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5th grade Math & Geo

Go to this links and practice:   http://www.mathsisfun.com/fractions_multiplication.html 

                                                       http://www.math.com/school/subject1/lessons/S1U4L4DP.html

 

Multiplication

Multiplying a fraction by another fraction

To multiply fractions, multiply the numerators and multiply the denominators. Thus:
\tfrac{2}{3} \times \tfrac{3}{4} = \tfrac{6}{12}
Why does this work? First, consider one third of one quarter. Using the example of a cake, if three small slices of equal size make up a quarter, and four quarters make up a whole, twelve of these small, equal slices make up a whole. Therefore a third of a quarter is a twelfth. Now consider the numerators. The first fraction, two thirds, is twice as large as one third. Since one third of a quarter is one twelfth, two thirds of a quarter is two twelfth. The second fraction, three quarters, is three times as large as one quarter, so two thirds of three quarters is three times as large as two thirds of one quarter. Thus two thirds times three quarters is six twelfths.
A short cut for multiplying fractions is called "cancellation". In effect, we reduce the answer to lowest terms during multiplication. For example:
\tfrac{2}{3} \times \tfrac{3}{4} = \tfrac{\cancel{2} ^{~1}}{\cancel{3} ^{~1}} \times \tfrac{\cancel{3} ^{~1}}{\cancel{4} ^{~2}} = \tfrac{1}{1} \times \tfrac{1}{2} = \tfrac{1}{2}
A two is a common factor in both the numerator of the left fraction and the denominator of the right and is divided out of both. Three is a common factor of the left denominator and right numerator and is divided out of both.

Multiplying a fraction by a whole number

Place the whole number over one and multiply.
6 \times \tfrac{3}{4} = \tfrac{6}{1} \times \tfrac{3}{4} = \tfrac{18}{4}
This method works because the fraction 6/1 means six equal parts, each one of which is a whole.

 

 

 

Multiplying Fractions 

 Multiply the tops, multiply the bottoms.

  

To multiply fractions, first we simplify the fractions if they are not in lowest terms. Then we multiply the numerators of the fractions to get the new numerator, and multiply the denominators of the fractions to get the new denominator. Simplify the resulting fraction if possible.

Note that multiplying fractions is frequently expressed using the word "of." For example, to find one-fifth of 10 pieces of candy, you would multiply 1/5 times 10, which equals 2. Study the example problems to see how to apply the rules for multiplying fractions.

 

 There are 3 simple steps to multiply fractions

1. Multiply the top numbers (the numerators).
2. Multiply the bottom numbers (the denominators).
3. Simplify the fraction if needed.

   Example 1





1 × 2
_____ _____
2 5
Step 1. Multiply the top numbers:
1 × 2 = 1 × 2 = 2
_______ _______ _________
2 5

Step 2. Multiply the bottom numbers:
1 × 2 = 1 × 2 = 2
_____ ______ ________ ________
2 5 2 × 5 10

Step 3. Simplify the fraction:
2 = 1
______ ______
10 5





ADDING AND SUBTRACTING FRACTIONS

 Like fractions are fractions with the same denominator. You can add and subtract like fractions easily - simply add or subtract the numerators and write the sum over the common denominator.

Before you can add or subtract fractions with different denominators, you must first find equivalent fractions with the same denominator, like this:
  1. Find the smallest multiple (LCM) of both numbers.
  2. Rewrite the fractions as equivalent fractions with the LCM as the denominator.
When working with fractions, the LCM is called the least common denominator (LCD).



 Some links to play and work:


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