Since you have to solve it mentally, you won't write it down. but anyways for you to understand how are you gonna solve it mentally, here's the thing,
when multiplying a fraction and a whole number, all you have to do is multiply the numerator with the whole number. and for you to find the product involving mixed numbers, just convert it to improper fraction first. and for the product involving 2 fractions, you just have to multiply the numerators and the denominators.
so let's have the given:
1.) 2 x 2 1/4
converting the mixed number into improper fraction you'll have
step 1. multiply the denominator and the whole number (2 x 4 = 8)
step 2. add the product with the numerator (8 + 1 = 9)
step 3. replace the numerator with the acquired value and the denominator as it is
so you'll have
2 x 9/4 = 18/4 or reducing it lowest term you'll have
= 9/2
2.) 6 x 7 x 1/3 = (6 x 7) x (1/3)
= 42 x 1/3
= 42/3 or reducing it to lowest term, 14
3.) 2 7/8 x 16 = 23/8 x 16
= 368/8 or reducing to lowest term, 46
4.) 1/4 x 8 1/2 = 1/4 x 17/2
= 17/8
5.) 1/6 x 15 x 18 x 1/5 = 270/30 or 9
for you to not come up with large numbers of numerator and denominator, take time to cancel those which are divisible by a certain factor. say in #5, notice that when you divide 15 by 5 and 5 you'll get 3 and 1 respectively and when you divide 18 and 6 you'll get 3 and 1 and you will be left with 3 x 3 = 9
