Multiplying Mixed Numbers: 1 1/2 x 3 1/7
This article will guide you through the steps of multiplying the mixed numbers 1 1/2 and 3 1/7.
Converting Mixed Numbers to Fractions
The first step is to convert the mixed numbers into improper fractions. To do this, we follow these steps:
- Multiply the whole number by the denominator of the fraction. For 1 1/2: 1 x 2 = 2.
- Add the numerator of the fraction to the product. 2 + 1 = 3.
- Keep the original denominator. The improper fraction for 1 1/2 is 3/2.
Following the same steps for 3 1/7:
- Multiply the whole number by the denominator of the fraction. 3 x 7 = 21.
- Add the numerator of the fraction to the product. 21 + 1 = 22.
- Keep the original denominator. The improper fraction for 3 1/7 is 22/7.
Multiplying the Fractions
Now we have the problem as 3/2 x 22/7. To multiply fractions, we simply multiply the numerators and the denominators:
(3 x 22) / (2 x 7) = 66/14
Simplifying the Result
The final step is to simplify the fraction 66/14. Both the numerator and denominator are divisible by 2:
66/14 = 33/7
Converting Back to a Mixed Number
The simplified fraction 33/7 is an improper fraction. To convert it back to a mixed number, we divide the numerator (33) by the denominator (7):
33 ÷ 7 = 4 with a remainder of 5.
The whole number part of the mixed number is the quotient, 4. The fraction part is the remainder, 5, over the original denominator, 7.
Therefore, 1 1/2 x 3 1/7 = 4 5/7.