How many groups of 7/4 are in 1 ?
The correct answer and explanation is:
Answer:
There are 4 groups of 7/4 in 1.
Explanation (300 words):
To determine how many groups of 74\frac{7}{4} are in 1, we are essentially asking:
How many times does 74\frac{7}{4} fit into 1?
This is a division problem: 174=1×47=47\frac{1}{\frac{7}{4}} = \frac{1 \times 4}{7} = \frac{4}{7}
So, there are 47\frac{4}{7} groups of 74\frac{7}{4} in 1.
That means the correct answer is actually 4/7, not 4.
Let’s understand why:
A “group” in math often means we’re dividing into equal parts. So, when we say “How many groups of 74\frac{7}{4} are in 1?”, we’re dividing 1 by 74\frac{7}{4}. Dividing by a fraction means multiplying by its reciprocal: 1÷74=1×47=471 \div \frac{7}{4} = 1 \times \frac{4}{7} = \frac{4}{7}
Real-World Analogy:
Imagine you have 1 liter of water and you want to pour it into bottles that each hold 74\frac{7}{4} liters (which is 1.75 liters). Since each bottle needs more than 1 liter, you can’t even fill one full bottle. Instead, you’ll be able to fill only 4/7 of one bottle.
Common Mistake:
Some people incorrectly multiply instead of dividing, thinking: How many 7/4s in 1=7÷4=1.75\text{How many 7/4s in 1} = 7 \div 4 = 1.75
But that would be how many 1s are in 7/4, not the reverse.
Always remember: To find how many groups of A are in B: do B÷A\text{To find how many groups of A are in B: do } B \div A
So: 1÷74=471 \div \frac{7}{4} = \frac{4}{7}
Final Answer: 47\boxed{\frac{4}{7}}
There are 4/7 groups of 7/4 in 1.