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 compute these expressions, we need to convert the mixed numbers to improper fractions and then perform the calculations.
1) 5 2/9 × 7/8 > 5 2/9
To convert 5 2/9 to an improper fraction:
5 × 9 = 45
45 + 2 = 47
So, 5 2/9 = 47/9
Now, we can perform the calculation:
47/9 × 7/8
To multiply fractions, multiply the numerators and multiply the denominators:
(47 × 7) / (9 × 8) = 329/72
Now we need to compare this value to 5 2/9 = 47/9.
Since 329/72 is greater than 47/9, the statement 5 2/9 × 7/8 > 5 2/9 is true.
2) 17/4 × 3/2 < 17/4
To compare these fractions, we can cross-multiply:
(17 × 3) / (4 × 2) = 51/8
Now we need to compare this value to 17/4.
51/8 is greater than 17/4.
So, the statement 17/4 × 3/2 < 17/4 is false.
3) 4 1/2 × 5/4 < 4 1/2
To convert 4 1/2 to an improper fraction:
4 × 2 = 8
8 + 1 = 9
So, 4 1/2 = 9/2
Now, we can perform the calculation:
9/2 × 5/4
(9 × 5) / (2 × 4) = 45/8
Now we need to compare this value to 4 1/2 = 9/2.
45/8 is greater than 9/2.
So, the statement 4 1/2 × 5/4 < 4 1/2 is false.
4) 3 5/8 × 9/4 > 3 5/8
To convert 3 5/8 to an improper fraction:
3 × 8 = 24
24 + 5 = 29
So, 3 5/8 = 29/8
Now, we can perform the calculation:
29/8 × 9/4
(29 × 9) / (8 × 4) = 261/32
Now we need to compare this value to 3 5/8 = 29/8.
261/32 is greater than 29/8.
So, the statement 3 5/8 × 9/4 > 3 5/8 is true.