Multiplying a Number by a Fraction
Write out the problem. If the problem you are working with is a word problem, first you need to write out all of the numbers involved in the calculation. If you were given the numbers written out already, you can skip this step. For example: What is one-third of seven? When you see “of” written between two numbers in a word problem, think of it as meaning multiply. Thus, one-third of seven actually means one-third multiplied by seven. Writing out the problem gives you (/3) x 7.
Multiply the whole number by the numerator. When working with whole numbers, you will only multiply the number by the numerator (the top number) of the fraction. The denominator remains the same throughout the multiplication process. For example: (/3) x 7 = /3.
Divide by the denominator. Divide the product by the denominator (the bottom number) of the fraction. At this stage, the fraction might be an improper fraction, meaning that the numerator is larger than the denominator, or it will just need to be reduced. For example: After multiplying, the fraction is /3. Three doesn’t divide evenly into seven so you will have a remainder. Three goes into seven twice with one leftover; therefore, the final answer is the mixed number 2/3.
Simplifying the Product
Simplify the improper fraction. An improper fraction is one where the numerator is a larger number than the denominator. Always simplify an improper fraction before writing the final answer. To simplify, divide the numerator by the denominator and write the remainder as a fraction. For example: /3 Divide: 10/3 = 9 remainder 1 Write the remainder as a fraction: /3
Write the mixed number. A mixed number contains both a whole number and a fraction. It is the simplest form of an improper fraction. To write the mixed number, simply write the whole number and the fraction that was created by the remainder. For example: /3, 3 goes into 10 3 times with a remainder of 1. The mixed number is 3/3.
Reduce a fraction to its simplest form. Once you have multiplied through, you need to reduce the fraction. You can divide by a smaller number until the fraction is completely reduced. For example: Simplify the fraction /8. Divide both numbers by four to simplify. The simplest form of /8 is /2.
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