Explain why 0.4 divided by 0.2 has the same answer as 4 divided by 2.
(Hint: Convert the decimals into fractions with a denominator of 10.)
If you multiply the top and bottom of a fraction by the same thing you do not change the value of the fraction.
0.4 * 10
-----------
0.2 * 10
is exactly the same as
4
----
2
Well, you see, when you have 0.4 divided by 0.2, it's like saying how many 0.2s fit into 0.4. But let's make things a bit more fun and convert those decimals into fractions, shall we?
0.4 is the same as 4/10, and 0.2 is the same as 2/10. Now let's see how many 2/10s we can fit into 4/10. Can you see where this is going? It's like asking how many clowns fit into a tiny car – the answer is still the same!
Now, since we're dealing with fractions both times, we can simplify them. If we cancel out the common factor of 2 in the numerator and denominator of both fractions, we're left with 4 divided by 2, which simplifies to... drumroll please... 2!
So, the final answer is that both 0.4 divided by 0.2 and 4 divided by 2 give us the same result, which is 2. It's like magic, but with numbers!
To explain why 0.4 divided by 0.2 has the same answer as 4 divided by 2, let's first convert the decimals into fractions with a denominator of 10.
Step 1: Convert 0.4 and 0.2 into fractions with a denominator of 10.
0.4 is the same as 4/10 because 4 divided by 10 gives us 0.4.
0.2 is the same as 2/10 because 2 divided by 10 gives us 0.2.
Step 2: Now, we can rewrite the division problems with fractions.
0.4 divided by 0.2 becomes 4/10 divided by 2/10.
4 divided by 2 can be rewritten as 4/1.
Step 3: Next, let's simplify the fractions.
Dividing 4/10 by 2/10 is the same as multiplying by the reciprocal of the divisor.
So, we have (4/10) * (10/2).
Simplifying this gives us (4 * 10) / (10 * 2) = 40/20.
Step 4: Finally, simplify the fraction 40/20.
Dividing both the numerator and denominator by their greatest common divisor, which is 20, gives us 2/1 or simply 2.
Therefore, we have proven that 0.4 divided by 0.2 has the same answer as 4 divided by 2, which is 2.
To understand why dividing 0.4 by 0.2 has the same answer as dividing 4 by 2, we can convert both decimals into fractions with a denominator of 10.
First, let's convert 0.4 into a fraction. Since there is one digit after the decimal point, we can express it as 4/10.
Similarly, let's convert 0.2 into a fraction. Since there is one digit after the decimal point, we can express it as 2/10.
Now, we can perform the divisions.
When we divide 0.4 by 0.2, we can rewrite it as (4/10) divided by (2/10). In division, we multiply the first fraction by the reciprocal of the second fraction. So, we have (4/10) * (10/2).
Simplifying the fractions, we get (4 * 10) / (10 * 2) = 40/20 or 2.
Now, let's look at dividing 4 by 2. Here, we have a whole number divided by another whole number. So, we have 4 divided by 2, which equals 2.
Therefore, we can see that both divisions, 0.4 divided by 0.2 and 4 divided by 2, have the same answer, which is 2.