Final answer:
To find the product in lowest terms, convert any mixed numbers to improper fractions. Multiply the numerators and denominators in the fractions separately, and then simplify the resulting fraction if possible. The answers for the given products in lowest terms are: a) 7/6, b) 72, c) 355, d) 72/7, and f) 135/32.
Step-by-step explanation:
a) 2/4 x 2 1/3:
To find the product in lowest terms, we first simplify the mixed number to an improper fraction. 2 1/3 = (2x3 + 1)/3 = 7/3. Now we multiply 2/4 by 7/3.
2/4 x 7/3 = (2x7)/(4x3) = 14/12 = (14/2)/(12/2) = 7/6. So, 2/4 x 2 1/3 = 7/6.
b) 42 x 1 5/7:
Similarly, we convert 1 5/7 to an improper fraction: (1x7 + 5)/7 = 12/7. Then we multiply 42 by 12/7.
42 x 12/7 = (42x12)/7 = 504/7 = (504/7)/(7/7) = 72. So, 42 x 1 5/7 = 72.
c) 8 7/8 x 40:
In this case, we convert 8 7/8 to an improper fraction: (8x8 + 7)/8 = 71/8. We then multiply 71/8 by 40.
71/8 x 40 = (71x40)/8 = 2840/8 = (284x10)/(8x10) = 355/1 = 355. So, 8 7/8 x 40 = 355.
d) 4 4/7 x 2 1/4:
We convert 4 4/7 to an improper fraction: (4x7 + 4)/7 = 32/7. Next, we convert 2 1/4 to an improper fraction: (2x4 + 1)/4 = 9/4. Then we multiply 32/7 by 9/4.
32/7 x 9/4 = (32x9)/(7x4) = 288/28 = (288/4)/(28/4) = 72/7. So, 4 4/7 x 2 1/4 = 72/7.
f) 1 7/8 x 2 1/4:
We convert 1 7/8 to an improper fraction: (1x8 + 7)/8 = 15/8. We also convert 2 1/4 to an improper fraction: (2x4 + 1)/4 = 9/4. Then we multiply 15/8 by 9/4.
15/8 x 9/4 = (15x9)/(8x4) = 135/32. So, 1 7/8 x 2 1/4 = 135/32.