Download To Find Equivalent Fractions

To Find Equivalent Fractions
Multiply the numerator and the denominator by the same number
×2
1
2
=
×2
2
4
=
4
×2
8
×2
Divide the numerator and the denominator by the same number
÷3
18
36
÷6
=
÷3
6
12
=
1
2
÷6
Link: http://www.mathsisfun.com/equivalent_fractions.html
Simplify each fraction to lowest terms
Divide the numerator and denominator by the greatest common factor
or you can divide by common factors (divide the numerator and the
denominator by the same number)
Method #1: Common Factors
(a slow and steady method)
Let's try another example:
30/36
Do 30 and 36 share any factors other than 1?
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
30 and 36 have three common factors: 2, 3, and 6.
Let's see what happens if we divide the numerator and denominator by their lowest common factor, 2. (In
fact, we'd know that they have 2 as a common factor without having to work out all their factors, because
both 30 and 36 are even numbers.)
30 ÷ 2/36
÷ 2 = 15/18
Are we done? Do 15 and 18 share any factors other than 1?
The factors of 15 are 1, 3, 5, 15.
The factors of 18 are 1, 2, 3, 6, 9, 18.
15 and 18 have one common factor: 3.
Once again, we divide the numerator and denominator by their common factor, 3.
15 ÷ 3/18
÷ 3 = 5/6
Are we done? Do 5 and 6 share any factors other than 1?
The factors of 5 are 1 and 5.
The factors of 6 are 1, 2, 3, and 6.
5 and 6 have no common factors other than 1.
This method will reduce a fraction to its lowest terms, but it can take several steps until you reach that
point. What would have happened if, instead of dividing the numerator and denominator by their lowest
common factor, we had started with their greatest common factor?
Method #2: Greatest Common Factor: (a more efficient method)
Let's try it again:
30/36
Do 30 and 36 share any factors other than 1?
The factors of 30 are 1, 2, 3, 5, 6, 10, 15.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18.
30 and 36 have three common factors: 2, 3, and 6.
The greatest common factor is 6.
Divide the numerator and denominator by the greatest common factor:
30 ÷ 6/36
÷ 6 = 5/6
*You can also use prime factorization to find the GCF as well.
2 X2 X 3X 3
2X3X5
GCF= 2 X 3= 6
30/6= 5
36/6= 6
Divide the numerator and denominator by the greatest common factor:
30 ÷ 6/36
÷ 6 = 5/6
Extra Links:
http://www.factmonster.com/ipka/A0933466.html
https://www.ixl.com/math/grade-6/reduce-fractions-to-lowest-terms
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/equivalent-fractions-pre-alg/v/fractionsin-lowest-terms
http://www.mathplayground.com/fractions_reduce.html
Turning a mixed number into improper fraction
Step 1: Write the mixed number
Step 2: Multiply the denominator by the whole number and then add
the numerator.
Step 3: Put the resulting number over the original denominator to
produce the improper fraction
Turning improper fraction into mixed number
Step 1: Write the improper fraction
Step 2: Divide the numerator by the denominator
Step 3: The quotient becomes the whole number and the remainder is
put over the denominator
Additional Resources:
http://www.mathplayground.com/fractions_mixed.html
https://www.mathsisfun.com/improper-fractions.html
http://www.factmonster.com/ipka/A0933459.html
https://www.ixl.com/math/grade-6/convert-between-improper-fractionsand-mixed-numbers