Module 2. Dividing Fractions & Mixed Numbers
Example
1 3/8 X 2 1/4=? 11/8X9/4=99/32=3 3/32
Example
1/3X2/7=? 1X2/3X7=2/21
Example
2/7X3/4=? 2X3/7X4=6/28(Divide 6 by 2)=3/(Divide 28 by 2) 14. =3/14
Consider the following operation: 4/5 x 5/4 = (4X5)/(5X4)= 20/20 = 1
4/5 and 5/4 are reciprocals because their product equals
X Mixed #'s
Step 1. Change any mixed numbers to improper fraction. Then same steps as above. Step 2. X the numertors. Step 3. X the denominators Step 4 Write the answer in fraction form Step 5 Reduce the new fraction to lowest terms Step 6 Change improper fractions to mixed numbers
Dividing Fractions
Step 1. Change division to multiplication Step 2. Write reciprocal of the 2nd fraction. Step 3. X the numertors. Step 4. X the denominators Step 5 Write the answer in fraction form Step 6 Reduce the new fraction to lowest terms
To divide mixed numbers, follow these steps:
1. Change any mixed numbers to improper fractions. 2. Change the division sign (÷) to a multiplication sign (×). 3. Write the reciprocal of the second frtly the numerators and denominators as usual. 5. Change the improper fraction to a mixed number. 6. Reduce the fraction to
To divide fractions, follow these steps:
1. Change the division sign (÷) to a multiplication sign (×). 2. Write the reciprocal of the second fraction. 3. Multiply the numerators. 4. Multiply the denominators. 5. Write the answer in the form of a fraction. 6. Reduce the fraction to the lowest terms, if necessary.
Example
4 3/4 divided by 1 3/7 =? 19/4divided by 10/7=? 19/4X7/10? 19X7/4X10=133/40= 3 13/40
Reciprocal
Dividing fractions is much like multiplying fractions, except you use the reciprocal* of the divisor, that is the number which if you multiply it by the divisor, gives you
The reciprocal of any number is just the numerator and denominator reversed. This even works with integers. The reciprocal of 5 is 1/5 because 5 is equal to 5/1. 1/5×5/1=5/5=1 .
Dividing by a fraction requires multiplying by the reciprocal. To understand why this is so, imagine dividing 2 pizzas into 5 slices each. How many slices would you have in total? 2 pizzas represented with 5 slices each. 2 divided by 1/5 = 2/1 x 5/1 = 10
Dividing Mixed Numbers
Dividing mixed numbers is similar to dividing fractions. However, you must first convert the mixed numbers to fractions. Then, for the final answer you convert the fraction back to a mixed number. To divide mixed numbers, follow these steps:
Divide the following fractions: 1/2÷2/3
Step 1. Change the division sign (÷ ) to a multiplication sign (×) 1/2× Step 2. Write the reciprocal of the divisor, or second fraction 1/2×3/2 Please notice that you cannot cancel the 2s which are both in the denominator. Step 3. Multiply the numerators (1×3)=3 ______ __ Step 4. Multiply the denominators 3/(2×2)=3/4 Step 5. Write the answer in fraction form 3/4 Step 6. Reduce the fraction to the lowest terms, if necessary 3/4 This fraction is already in its reduced form. Check your answer by multiplying the result by the divisor. You should get an answer that equals the original dividend. 3/4×2/3=(3×2)/(4×3)=6/12=1/2
Divide the following fractions: 1/2÷1/2 Note, any number divided by itself is 1, so we expect the answer to this problem to be 1, but let's work through it.
Step 1. Change the division sign (÷ ) to a multiplication sign (×) 1/2× Step 2. Write the reciprocal of the divisor, or second fraction 1/2×2/1 Please note that we could cancel the 2s in the numerator and denominator, but we will follow this simple problem through with no cancellation. Step 3. Multiply the numerators (1×2)=2 ______ __ Step 4. Multiply the denominators 2(2×1)=2/2 Step 5. Write the answer in fraction form 2/2 Step 6. Reduce the fraction to the lowest terms, if necessary 1/1=1
Example. Divide the following mixed number and fraction: −2 2/7÷3/7
Step 1. Convert all mixed numbers to improper fractions −2 /=−(2×7+2)/7=−16/7 Step 2. Change the division sign (÷) to a multiplication sign (×) −16/7 Step 3. Write the reciprocal of the second fraction −16/7×7/3= Step 4. Multiply by the reciprocal of the divisor (−16×7)/(7×3)=−112/21 Step 5. Convert the improper fraction to a mixed number −112/21=−5 7/21 Step 6. Reduce the fraction to the lowest terms, if necessary −5 7/21=−5 1/3
Example. Divide the following mixed number and fraction: 6 1/3÷1/4
Step 1. Convert all mixed numbers to improper fractions. 6 1/3=6×3+1/3=19/3 Step 2. Change the division sign (÷) to a multiplication sign (×) 19/3÷ 19/3× Step 3. Write the reciprocal of the second fraction 19/3×4/1= Step 4. Multiply by the reciprocal of the divisor (19×4)/(3×1)=76/3 Step 5. Convert the improper fraction to a mixed number 76/3=25 1/3 Step 6. Reduce the fraction to the lowest terms, if necessary 25 1/3 The fraction in this mixed number is already in its reduced form.
MindEdge video: X Fractions
Step 1. X the numertors. Step 2. X the denominators Step 3 Reduce the new fraction to lowest terms Step 4 Change improper fractions to mixed numbers