Without multiplying, Emily knew that 4/9 was greater than 4/10. Explain how she knew
same numerator, smaller denominator
1/4 is greater than 1/8 :)
To determine if 4/9 is greater than 4/10 without multiplying, Emily likely compared the denominators (the numbers at the bottom of the fractions). Here's how Emily might have reasoned it out:
Emily observed that the denominator of 4/9 is 9, while the denominator of 4/10 is 10. She recognized that a larger denominator indicates that the fraction represents smaller parts of a whole. This is because the larger the denominator, the more equal parts the whole is divided into.
Since 9 is smaller than 10, Emily inferred that a fraction with a smaller denominator would represent larger parts compared to a fraction with a larger denominator. Therefore, 4/9 is greater than 4/10 because the fraction 4/9 indicates larger parts than 4/10.
By understanding the relationship between the size of the denominator and the size of the parts represented by a fraction, Emily could conclude that 4/9 is greater than 4/10 without multiplying.