What is 8/9 divided by 4 as a fraction
The Correct Answer and Explanation is:
Correct Answer:89÷4=29\frac{8}{9} \div 4 = \frac{2}{9}98÷4=92
Explanation
To divide a fraction by a whole number, you follow a consistent mathematical process. The operation can be expressed using the rule:
Dividing by a number is the same as multiplying by its reciprocal.
Let’s apply this to the given expression:89÷4\frac{8}{9} \div 498÷4
Step 1: Rewrite the whole number as a fraction.
Any whole number can be written as a fraction by placing it over 1:4=414 = \frac{4}{1}4=14
Now the expression becomes:89÷41\frac{8}{9} \div \frac{4}{1}98÷14
Step 2: Multiply by the reciprocal of the second fraction.
The reciprocal of a fraction is obtained by flipping its numerator and denominator. The reciprocal of 41\frac{4}{1}14 is 14\frac{1}{4}41. So we change the division to multiplication:89×14\frac{8}{9} \times \frac{1}{4}98×41
Step 3: Multiply the numerators and denominators.
Now multiply the two fractions:
- Multiply the numerators: 8×1=88 \times 1 = 88×1=8
- Multiply the denominators: 9×4=369 \times 4 = 369×4=36
This gives:836\frac{8}{36}368
Step 4: Simplify the fraction.
To simplify, divide both the numerator and denominator by their greatest common factor. The GCF of 8 and 36 is 4:8÷436÷4=29\frac{8 \div 4}{36 \div 4} = \frac{2}{9}36÷48÷4=92
Final Answer:
89÷4=29\frac{8}{9} \div 4 = \frac{2}{9}98÷4=92
This result shows that when you divide a fraction by a whole number, the overall quantity becomes smaller. In this case, one-fourth of 89\frac{8}{9}98 is 29\frac{2}{9}92, which makes sense logically as well.
