what is 11 divided by 3/4 in fraction form
The correct answer and explanation is:
Correct Answer:
11÷34=44311 \div \frac{3}{4} = \frac{44}{3}
Step-by-Step Explanation:
To divide a whole number by a fraction, we use the rule of reciprocals. This means we multiply the whole number by the reciprocal (or the “flipped” version) of the fraction.
Let’s solve: 11÷3411 \div \frac{3}{4}
- Find the reciprocal of 34\frac{3}{4}: Reciprocal of 34=43\text{Reciprocal of } \frac{3}{4} = \frac{4}{3}
- Multiply 11 by the reciprocal: 11×43=44311 \times \frac{4}{3} = \frac{44}{3}
So, 11÷34=44311 \div \frac{3}{4} = \frac{44}{3}
Understanding the Concept (Why this works):
Dividing by a fraction is the same as asking: “How many times does that fraction fit into the whole number?”
Let’s think about what 34\frac{3}{4} means. It’s three-quarters of 1. So when we ask how many 34\frac{3}{4} units fit into 11, we’re asking how many 75%-sized portions we can get from 11 full units.
To do that, instead of performing division directly, we convert the operation into multiplication using the reciprocal. Multiplying by the reciprocal is mathematically equivalent to division but easier to compute.
Why Fraction Form Is Useful:
Leaving the answer as 443\frac{44}{3} keeps it in exact terms rather than a rounded decimal (which would be about 14.67). This is especially important in math problems that require exact quantities, like measurements, ratios, or algebraic expressions.
You can also express 443\frac{44}{3} as a mixed number if needed: 443=1423\frac{44}{3} = 14 \frac{2}{3}
But unless specified, 443\frac{44}{3} is the correct fraction form.