im semi good with math, but i never caught on to fractions and im taking the asvab in a few days so i need to know this. i get so puzzled when i have to add, subtract, multiply or divide fractions. is there any simple explanation to this?!
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===Numerator & Denominator===
a fraction has a Numerator on top the and a Denominator on the bottom:
Numerator/Denominator
===Multiply===
3/4 * 2/5
= (3*2) / (4*5) [multiply the Numerators and multiply the Denominators]
= 6/20
===Divide===
(3/4) / (2/5)
= 3/4 * 5/2 [flip the fraction that's doing the division, and Multiply like before]
= (3*5) / (4*2)
= 15/8
= 1 + 7/8
===Add===
3/4 + 2/5
= (3*5)/(4*5) + (4*2)/(4*5) [Make Denominators Match]
= 15/20 + 8/20
= (15+8)/20 [add the Numerators]
= 23/20
= 1 + 3/20
===Subtract===
3/4 - 2/5
= (3*5)/(4*5) - (4*2)/(4*5) [Make Denominators Match]
= 15/20 - 8/20
= (15-8)/20 [subtract the Numerators]
= 7/20
===Make Denominators Match===
when you multiply the Numerator and Denominator of a fraction by the same number, it doesn't change the fraction. to make the Denominator of 2 fractions match, you need to multiply the Denominator of each fraction by the other's Denominator. but because we want to keep the same fractions we have to multiply the Numerator by the same number.
example:
a/b + c/d = (a*d)/(b*d) + (b*c))/(b*d)
for each fraction both the Numerator and the Denominator are multiplied by the same value. on the left we multiplied them both by d. and on the right by b. see how the Denominators (bottoms) are the same now.
===Simplify===
you can also divide the Numerator and Denominator by the same number and the value of the fraction also won't change.
example:
6/20
= 3/10 [divided the Numerator and Denominator by 2]
a fraction has a Numerator on top the and a Denominator on the bottom:
Numerator/Denominator
===Multiply===
3/4 * 2/5
= (3*2) / (4*5) [multiply the Numerators and multiply the Denominators]
= 6/20
===Divide===
(3/4) / (2/5)
= 3/4 * 5/2 [flip the fraction that's doing the division, and Multiply like before]
= (3*5) / (4*2)
= 15/8
= 1 + 7/8
===Add===
3/4 + 2/5
= (3*5)/(4*5) + (4*2)/(4*5) [Make Denominators Match]
= 15/20 + 8/20
= (15+8)/20 [add the Numerators]
= 23/20
= 1 + 3/20
===Subtract===
3/4 - 2/5
= (3*5)/(4*5) - (4*2)/(4*5) [Make Denominators Match]
= 15/20 - 8/20
= (15-8)/20 [subtract the Numerators]
= 7/20
===Make Denominators Match===
when you multiply the Numerator and Denominator of a fraction by the same number, it doesn't change the fraction. to make the Denominator of 2 fractions match, you need to multiply the Denominator of each fraction by the other's Denominator. but because we want to keep the same fractions we have to multiply the Numerator by the same number.
example:
a/b + c/d = (a*d)/(b*d) + (b*c))/(b*d)
for each fraction both the Numerator and the Denominator are multiplied by the same value. on the left we multiplied them both by d. and on the right by b. see how the Denominators (bottoms) are the same now.
===Simplify===
you can also divide the Numerator and Denominator by the same number and the value of the fraction also won't change.
example:
6/20
= 3/10 [divided the Numerator and Denominator by 2]
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The inverse of a number is 1 / that number
For example, inverse of 2 is 1/2
Any number can be in the top part of the fraction: 0, negative numbers, fractions, etc.
But, the bottom part cannot equal zero, because "Division by zero is undefined."
To DIVIDE by a fraction, like 12 / (1/3) "Twelve divided by one-third" take the bottom fraction OUT of the number, invert it, and multiply:
12 / (1/3) = 12 x (3/1) = 12 x 3 = 36
"Twelve divided by (one third) equals twelve times (three over one) equals twelve times three
All of of the above is absurdly simple - it takes no thinking at all.
I'll let someone else explain subtraction.
For example, inverse of 2 is 1/2
Any number can be in the top part of the fraction: 0, negative numbers, fractions, etc.
But, the bottom part cannot equal zero, because "Division by zero is undefined."
To DIVIDE by a fraction, like 12 / (1/3) "Twelve divided by one-third" take the bottom fraction OUT of the number, invert it, and multiply:
12 / (1/3) = 12 x (3/1) = 12 x 3 = 36
"Twelve divided by (one third) equals twelve times (three over one) equals twelve times three
All of of the above is absurdly simple - it takes no thinking at all.
I'll let someone else explain subtraction.
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http://www.coolmath4kids.com/fractions/
this might be helpful
this might be helpful
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wat grade