First estimate 1 1/8 ÷ 5 5/8. Then divide to find the exact answer. Simplify all answers.
What is your estimate?
5/8
To estimate the division of 1 1/8 ÷ 5 5/8, we can round the numbers to the nearest whole number. The nearest whole number for 1 1/8 is 1, and for 5 5/8 is 6. So, the estimated answer is 1 ÷ 6.
To find the exact answer, we need to convert the mixed numbers into improper fractions and then divide.
Converting 1 1/8 to an improper fraction:
1 × 8 + 1 = 9
So, 1 1/8 is equal to 9/8.
Converting 5 5/8 to an improper fraction:
5 × 8 + 5 = 45
So, 5 5/8 is equal to 45/8.
Now, we can divide 9/8 ÷ 45/8.
Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by switching the numerator and the denominator.
So, the reciprocal of 45/8 is 8/45.
Now, we can multiply:
9/8 × 8/45
To simplify the multiplication, we can cancel out common factors between the numerators and denominators.
The number 8 can be canceled out:
(9/1) × (1/45)
Now, we can simply multiply the numerators and denominators:
9 × 1 = 9
1 × 45 = 45
Therefore, the exact answer is 9/45.
To simplify the answer, we can further reduce the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 9 and 45 is 9. We can divide both the numerator and denominator by 9:
(9 ÷ 9) / (45 ÷ 9) = 1/5
So, the simplified exact answer is 1/5.