Dividing Mixed Numbers: 1 1/4 ÷ 4 7/8
Dividing mixed numbers can seem daunting, but it's actually quite straightforward. Here's how to solve 1 1/4 ÷ 4 7/8 as a fraction:
1. Convert Mixed Numbers to Improper Fractions
- 1 1/4: (1 x 4) + 1 = 5. Keep the denominator, so 1 1/4 becomes 5/4.
- 4 7/8: (4 x 8) + 7 = 39. Keep the denominator, so 4 7/8 becomes 39/8.
2. Invert the Second Fraction and Multiply
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 39/8 is 8/39.
Our problem now looks like this: 5/4 x 8/39
3. Multiply the Numerators and Denominators
- 5 x 8 = 40
- 4 x 39 = 156
This gives us 40/156.
4. Simplify the Fraction (Optional)
Both 40 and 156 are divisible by 4.
- 40 ÷ 4 = 10
- 156 ÷ 4 = 39
Therefore, 1 1/4 ÷ 4 7/8 simplified to its lowest terms is 10/39.