Answer:
Explanation:
To compare these two values, we first need to convert the mixed number 7 3/8 to an improper fraction. To do so, we multiply the whole number (7) by the denominator of the fraction (8), then add the numerator (3), and put the result over the denominator:
7 3/8 = (7 x 8 + 3) / 8 = 59/8
Now we can rewrite the inequality as:
(59/8) × (4/5) < 59/8
To simplify the left-hand side of the inequality, we multiply the numerators and denominators:
(59/8) × (4/5) = (59 × 4) / (8 × 5) = 236/40 = 59/10
So the inequality becomes:
59/10 < 59/8
To compare these fractions, we need to find a common denominator. The least common multiple of 8 and 10 is 40, so we can convert both fractions to have a denominator of 40:
59/10 = (59 x 4) / (10 x 4) = 236/40
59/8 = (59 x 5) / (8 x 5) = 295/40
Now we can see that 236/40 < 295/40, which means that:
59/10 < 59/8
Therefore, the inequality 7 3/8 × 4/5 < 7 3/8 is true.