When multiplying a number by a fraction, the product can be greater than, less than, or equal to the original number.
4/7 > 9/10 * 4/7
Practice makes perfect
We want to compare the two given expressions and complete the statement.
4/7 9/10 * 4/7
Notice that the expression on the right-hand side is 47 multiplied by a fraction. When multiplying by a fraction, the product can be greater than, less than, or equal to the original number. If the fraction by which we multiply is greater than 1, the result will be greater than the original number. Let's see an example!
1/2 * 2 = 1
1 > 1/2
If the multiplier fraction is less than 1, the result will be less than the original number.
1/2 * 1/2 = 1/4 [0.8em]
1/4 < 1/2
Finally, if the fraction is equivalent to 1, the result will be equal to the original number.
1/2 * 2/2 = 2/4 [0.8em]
2/4 = 1/2
Let's focus on our exercise. We are multiplying by 910. We know that this fraction is less than 1 because the numerator is less than the denominator. Therefore, the product of 910 and 47 is less than 47. With this in mind, we can complete the statement.
4/7 > 9/10 * 4/7
Extra
Comparing Negative Numbers
Let's see what happens if one of the numbers we multiply is negative. If we multiply a negative number by a fraction that is less than 1, the result will be greater than the original number.
(- 1/2) * 1/2 = - 1/4
- 1/4 > - 1/2
We can also multiply a number by a negative fraction. This is the same as multiplying the opposite of that number by a positive fraction. Let's see an example!
2 * ( - 1/2) = (- 2) * 1/2
(- 2) * 1/2 = - 1
- 1 > - 2
If a positive number is multiplied by a negative fraction, the result will be negative. Similarly, if a negative number is multiplied by a negative fraction, the result will be positive. Therefore, if we multiply a number by a negative fraction, the result will have the opposite sign.
