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Algebra 3-4 Name: ________________________ Per:_____
Rationals HW Day 0 NO CALC!! April 14/17, 2017
NOTES: How do you add, subtract, multiply and divide fractions?
Adding fractions
You can add fractions if the denominators (bottom number of the fraction) are the same. You simply add the numerators (top number of the fraction).
1 + 3 = 4
5 5 5
If the fractions have different denominators, determine the lowest common denominator (LCD) so that you can express each fraction in equivalent form. The lowest common denominator is the lowest number that the denominator of each individual fraction will divide into. Multiply both numerator and denominator of each fraction by the same number.
3/5 + 2/3 The lowest common denominator of 5 and 3 is 15.
Multiply 3/5 by 3/3 and multiply 2/3 by 5/5. This will create two equivalent fractions with the same denominator.
3 + 2 = 9 + 10 = 19 (Note LCD is 15.)
5 3 15 15 15
Subtracting fractions
Subtracting fractions is very similar to adding in that all fractions in your calculation need to have the same denominator. You may need to determine the lowest common denominator (LCD) as you did with addition.
Subtract 1/3 from 3/4.
3 – 1 = 9 – 4 = 5 (Note LCD is 12.)
4 3 12 12 12
Multiplying fractions
Multiplication of fractions is carried out by multiplying all the numerators together and all the denominators together.
Multiply 2/5 by 3/7.
2 x 3 = 2 x 3 = 6
5 7 5 x 7 35
Sometimes the answer to a multiplication calculation can be simplified by dividing both numerator and denominator by the same number.
25 = 5 (divide numerator by 5.)
30 = 6 (divide denominator by 5.)
Dividing fractions
To divide by a fraction, invert it and multiply.
Divide 23/4 by 5/8.
23/4 ÷ 5/8 = 11 ÷ 5 = 11 x 8 = 88 = 22 = 42/5
4 8 4 5 20 5
Complete the following problems. You may NOT use a calculator.
You must show EACH and EVERY step.
NO WORK = NO CREDIT!!
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