Answer:
[tex]\frac{9}{4} - \frac{5}{10} = 1\frac{3}{4}[/tex]
Step-by-step explanation:
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
LCD(9/4, 5/10) = 20
[tex](\frac{9}{4} * \frac{5}{5} ) - (\frac{5}{10} * \frac{2}{2} ) = ?[/tex]
Complete the multiplication and the equation becomes
[tex]\frac{45}{20} - \frac{10}{20}[/tex]
The two fractions now have like denominators so you can subtract the numerators.
Then:
[tex]\frac{45 - 10}{20} = \frac{35}{20}[/tex]
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 35 and 20 using
GCF(35,20) = 5
[tex]\frac{35 / 5 }{20 / 5} = \frac{7}{4}[/tex]
The fraction
[tex]\frac{7}{4}[/tex]
is the same as
7 ÷ 4
Therefore:
[tex]\frac{9}{4} - \frac{5}{10} = 1\frac{3}{4}[/tex]
Apply the fractions formula for subtraction, to
[tex]\frac{9}{4} - \frac{5}{10}[/tex]
and solve
[tex]\frac{(9 * 10)- (5* 4) }{4 * 10}[/tex]
[tex]= \frac{90-20}{40}[/tex]
[tex]= \frac{70}{40}[/tex]
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(70,40) = 10
[tex]\frac{70/ 10 }{40 / 10} = \frac{7}{4}[/tex]
Convert to a mixed number using
long division for 7 ÷ 4 = 1R3, so
[tex]\frac{7}{4} = 1\frac{3}{4}[/tex]
Therefore:
[tex]\frac{9}{4} - \frac{5}{10} = 1\frac{3}{4}[/tex]
