Learning how to multiply a mixed number by a whole number is an essential math skill that appears in many lessons, from fraction operations to everyday calculations. The process becomes much easier when you first convert the mixed number into an improper fraction, multiply, and then convert the answer back into a mixed number when necessary Worth keeping that in mind..
What Is a Mixed Number?
A mixed number combines a whole number and a proper fraction. For example:
[ 2\frac{3}{4} ]
This means two whole units plus three-fourths of another unit. It is different from the improper fraction (\frac{11}{4}), although the two forms have the same value Surprisingly effective..
A whole number has no fractional part. Examples include 3, 7, 10, and 25. Zero is also a whole number.
When multiplying a mixed number by a whole number, you can use the same basic fraction operation you already know: multiply the numerators and multiply the denominators. The only additional step is converting the mixed number into an improper fraction first.
Not obvious, but once you see it — you'll see it everywhere It's one of those things that adds up..
How to Multiply a Mixed Number by a Whole Number
Follow these steps for how to multiply a mixed number by a whole number:
- Convert the mixed number into an improper fraction.
- Write the whole number as a fraction with a denominator of 1.
- Multiply the numerators.
- Multiply the denominators.
- Simplify the resulting fraction.
- Convert the answer back into a mixed number if it is improper.
Step 1: Convert the Mixed Number Into an Improper Fraction
Suppose you want to calculate:
[ 2\frac{3}{4}\times 6 ]
To convert (2\frac{3}{4}) into an improper fraction:
- Multiply the whole number by the denominator:
[ 2\times4=8 ]
- Add the original numerator:
[ 8+3=11 ]
- Keep the original denominator:
[ 2\frac{3}{4}=\frac{11}{4} ]
A helpful formula is:
[ \text{Improper fraction numerator} =(\text{whole number}\times\text{denominator})+\text{numerator} ]
Step 2: Multiply the Numerators and Denominators
Now multiply the improper fraction by the whole number:
[ \frac{11}{4}\times6 ]
You can write 6 as (\frac{6}{1}):
[ \frac{11}{4}\times\frac{6}{1} =\frac{11\times6}{4\times1} =\frac{66}{4} ]
Step 3: Simplify the Answer
The fraction (\frac{66}{4}) can be simplified. The greatest common factor of 66 and 4 is 2:
[ \frac{66}{4}=\frac{33}{2} ]
Step 4: Convert the Improper Fraction Into a Mixed Number
Divide 33 by 2:
[ 33\div2=16\text{ remainder }1 ]
Therefore:
[ \frac{33}{2}=16\frac{1}{2} ]
The final answer is:
[ \boxed{2\frac{3}{4}\times6=16\frac{1}{2}} ]
More Worked Examples
Example 1: Multiplying (3\frac{2}{5}) by 4
First, convert the mixed number:
[ 3\frac{2}{5}=\frac{3\times5+2}{5} =\frac{17}{5} ]
Now multiply by 4:
[ \frac{17}{5}\times4 =\frac{17\times4}{5} =\frac{68}{5} ]
Convert the improper fraction into a mixed number:
[ 68\div5=13\text{ remainder }3 ]
So the answer is:
[ \boxed{13\frac{3}{5}} ]
Example 2: Multiplying (1\frac{1}{3}) by 9
Convert the mixed number into an improper fraction:
[ 1\frac{1}{3}=\frac{1\times3+1}{3} =\frac{4}{3} ]
Multiply by 9:
[ \frac{4}{3}\times9 =\frac{4\times9}{3} =\frac{36}{3} ]
Simplify:
[ \frac{36}{3}=12 ]
The final answer is:
[ \boxed{12} ]
Example 3: Multiplying (4\frac{5}{6}) by 3
Convert the mixed number:
