Solve the Division Equation: 15.6 ÷ ? = 1.56

Q: How do I remember which number to divide by which?

Think of the division equation as: dividend ÷ divisor = quotient. To find the missing divisor, you calculate dividend ÷ quotient. So 15.6 ÷ 1.56 gives you the missing number.

Q: What if my calculator gives me a long decimal answer?

For this type of problem, you should get a whole number or simple decimal. If you get something like 9.999999, it's probably 10! Check your setup - you might have divided in the wrong order.

Q: Can I solve this by setting up an equation with x?

Absolutely! You can write $ \frac{15.6}{x} = 1.56 $, then multiply both sides by x and divide by 1.56. Both methods work - choose what feels more comfortable!

Q: How do I check if 10 is really the right answer?

Simple! Just calculate $ 15.6 ÷ 10 $. If you get 1.56, then 10 is correct. You can also multiply: $ 1.56 × 10 = 15.6 $ ✓

Division Equations with Decimal Numbers

$15.6:?=1.56$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Based on the point shift amount, we can find the appropriate factor

00:09 As the amount of shifts, multiply this amount by 10 and that's the factor

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$15.6:?=1.56$

Step-by-step solution

To solve this problem, we need to determine the value that, when multiplied with 1.56, results in 15.6. Let's proceed with a step-by-step approach:

Step 1: Identify the task. We have the division relationship $15.6 : x = 1.56$ , where $x$ is the missing number we want to find.
Step 2: Set up an equation based on this relationship: $x = \frac{15.6}{1.56}$ .
Step 3: Perform the division. Convert 15.6 and 1.56 to eliminate decimals, facilitating easier division: - Multiply both numerator and denominator by 100 to make it an integer division: $\frac{15.6 \times 100}{1.56 \times 100} = \frac{1560}{156}$ .
Step 4: Simplify the fraction $\frac{1560}{156}$ : - Divide both numbers by the greatest common divisor, which is 156: $\frac{1560 \div 156}{156 \div 156} = \frac{10}{1} = 10$ .
Step 5: Verify. Multiply 1.56 by 10 to check: $1.56 \times 10 = 15.6$ , confirming our calculation.

Therefore, the solution to the problem is that the missing number is $10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: Transform division equations into multiplication using inverse operations
Technique: Calculate $\frac{15.6}{1.56}$ by multiplying both by 100 first
Check: Multiply answer by divisor: $1.56 \times 10 = 15.6$ ✓

Common Mistakes

Avoid these frequent errors

Dividing 1.56 by 15.6 instead of the opposite
Don't divide the smaller number by the larger = gives 0.1 instead of 10! This reverses the division relationship completely. Always divide the dividend (15.6) by the quotient (1.56) to find the divisor.

Practice Quiz

Test your knowledge with interactive questions

$0.26\times10=$

FAQ

Everything you need to know about this question

Why do I multiply both numbers by 100 before dividing?

Multiplying by 100 eliminates the decimals, making it easier to divide! $\frac{15.6}{1.56}$ becomes $\frac{1560}{156}$ , which is much simpler to work with.

How do I remember which number to divide by which?

Think of the division equation as: dividend ÷ divisor = quotient. To find the missing divisor, you calculate dividend ÷ quotient. So 15.6 ÷ 1.56 gives you the missing number.

What if my calculator gives me a long decimal answer?

For this type of problem, you should get a whole number or simple decimal. If you get something like 9.999999, it's probably 10! Check your setup - you might have divided in the wrong order.

Can I solve this by setting up an equation with x?

Absolutely! You can write $\frac{15.6}{x} = 1.56$ , then multiply both sides by x and divide by 1.56. Both methods work - choose what feels more comfortable!

How do I check if 10 is really the right answer?

Simple! Just calculate $15.6 ÷ 10$ . If you get 1.56, then 10 is correct. You can also multiply: $1.56 × 10 = 15.6$ ✓

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