DIVIDING FRACTIONS NOTES
DIVIDING FRACTIONS NOTES
****You do not need common denominators to divide fractions
Dividing a whole number by a fraction
Step 1: Write the whole number as a fraction with 1 as the denominator.
[pic] = [pic]
Step 2: Write a multiplication problem by inverting* the second fraction.
*Note – invert means to reverse the placement of the numbers in the numerator & denominator. Example: [pic] inverts to [pic] ALSO KNOWN AS RECIPROCAL - When you multiply a number by its RECIPROCAL the product is 1.
Example: [pic] = [pic] = 1
[pic] [pic] =
Step 3: Cross cancel if you can.
1
[pic]
1
Step 4: Multiply the numerators.
Multiply the denominators.
[pic] = [pic]
Step 5: Write the answer in simplest form. [pic] = 5
Dividing a fraction by a whole number
Step 1: Write the whole number as a fraction with 1 as the denominator.
[pic]4 = [pic]
Step 2: Re-write as a multiplication problem by inverting the second fraction.
[pic] [pic]
Step 3: Cross cancel if you can.
1
[pic]
2
Step 4: Multiply the numerators.
Multiply the denominators.
[pic] = [pic][pic]
Step 5: Write the answer in simplest form.
[pic] = [pic] (already in simplest form)
Dividing a fraction by a fraction
Step 1: Invert the divisor (the second fraction).
[pic] = [pic]
Step 2: Re-write as a multiplication problem by inverting the second fraction.
[pic] [pic]
Step 3: Cross cancel if you can.
4
[pic]
1
Step 4: Multiply the numerators.
Multiply the denominators.
[pic] = [pic]
Step 5: Write the answer in simplest form.
[pic] = [pic] (already in simplest form)
Dividing Mixed Numbers
Step 1: Write each mixed number as an improper fraction.
[pic] = [pic]
Step 2: Re-write as a multiplication problem by inverting the second fraction.
[pic] [pic]
Step 3: Cross cancel if you can.
4
[pic]
1
Step 4: Multiply the numerators.
Multiply the denominators.
[pic] = [pic]
Step 5: Write the answer in simplest form.
[pic] = [pic]
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