Calculate the Quotient: 97.2 ÷ 48.6 Step-by-Step

Q: Why multiply both numbers by 10 instead of just removing the decimal points?

When you multiply both the numerator and denominator by the same number, the fraction value stays the same! Just removing decimals without understanding this rule can lead to wrong answers.

Q: How do I know what power of 10 to multiply by?

Count the decimal places in both numbers and use the largest count. Since 97.2 and 48.6 each have 1 decimal place, multiply both by $ 10^1 = 10 $.

Q: Can I use a calculator instead of this method?

Calculators work, but understanding this method helps you verify calculator results and solve problems when calculators aren't available. Plus, it builds number sense!

Q: How do I check if 972 ÷ 486 really equals 2?

Multiply backwards: $ 486 \times 2 = 972 $. Since this matches our original numerator, we know the answer is correct!

Decimal Division with Simplification Methods

Solve the following:

$\frac{97.2}{48.6}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following:

$\frac{97.2}{48.6}=$

Step-by-step solution

To solve the division $\frac{97.2}{48.6}$ , we will simplify by removing the decimals:

Step 1: Multiply both the numerator and denominator by 10 to eliminate the decimals since 97.2 and 48.6 each have one decimal place.
Step 2: The problem becomes equivalent to $\frac{972}{486}$ .
Step 3: Simplifying $\frac{972}{486}$ involves performing the division 972 ÷ 486.

By performing the division directly, we note that:

972 divided by 486 equals 2 because 972 is exactly double 486.

Therefore, the solution to the problem is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerator and denominator by same power of 10
Technique: Convert $\frac{97.2}{48.6}$ to $\frac{972}{486}$ by multiplying by 10
Check: Verify 486 × 2 = 972, so the quotient is exactly 2 ✓

Common Mistakes

Avoid these frequent errors

Ignoring decimal places during division
Don't divide 97.2 ÷ 48.6 using long division with decimals = messy calculations and errors! This makes the problem unnecessarily complex. Always eliminate decimals first by multiplying both numbers by the same power of 10.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why multiply both numbers by 10 instead of just removing the decimal points?

When you multiply both the numerator and denominator by the same number, the fraction value stays the same! Just removing decimals without understanding this rule can lead to wrong answers.

How do I know what power of 10 to multiply by?

Count the decimal places in both numbers and use the largest count. Since 97.2 and 48.6 each have 1 decimal place, multiply both by $10^1 = 10$ .

What if the division doesn't come out to a whole number?

That's normal! Many decimal divisions result in fractions or more decimals. The key is to simplify correctly and check your work by multiplying back.

Can I use a calculator instead of this method?

Calculators work, but understanding this method helps you verify calculator results and solve problems when calculators aren't available. Plus, it builds number sense!

How do I check if 972 ÷ 486 really equals 2?

Multiply backwards: $486 \times 2 = 972$ . Since this matches our original numerator, we know the answer is correct!

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