Foundations
Multiply and divide fractions
ALEKS · foundation repairTEAS math
Multiply straight across; divide by flipping the second fraction.
What this covers
ba÷dc=ba⋅cd- Neither operation needs a common denominator — that requirement belongs to adding and subtracting only.
- Cancel common factors between any numerator and any denominator before multiplying.
- For division, change ÷ to × and turn the second fraction upside down.
- A fraction turned upside down is called its reciprocal. The reciprocal of 8/3 is 3/8, and the reciprocal of 5 is 1/5.
- Multiply the numerators, then the denominators.
Worked example
Worked example
Divide 4/9 ÷ 8/3.
- 94⋅83Dividing is multiplying by the reciprocal.
- 31⋅21Cancel 4 against 8 and 3 against 9 first.
- 61Multiply across what is left.
Another worked example
Find (3/4)(2/9).
- 43⋅92=4⋅93⋅2=366Multiply numerators and denominators; equal-sized denominators are not required.
- 366=61Divide numerator and denominator by their common factor 6.
A common mistake
A mistake Lemma catches
From 65÷32
65÷32=56⋅2365÷32=65⋅23
“Only the second fraction flips. Dividing by 2/3 is multiplying by 3/2, and 5/6 stays as it is: 5/6 · 3/2 = 15/12 = 5/4. Flipping 5/6 too gives 6/5 · 3/2 = 18/10 = 9/5, a different number.”
Try one
Sample problem
Multiply and reduce completely.
93⋅84Practice fraction products free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
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