4 for an answer of 1 1/4. -7/3... -7 divided by 3 = -2 with a remainder of -1/3 and is written -2 1/3.
If you are given a multiplication problem with mixed numbers like 1 1/2 x 4, you can to change the mixed number 1 1/2 to an improper fraction before multiplying. The process is: Multiply the denominator 2 by the whole number part 1 which equals 2 then add it to the numerator 1 for an improper fraction of 3/2. 3/2 x 4/1 =? Multiply the numerators across the top, 3x4 for a product of 12. Multiply the denominators across the bottom 2x1 for a product of 2 leaving you with the answer of 12/2. 12/2 Means the same thing as 12 divided by 2 and in this case come out to an even number 6 with no remainders so the answer is 6.
With the problem 1 1/2 x 4=? You could also factor it out like (1x4)+(1/2x4)=? You would multiply 1x4 for a product of 4 then 1/2x4/1 for a product of 4/2 giving you an answer of 4 4/2. Then you reduce the 4/2 part by dividing 4 by 2 which in this case is 2 then add 2 to 4 for a final answer of 6.
Reducing the fraction to its simplest form.
If the fraction has a numerator that is larger than or equal to the denominator, divide the numerator by the denominator first to get the whole number part of your answer. If there is a remainder is goes over the denominator. 20/3 For example. 20 divided by 3 is 6. 3x6 Equals 18 and 20-18 = 2 so you have a remainder of 2/3 and write your answer as 6 2/3. In this case 2/3 doesn't reduce any farther. Then reduce the proper fraction part of your answer using the following steps.
we reduce the fraction portion of our product by finding numbers that divide into the numerator and the denominator equal amounts of times with no remainders.
If you follow these 6 steps you'll always find the simplest form of the fraction. You can do these steps in any order and sometimes it will be quicker to start at step 6, but do check each possibility in step 5. Odd numbers are numbers that can't be divided by 2 without having any remainders. It is necessary to try all the odd numbers until you reach the value of the numerator because the numerator and denominator may be products of prime numbers or the numerator may be a prime number and be a factor of the denominator.
A prime number is a number that is divisible by 1 and its own value without any remainder and not divisible by any other numbers without a remainder. 3 is prime. 3/3=1 and 3/1=3 but there are no other whole numbers we can divide it by and not have a remainder. 1, 2, 3, 5, 7, 11, 13, 17, 19 Are also prime numbers. 2 Is prime also and it seems strange that it is because all the other prime numbers are odd and not divisible by 2. 2 Meets the requirements of the definition though. 2 Can be divided by itself and 1 and no other whole numbers without leaving a remainder. As of the year 2007 no one has come up with a pattern for finding what the next prime number will be on a number line. Look at the spacing of the prime numbers on a number line. 1 Space between 1 and 2. 1 Space between 2 and 3. Then 2 spaces between 3 and 5. Then 2 spaces between 5 and 7. Next 4 spaces between 7 and 11. You can make a large number line with hundreds of numbers and look at the spacing and there doesn't seem to be any predictable pattern. This makes you have to try all those prime numbers until you reach the value of the numerator while reducing. A factor of a number is a whole number that when multiplied by some other whole number, equals that number. 6 Is a factor of 42 because 6x7=42. 7, 2 And 21 are also factors of 42; 21x2=42. A whole number is a number that doesn't have any fractional part. 2 1/2, 3.25 are not whole numbers because they contain fractional parts. 1,2,3 and 4 are whole numbers and do not have any fractional parts. Integer means the same thing as whole number and will be used in its place in many math problems you will come across.
Back in step 1, by dividing by 2 as many times as you can, you get rid of all the even factors in the numerator and denominator so that you only need to check the odd numbers up to the value of the numerator.
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Copyright 2008 Robert Lee Thomas
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