## Want to practice?

In the fraction 5/7, the number 5 is

• Numerator
• Denominator
• Decimal
• Fraction

In the fraction 5/7, the number 7 is

• Numerator
• Denominator
• Decimal
• Fraction

What is the equivalent fraction to 5/7?

• 25/35
• 35/45
• 40/65
• 10/15

What is the equivalent fraction to 5/7?

• 25/40
• 55/78
• 40/65
• 10/14

The decimal form of a fraction is the value of the fraction when the values are divided.

## Solution

We perform a long division by dividing 5 by 7.

Here we can see that 7 > 5 and 5 cannot be divided by 7, we start our division by placing a decimal point in the quotient (0.) and adding 0 to make it 50.

As we divide, we get a new remainder in each step, we keep dividing until we get the same remainder again. We can stop dividing when a remainder gets repeated.

Here you can see that the remainder 5 is repeated after 6 steps of division.

## What will happen if we continue dividing?

If we continue dividing, we will be getting the same digits in the quotient over and over again. Hence when we do long division, we can always stop dividing once we get any of the remainders we got in the previous steps.

So here our answer to the fraction would be 0.714285714285…….
To indicate that the sequence of digits 714285 is going to be repeated, we use a bar over these numbers and write the answer as .

The decimal form of the fraction is .

## Remember

Here are some common terms you should be familiar with.

• In the fraction , the number 5 is the dividend (our numerator)
• The number 7 is our divisor (our denominator)

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