When multiplying a number by a fraction, the product can be greater than, less than, or equal to the original number.
5/6 = 5/6 * 7/7
Practice makes perfect
We want to compare the two given expressions and complete the statement.
5/6 5/6 * 7/7
Notice that the expression on the right-hand side is 56 multiplied by a fraction. When multiplying by a fraction, the product can be greater than, less than, or equal to the original number. If we multiply a number by a fraction 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. The fraction by which we multiply is 77. We know that this fraction is equal to 1 because the numerator is equal to the denominator. Therefore, the product of 77 and 56 is equal to 56. With this in mind, we can complete the statement.
5/6 = 5/6 * 7/7
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.
