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Cross Multiplication
Example:
Comparing fractions using crossmultiplication
Unlike fractions can be compared using crossmultiplication.
Example:
Compare ^{3}⁄_{7} and ^{5}⁄_{8 }using crossmultiplication.
To compare two fractions with different denominators, we make their denominators the same.
We do it by changing the denominators to the product of both the denominators.
So, the denominator of both the fractions becomes 7 × 8 = 56
Now, we use crossmultiplication, to find the numerators. First, we multiply the numerator of the first fraction with the denominator of the second fraction.
3 × 8 = 24
So, the first fraction becomes: ^{24}⁄_{56}
Next, we multiply the numerator of the second fraction by the denominator of the first fraction.
5 × 7 = 35
So, the second fraction becomes: ^{35}⁄_{56}
Since ^{24}⁄_{56 }< ^{35}⁄_{56}
Example: Which is bigger, ^{2}⁄_{5} or ^{3}⁄_{4} ?
Using crossmultiplication we find,
2 × 4 = 8 and 3 × 5 = 15
As, 8 < 15
Solving equations involving ratios using crossmultiplication
We can use crossmultiplication to solve an equation with 2 ratios and find the value of the variable.
If we have ^{a}⁄_{b }= ^{c}⁄_{d} , then
where b and d are not equal to zero, then we cross multiply as
to get:
Example: If 8 candle holders cost $40. How much will 12 such candle stands cost?
Cost of 8 candle holders = $40
Cost of 1 candle holder = ^{40}⁄_{8}................................................(i)
Let the cost of 12 candle holders be x
Therefore, the cost of 1 candle holder will be ^{x}⁄_{12}....................(ii)
Equating (i) and (ii) we get
^{40}⁄_{8} = ^{x}⁄_{12}
On crossmultiplying:
40 × 12 = 8 × x
^{480}⁄_{8} = x
60 = x
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