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When multiplying by a fraction, multiply numerators and multiply denominators, if possible,reduce it to the lowest fraction.
Some more examples :
1) 5/8 x 7/5
First multiply numerators (top numbers) and then multiply bottom numbers.
5/8 x 7/5 = ( 5 x 7)/(8 x 5)
Now write the fraction in lowest form.
As both the numbers are divisible by 5.
So, (35 ÷5)/( 40 ÷ 5)
2) 11/4 x 3/7
11/4 x 3/7 = (11 x 3)/(4 x 7)
As both the numbers are not divisible by any common number
So, 11/4 x 3/7 = 33/28
Application on product of fractions:
1)Tara is using boards and cement blocks to make shelves for her dorm room. Each shelf uses ½ of a board and 2 cement blocks. If Tara has 7 boards and 16 cement blocks, how many shelves can she make?
Number of boards =7
Required board for one shelf = 1/2
So total boards we have = 14 (half boards)(7 x 2/1=14)
Number of cement blocks = 16
Required cement blocks =2
See the diagram
In this way number of shelves = 8 (calculation) Number of shelves = (14 + 2)/2 = 16/2 = 8
2) What is one-third of two-fifth?
One-third = 1/3
two-fifth = 2/5
So, 1/3 of 2/5 = 1/3 x 2/5
= (1 x 2)/(3 x 5)
3) What is one-half of one dozen mango?
One-half = 1/2
one dozen mango = 12 mangoes
So, 1/2 of 12 = 12/2
= 6 mangoes