Solve Division Problem: Positive 1 ÷ 0.25

Q: Why is 1 ÷ 0.25 equal to 4 instead of something smaller?

Think of it this way: How many quarters (0.25) fit into 1 whole? Since 0.25 = 1/4, you're asking how many fourths make one whole. The answer is 4!

Q: What if I get confused about flipping fractions?

Remember: dividing by a fraction means multiplying by its reciprocal. So $ a ÷ \frac{b}{c} = a × \frac{c}{b} $. The numerator and denominator switch places!

Q: How can I check my division answer quickly?

Use multiplication to check! If 1 ÷ 0.25 = 4, then 4 × 0.25 should equal 1. Indeed: 4 × 0.25 = 1.00 ✓

Q: Why do the signs matter in division?

Signs follow simple rules: Same signs: positive ÷ positive = positiveDifferent signs: positive ÷ negative = negative Since both numbers are positive here, the answer must be positive.

Division Operations with Decimal Conversion

$(+1):(+0.25)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem together!

00:13 Remember, when you divide a positive number by another positive number, the result is always positive.

00:21 Now, let's convert the decimal into a fraction. It's an important step to make things easier.

00:37 Next, change the division sign to multiplication by using the reciprocal of the second fraction.

00:49 Simply switch the numerator and denominator of the second fraction.

00:55 Don't forget! Multiply the numerators together and the denominators together.

01:01 And there you have it! That's our solution to this math question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(+1):(+0.25)=\text{ ?}$

Step-by-step solution

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, let's convert the numbers into fractions:

$1=\frac{1}{1}$

$0.25=\frac{25}{100}$

This leaves us with the folowing:

$\frac{1}{1}:\frac{25}{100}=$

Let's now convert the division into a multiplication, remembering to switch the numerator and denominator:

$\frac{1}{1}\times\frac{100}{25}=$

Let's now combine everything into one single exercise:

$\frac{1\times100}{1\times25}=$

Finally, we can solve the multiplication in the numerator and denominator to get our answer:

$\frac{100}{25}=4$

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by positive always equals positive
Technique: Convert 0.25 to fraction $\frac{25}{100}$ then flip and multiply
Check: Multiply answer by divisor: 4 × 0.25 = 1 ✓

Common Mistakes

Avoid these frequent errors

Calculating 1 ÷ 0.25 as 0.25
Don't think smaller number divided by larger decimal gives smaller result = 0.25 or 1/4! This ignores that 0.25 is actually 1/4, making this 1 ÷ (1/4). Always convert decimals to fractions first, then flip and multiply.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why is 1 ÷ 0.25 equal to 4 instead of something smaller?

Think of it this way: How many quarters (0.25) fit into 1 whole? Since 0.25 = 1/4, you're asking how many fourths make one whole. The answer is 4!

Do I always need to convert decimals to fractions?

Not always, but it helps with understanding! You can also think: 0.25 = 25/100 = 1/4, so dividing by 0.25 is the same as multiplying by 4.

What if I get confused about flipping fractions?

Remember: dividing by a fraction means multiplying by its reciprocal. So $a ÷ \frac{b}{c} = a × \frac{c}{b}$ . The numerator and denominator switch places!

How can I check my division answer quickly?

Use multiplication to check! If 1 ÷ 0.25 = 4, then 4 × 0.25 should equal 1. Indeed: 4 × 0.25 = 1.00 ✓

Why do the signs matter in division?

Signs follow simple rules:

Same signs: positive ÷ positive = positive
Different signs: positive ÷ negative = negative

Since both numbers are positive here, the answer must be positive.

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