Fractions

Question 1

Adding Fractions and Mixed Numbers:

Answer 1

Fraction
1: Make both denominators the same.
2: Simplify if possible.

e.g. 2/4 + 5/7
=> x7 x4
=> 14/28 + 20/28
= 34/28
=> ÷2
= 17/14 or 1 3/14

Mixed Numbers
1: Add the Mixed Numbers.
2: Make both denominators the same.
3: Simplify if possible.

e.g. 3 5/9 + 6 3/4
=> x4 x9
=> 9 20/36 + 27/36
= 9 47/36
=> 9 + 1 11/36
= 10 11/36

Question 2

Subtracting Fractions and Mixed Numbers:

Answer 2

Fraction
1: Make both denominators the same.

e.g. 7/8 - 2/5
=> x5 x8
=> 35/40 - 16/40
= 19/40

Mixed Numbers
1: Subtract the Mixed Numbers.
2: Make both denominators the same.

e.g. 9 5/8 - 5 8/9
=> x9 x8
=> 4 45/72 - 64/72
= 4 -19/72
=> 3 72/72 - 19/72
=3 63/72

Question 3

Multiplying Fractions and Mixed Numbers:

Answer 3

Fractions
1: Denominators don’t need to be the same, just multiply left to right as normal.
2: Simplify if possible.

e.g. 2/3 x 4/5
= 8/15

Mixed Numbers
1: Times Mixed Number and denominator, add the numerator (turns equation to fraction times fraction).
2: Denominators don’t need to be the same, just multiply left to right as normal.
3: Simplify if possible (into a MN or fraction).

e.g. 1 8/9 x 3/4
=> 17/9 x 3/4
= 17/12 or 1 5/12

Question 4

Dividing Fractions and Mixed Numbers:

Answer 4

Fractions
1: Flip second fraction (turns equation into a times).
2: Denominators don’t need to be the same, just multiply left to right as normal.
3: Simplify if possible.

e.g. 3/5 ÷ 9/10
=> 3/5 x 10/9
= 30/45
=> ÷ 15
= 2/3

Mixed Numbers
1: Times Mixed Number and denominator, add the numerator (turns equation to fraction times fraction).
2: Flip second fraction (turns equation into a times).
3: Denominators don’t need to be the same, just multiply left to right as normal.
4: Simplify if possible (into a MN or fraction).

e.g. 5 6/7 ÷ 2 2/5
=> 41/7 ÷ 12/5
=> 41/7 x 5/12
= 205/84 or 2 37/84