Using computation which of the following statements is true
5 2/9×7/8>5 2/9
17/4×3/2<17/4
4 1/2×5/4<4 1/2
3 5/8×9/4>3 5/8
To determine which of the statements is true, we will compute the given expressions:
1) 5 2/9 × 7/8 > 5 2/9
To compute this expression, we need to convert the mixed numbers into improper fractions:
5 2/9 = (9 * 5 + 2)/9 = 47/9
Now we can multiply:
47/9 × 7/8 = (47 × 7)/(9 × 8) = 329/72
Therefore, the first statement becomes: 329/72 > 47/9.
2) 17/4 × 3/2 < 17/4
We can solve this straightforwardly:
17/4 × 3/2 = (17 × 3)/(4 × 2) = 51/8
Therefore, the second statement becomes: 51/8 < 17/4.
3) 4 1/2 × 5/4 < 4 1/2
Converting the mixed numbers to improper fractions:
4 1/2 = (2 * 4 + 1)/2 = 9/2
Performing the multiplication:
9/2 × 5/4 = (9 × 5)/(2 × 4) = 45/8
Hence, the third statement becomes: 45/8 < 9/2.
4) 3 5/8 × 9/4 > 3 5/8
Converting the mixed numbers to improper fractions:
3 5/8 = (8 * 3 + 5)/8 = 29/8
We can perform the multiplication:
29/8 × 9/4 = (29 × 9)/(8 × 4) = 261/32
Therefore, the fourth statement becomes: 261/32 > 29/8.
To summarize the computations and determine which statements are true:
1) 329/72 > 47/9 - True
2) 51/8 < 17/4 - False
3) 45/8 < 9/2 - False
4) 261/32 > 29/8 - True
Hence, the true statements are 1) 329/72 > 47/9 and 4) 261/32 > 29/8.