Multiplying Mixed Numbers: 1 2/9 times 1 4/5
This article will guide you through the steps of multiplying the mixed numbers 1 2/9 and 1 4/5.
Understanding Mixed Numbers
A mixed number combines a whole number with a fraction. For example, 1 2/9 means one whole and two-ninths. To multiply mixed numbers, we need to convert them into improper fractions.
Converting Mixed Numbers to Improper Fractions
1. Multiply the whole number by the denominator of the fraction. * For 1 2/9: 1 x 9 = 9
2. Add the numerator of the fraction to the result from step 1. * 9 + 2 = 11
3. Keep the same denominator. * The improper fraction is 11/9.
4. Repeat the process for the other mixed number. * For 1 4/5: 1 x 5 = 5 * 5 + 4 = 9 * The improper fraction is 9/5.
Multiplying Improper Fractions
Now we have the problem: 11/9 x 9/5.
1. Multiply the numerators. * 11 x 9 = 99
2. Multiply the denominators. * 9 x 5 = 45
3. Simplify the resulting fraction. * 99/45 can be simplified by dividing both numerator and denominator by their greatest common factor, 9. * 99 / 9 = 11 * 45 / 9 = 5
Therefore, 1 2/9 times 1 4/5 is equal to 11/5.
Converting Back to a Mixed Number (Optional)
If you wish to express the answer as a mixed number, divide the numerator (11) by the denominator (5).
- 11 ÷ 5 = 2 with a remainder of 1.
- The quotient (2) becomes the whole number, and the remainder (1) becomes the numerator of the fraction.
- The denominator stays the same.
Therefore, 11/5 as a mixed number is 2 1/5.