use -10, -5/2, -2/5, 5 to write a division expression greater than 10?
To write a division expression greater than 10 using the given numbers, we can use the number 5 as the divisor. We'll need to find a dividend that will result in a quotient greater than 10.
Let's try using -10 as the dividend.
-10 divided by 5 can be written as: -10 ÷ 5 = -2
Since the quotient is -2, which is less than 10, let's try using the next number, -5/2, as the dividend.
-5/2 divided by 5 can be written as: -5/2 ÷ 5
To divide a fraction by a whole number, we can multiply the numerator of the fraction by the reciprocal of the whole number. The reciprocal of 5 is 1/5.
So, -5/2 ÷ 5 can be rewritten as: -5/2 * 1/5 = (-5 * 1) / (2 * 5) = -5/10 = -1/2
The quotient -1/2 is also less than 10. Let's try using the next number, -2/5, as the dividend.
-2/5 divided by 5 can be written as: -2/5 ÷ 5
Again, we can rewrite this expression by multiplying the numerator of the fraction by the reciprocal of the whole number.
-2/5 ÷ 5 can be rewritten as: -2/5 * 1/5 = (-2 * 1) / (5 * 5) = -2/25
The quotient -2/25 is still less than 10. Finally, let's try using 5 as the dividend.
5 divided by 5 can be written as: 5 ÷ 5 = 1
Since the quotient is 1, which is less than 10, none of the given numbers -10, -5/2, -2/5, and 5 can be used as the dividend to create a division expression greater than 10 when divided by 5.
To write a division expression greater than 10 using the numbers -10, -5/2, -2/5, and 5, we need to find a combination of these numbers that when divided, results in a value greater than 10.
Let's go through each possibility:
1. -10 divided by -5/2:
-10 / (-5/2) = -10 * (2/-5) = -20/-5 = 4
The result 4 is less than 10, so this combination does not work.
2. -10 divided by -2/5:
-10 / (-2/5) = -10 * (5/-2) = -50/-2 = 25
The result 25 is greater than 10, so this combination satisfies the condition.
3. -10 divided by 5:
-10 / 5 = -2
The result -2 is less than 10, so this combination does not work.
4. -5/2 divided by -2/5:
(-5/2) / (-2/5) = (-5/2) * (5/-2) = -5/2 * -5/2 = 25/4
The result 25/4 is greater than 10, so this combination satisfies the condition.
5. -5/2 divided by 5:
(-5/2) / 5 = (-5/2) * (1/5) = -5/10 = -1/2
The result -1/2 is less than 10, so this combination does not work.
6. -2/5 divided by 5:
(-2/5) / 5 = (-2/5) * (1/5) = -2/25
The result -2/25 is less than 10, so this combination does not work.
7. 5 divided by -10:
5 / -10 = 5 * (-1/10) = -5/10 = -1/2
The result -1/2 is less than 10, so this combination does not work.
8. 5 divided by -5/2:
5 / (-5/2) = 5 * (2/-5) = -10/5 = -2
The result -2 is less than 10, so this combination does not work.
Therefore, the only division expression greater than 10 using the given numbers is -10 / (-2/5), which equals 25.