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What Is 40/70 as a Decimal + Solution With Free Steps

The fraction 40/70 as a decimal is equal to 0.57142857.

Proper fractions, improper fractions, and mixed fractions are the three main categories of Fractions. Because Decimal values might be more helpful in solving mathematical difficulties, we transform fractions into decimal values. We employ the Division mathematical operation for this conversion.

Here, we are more interested in the division types that result in a Decimal value, as this can be expressed as a Fraction. We see fractions as a way of showing two numbers having the operation of Division between them that result in a value that lies between two Integers.

Now, we introduce the method used to solve said fraction-to-decimal conversion, called Long Division, which we will discuss in detail moving forward. So, let’s go through the Solution of fraction 40/70.

Solution

First, we convert the fraction components, i.e., the numerator and the denominator, and transform them into the division constituents, i.e., the Dividend and the Divisor, respectively.

This can be done as follows:

Dividend = 40

Divisor = 70

Now, we introduce the most important quantity in our division process: the Quotient. The value represents the Solution to our division and can be expressed as having the following relationship with the Division constituents:

Quotient = Dividend $\div$ Divisor = 40 $\div$ 70

This is when we go through the Long Division solution to our problem. The following figure shows the long division:

40/70 Long Division Method

Figure 1

40/70 Long Division Method

We start solving a problem using the Long Division Method by first taking apart the division’s components and comparing them. As we have 40 and 70, we can see how 40 is Smaller than 70, and to solve this division, we require that 40 be Bigger than 70.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. If so, we calculate the Multiple of the divisor closest to the dividend and subtract it from the Dividend. This produces the Remainder, which we then use as the dividend later.

Now, we begin solving for our dividend 40, which after getting multiplied by 10 becomes 400.

We take this 400 and divide it by 70; this can be done as follows:

 400 $\div$ 70 $\approx$ 5

Where:

70 x 5 = 350

This will lead to the generation of a Remainder equal to 400 – 350 = 50. Now this means we have to repeat the process by Converting the 50 into 500 and solving for that:

500 $\div$ 70 $\approx$ 7 

Where:

70 x 7 = 490

This, therefore, produces another Remainder which is equal to 500 – 490 = 10. Now we must solve this problem to the Third Decimal Place for accuracy, so we repeat the process with dividend 100.

100 $\div$ 70 $\approx$ 1 

Where:

70 x 1 = 70

Finally, we have a Quotient generated after combining the three pieces of it as 0.571=z, with a Remainder equal to 30.

Images/mathematical drawings are created with GeoGebra.

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