A mixed number is an integer close to a fraction, for example 3 ½. Multiplying two mixed numbers can be tricky, because they have to be converted into improper fractions first. To learn how to multiply mixed numbers, follow the simple steps described below.
Steps
Step 1. Multiply 41/2 for 62/5
Step 2. Convert the first mixed number to an improper fraction
An improper fraction is formed by a numerator greater than the denominator. Here's how to convert a mixed number to an improper fraction:
-
Multiply the whole number by the denominator of the fraction.
If you need to convert 41/2 in an improper fraction, first multiply the integer 4 by the denominator of the fraction, in other words 2. Hence, 4 x 2 = 8
-
Add this number to the numerator of the fraction.
By adding 8 to the numerator 1, we will have 8 + 1 = 9.
-
Put this new number above the starting denominator.
The new number is 9, so write it above the 2, the initial denominator.
The mixed number 41/2 becomes the improper fraction 9/2.
Multiply Mixed Numbers Step 3 Step 3. Convert the second mixed number to an improper fraction
Follow the same steps as described above:
-
Multiply the whole number by the denominator of the fraction.
If you need to convert 62/5 in an improper fraction, first multiply the integer 6 by the denominator of the fraction, in other words 5. Hence, 6 x 5 = 30
-
Add this number to the numerator of the fraction.
Adding 30 to numerator 2, we will have 30 + 2 = 32.
-
Put this new number above the starting denominator.
The new number is 32, so write it above 5, the initial denominator.
The mixed number 62/5 becomes the improper fraction 32/5.
Multiply Mixed Numbers Step 4 Step 4. Multiply the two improper fractions
After converting all the mixed numbers into improper fractions, you can multiply the fractions together. Multiply the numerators and denominators.
- To multiply 9/2 And 32/5, multiply the numerators, 9 and 32. 9 x 32 = 288.
-
Then multiply the denominators 2 and 5, to give 10.
-
Write the new numerator above the new denominator, getting 288/10.
Multiply Mixed Numbers Step 5 Step 5. Reduce the result to a minimum
To reduce the fraction to its lowest terms, find the greatest common factor (MFC), which is the largest number by which both numerator and denominator are divisible. Then divide the numerator and denominator by this number.
-
2 is the greatest common factor of 288 and 10. Divide 288 by 2 to give 144, and divide 10 by 2 to give 5.
288/10 is reduced to 144/5.
Multiply Mixed Numbers Step 6 Step 6. Convert the result to a mixed number
Since the question is in the form of a mixed number, the result must be a mixed number. To convert it to a mixed number, you have to work in reverse. Here's how to do it:
-
First, divide the top number by the one below.
Do the division to divide 144 by 5. 5 is contained 28 times in 144. The quotient is then 28. The remainder, or the number that remains, is 4.
-
Transform the quotient into the new integer. Take the remainder and put it above the starting denominator to finish converting the improper fraction to a mixed number.
The quotient is 28, the remainder is 4, and the initial denominator was 5, hence 144/5 expressed as a mixed fraction is 284/5.
Multiply Mixed Numbers Step 7 Step 7. Finished
41/2 x 62/5 = 284/5
Advice
- To multiply mixed numbers, do not multiply the whole numbers first and then the fractions with each other, otherwise you will get a wrong result.
- When you are multiplying mixed numbers crosswise, you can multiply the numerator of the first number with the denominator of the second, and the denominator of the first number with the numerator of the second.
-
-
